%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW252+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n021.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 : Fri Sep  1 00:20:08 EDT 2023

% Result   : Theorem 1.18s 1.60s
% Output   : Proof 1.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.25  % Problem    : SWW252+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.26  % Command    : do_cvc5 %s %d
% 0.26/0.47  % Computer : n021.cluster.edu
% 0.26/0.47  % Model    : x86_64 x86_64
% 0.26/0.47  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.47  % Memory   : 8042.1875MB
% 0.26/0.47  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.26/0.47  % CPULimit   : 300
% 0.26/0.47  % WCLimit    : 300
% 0.26/0.47  % DateTime   : Sun Aug 27 20:52:13 EDT 2023
% 0.26/0.47  % CPUTime    : 
% 0.32/0.76  %----Proving TF0_NAR, FOF, or CNF
% 1.18/1.60  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.8Jj9n7ie1l/cvc5---1.0.5_2612.p...
% 1.18/1.60  ------- get file name : TPTP file name is SWW252+1
% 1.18/1.60  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2612.smt2...
% 1.18/1.60  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.18/1.60  % SZS status Theorem for SWW252+1
% 1.18/1.60  % SZS output start Proof for SWW252+1
% 1.18/1.60  (
% 1.18/1.60  (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____))) (let ((_let_3 (tptp.hAPP _let_2 _let_1))) (let ((_let_4 (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex _let_3))) (let ((_let_5 (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex _let_4 tptp.v_q____))) (let ((_let_6 (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal))) (let ((_let_7 (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool))) (let ((_let_8 (tptp.tc_fun tptp.tc_Nat_Onat _let_7))) (let ((_let_9 (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))) (let ((_let_10 (tptp.hAPP (tptp.c_COMBB _let_8 (tptp.tc_fun _let_9 _let_9) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB _let_9 _let_8 tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool _let_7 tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))))) (let ((_let_11 (tptp.c_COMBB _let_9 tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)))) (let ((_let_12 (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP _let_11 (tptp.c_COMBC tptp.tc_Nat_Onat _let_9 _let_9 _let_10 (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP _let_6 (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex _let_5)) _let_1)))))) (let ((_let_13 (tptp.hAPP tptp.c_Nat_OSuc _let_12))) (let ((_let_14 (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP _let_11 (tptp.c_COMBC tptp.tc_Nat_Onat _let_9 _let_9 _let_10 (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP _let_6 (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) _let_1)))))) (let ((_let_15 (tptp.hAPP tptp.c_Nat_OSuc _let_14))) (let ((_let_16 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (let ((_let_17 (= tptp.v_q____ _let_16))) (let ((_let_18 (not _let_17))) (let ((_let_19 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_20 (=> _let_17 (= _let_19 _let_13)))) (let ((_let_21 (= _let_5 _let_16))) (let ((_let_22 (not _let_21))) (let ((_let_23 (not (and (=> _let_21 (=> _let_18 (= _let_15 _let_19))) (=> _let_22 (and _let_20 (=> _let_18 (= _let_15 _let_13)))))))) (let ((_let_24 (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex))) (let ((_let_25 (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_26 (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex))) (let ((_let_27 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_28 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_29 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (let ((_let_30 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_31 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_30))) (let ((_let_32 (tptp.hAPP tptp.c_Nat_OSuc _let_19))) (let ((_let_33 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (let ((_let_34 (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))))) (let ((_let_35 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (let ((_let_2 (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Oidom T_a) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not _let_2) (= _let_1 (tptp.c_Polynomial_Odegree T_a V_p)))))))))) (let ((_let_36 (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.tc_fun tptp.tc_Nat_Onat _let_1))) (let ((_let_3 (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat _let_3 _let_3 (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_3 _let_3) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool _let_1 tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))))))) (let ((_let_37 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____))) (let ((_let_38 (tptp.hAPP _let_37 tptp.v_c____))) (let ((_let_39 (= _let_38 _let_1))) (let ((_let_40 (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))) (let ((_let_41 (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a _let_1)) (not (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) _let_1)))))))) (let ((_let_42 (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) _let_1) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 _let_1)))))))) (let ((_let_43 (not (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex _let_2)))) (let ((_let_44 (not (= _let_3 _let_1)))) (let ((_let_45 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) _let_33))) (let ((_let_46 (= _let_13 (tptp.hAPP _let_45 _let_12)))) (let ((_let_47 (= _let_15 (tptp.hAPP _let_45 _let_14)))) (let ((_let_48 (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) (let ((_let_49 (= _let_14 _let_48))) (let ((_let_50 (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex _let_5))) (let ((_let_51 (= _let_12 _let_50))) (let ((_let_52 (= _let_48 _let_50))) (let ((_let_53 (= _let_13 _let_15))) (let ((_let_54 (_let_34))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 ((tptp.hAPP tptp.c_Nat_OSuc V_n)))) (let ((_let_57 (not _let_25))) (let ((_let_58 (or _let_57 _let_49))) (let ((_let_59 (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool))) (let ((_let_2 (tptp.tc_fun tptp.tc_Nat_Onat _let_1))) (let ((_let_3 (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool))) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB _let_3 tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat _let_3 _let_3 (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_3 _let_3) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB _let_3 _let_2 tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool _let_1 tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (_let_59))) (let ((_let_62 ((tptp.c_Polynomial_Ocoeff T_a V_pb_2)))) (let ((_let_63 (ASSUME :args (_let_25)))) (let ((_let_64 (or _let_57 _let_51))) (let ((_let_65 (= _let_1 _let_4))) (let ((_let_66 (or _let_65 _let_52))) (let ((_let_67 (not _let_65))) (let ((_let_68 (and (or _let_67 (= _let_19 _let_50)) _let_66))) (let ((_let_69 (not _let_24))) (let ((_let_70 (or _let_69 _let_68))) (let ((_let_71 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (let ((_let_2 (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not _let_2) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) _let_1)) (or _let_2 (= _let_1 (tptp.c_Polynomial_Odegree T_a V_p)))))))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (ASSUME :args (_let_24)))) (let ((_let_74 (= _let_1 _let_3))) (let ((_let_75 (not _let_26))) (let ((_let_76 (or _let_75 _let_74 _let_67))) (let ((_let_77 (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a _let_1) (not (= _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (SYMM (ASSUME :args (_let_44))))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_74 _let_75 _let_67 (not _let_76)))) _let_79 (ASSUME :args (_let_26)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_78 :args (_let_3 tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))) :args (_let_77)))) _let_78 :args (_let_76 false _let_77)) :args (_let_67 true _let_74 false _let_26 false _let_76)))) (let ((_let_81 (=> _let_18 _let_53))) (let ((_let_82 (and _let_20 _let_81))) (let ((_let_83 (or _let_17 (not (= _let_19 (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex _let_1 tptp.v_q____)))))) (let ((_let_84 (= _let_74 _let_83))) (let ((_let_85 (not _let_83))) (let ((_let_86 (or _let_69 _let_84))) (let ((_let_87 (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_40)) (MACRO_SR_EQ_INTRO :args (_let_40 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_83 0)) :args ((or _let_18 _let_83))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_84)) :args ((or _let_74 _let_85 (not _let_84)))) _let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_69 _let_84 (not _let_86)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_88 :args (_let_1 tptp.v_q____ tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2)))) :args (_let_87)))) _let_88 :args (_let_86 false _let_87)) :args (_let_84 false _let_24 false _let_86)) :args (_let_85 true _let_74 false _let_84)) :args (_let_18 true _let_83)))) (let ((_let_90 (=> _let_22 _let_82))) (let ((_let_91 (=> _let_21 (=> _let_18 (= _let_19 _let_15))))) (let ((_let_92 (or _let_65 _let_17))) (let ((_let_93 (= _let_21 _let_92))) (let ((_let_94 (or _let_69 _let_93))) (let ((_let_95 (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 _let_1)) (= _let_1 (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2)))))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (not _let_92))) (let ((_let_98 (and _let_49 _let_51 _let_52 _let_46 _let_47))) (let ((_let_99 (ASSUME :args (_let_47)))) (let ((_let_100 (ASSUME :args (_let_49)))) (let ((_let_101 (ASSUME :args (_let_52)))) (let ((_let_102 (ASSUME :args (_let_51)))) (let ((_let_103 (ASSUME :args (_let_46)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_98)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_99 _let_100 _let_101 _let_102 _let_103) (SCOPE (TRANS (SYMM (SYMM _let_103)) (CONG (REFL :args (_let_45)) (TRANS (SYMM (SYMM _let_102)) (SYMM _let_101) (SYMM _let_100)) :args (APPLY_UF tptp.hAPP)) (SYMM _let_99)) :args (_let_47 _let_49 _let_52 _let_51 _let_46))) :args (_let_49 _let_51 _let_52 _let_46 _let_47))) :args (true _let_98)) :args ((or _let_53 (not _let_49) (not _let_51) (not _let_52) (not _let_46) (not _let_47)))) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_81)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_82)) (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args (_let_90)) (MACRO_RESOLUTION_TRUST (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args (_let_91)) :args ((or _let_21 _let_91))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_93)) :args ((or _let_22 _let_92 (not _let_93)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_17 _let_65 _let_97))) _let_89 _let_80 :args (_let_97 true _let_17 true _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) 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(REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_69 _let_68 (not _let_70)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_72 :args (tptp.v_q____ _let_4 tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Polynomial_Osmult T_a V_a V_p)))) :args (_let_71)))) _let_72 :args (_let_70 false _let_71)) :args (_let_68 false _let_24 false _let_70)) :args (_let_66 false _let_68)) :args (_let_52 true _let_65 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_57 _let_51 (not _let_64)))) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_5 tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62)) :args _let_61))) _let_60 :args (_let_64 false _let_59)) :args (_let_51 false _let_25 false _let_64)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_57 _let_49 (not _let_58)))) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.v_q____ tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62)) :args _let_61))) _let_60 :args (_let_58 false _let_59)) :args (_let_49 false _let_25 false _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_54)) _let_55 :args (_let_47 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_54)) _let_55 :args (_let_46 false _let_34)) :args (false true _let_53 false _let_52 false _let_51 false _let_49 false _let_47 false _let_46)) :args ((forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))) _let_44 (not (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p))) _let_43 _let_43 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP tptp.c_Nat_OSuc V_n)))) (forall ((B_z $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP _let_1 B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex _let_2) tptp.v_q____)) B_z)) _let_2))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.hAPP tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m)) (tptp.hAPP tptp.c_Nat_OSuc V_n)))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat V_P_2) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_Nat_Onat V_P_2) tptp.c_Nat_OSuc))))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.hAPP 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(tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) (tptp.hAPP tptp.c_Nat_OSuc _let_1))) (= V_n_2 _let_1)))) (not (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex _let_37)) (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))) (forall ((V_p $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Polynomial_Osmult T_a V_b V_p)) (tptp.c_Polynomial_Osmult T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_p)))) (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant T_a T_b V_f_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y))))) (forall ((V_x $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x))))) (forall ((V_n $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.hAPP tptp.c_Nat_OSuc V_x) (tptp.hAPP tptp.c_Nat_OSuc V_y)) (= V_x V_y))) (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= (tptp.hAPP tptp.c_Nat_OSuc V_nat_2) (tptp.hAPP tptp.c_Nat_OSuc V_nat_H_2)) (= V_nat_2 V_nat_H_2))) (forall ((V_n $$unsorted)) (not (= (tptp.hAPP tptp.c_Nat_OSuc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.hAPP tptp.c_Nat_OSuc V_n)))) (forall ((V_P_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2)))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_m_2) V_n_2)) _let_1) (=> (=> (= V_m_2 V_n_2) _let_1) (=> (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_n_2) V_m_2)) _let_1) _let_1)))))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_s) V_t)) (not (= V_s V_t)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_m)) (not (= V_m V_n)))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_n)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (not (= V_x V_y)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (= (not (= V_m_2 V_n_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n_2) V_m_2)))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_n)))) (forall ((V_qa_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Oring__char__0 T_a) (tptp.class_Rings_Oidom T_a)) (= (= (tptp.c_Polynomial_Opoly T_a V_pb_2) (tptp.c_Polynomial_Opoly T_a V_qa_2)) (= V_pb_2 V_qa_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Polynomial_Ocoeff T_a V_x_2) (tptp.c_Polynomial_Ocoeff T_a V_y_2)) (= V_x_2 V_y_2)))) (forall ((V_qa_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= V_pb_2 V_qa_2) (forall ((B_n $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_pb_2) B_n) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_qa_2) B_n)))))) (forall ((V_m $$unsorted)) (not (= (tptp.hAPP tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)))) (forall ((V_nat_H_1 $$unsorted)) (not (= (tptp.hAPP tptp.c_Nat_OSuc V_nat_H_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_m $$unsorted)) (not (= (tptp.hAPP tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_nat_H)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_n _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) _let_1) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (not (= V_n_2 _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) _let_1) V_n_2))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m)) (tptp.hAPP tptp.c_Nat_OSuc V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (= V_m V_n))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_i)) V_k)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) (=> (not (= _let_1 V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_n))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m))) (= V_m V_n))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 V_m_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m_2))) (= V_n_2 V_m_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m_2)) (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_n_2)) (= V_m_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n_2) (tptp.hAPP tptp.c_Nat_OSuc V_m_2)))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (and (tptp.class_Int_Oring__char__0 T_a) (tptp.class_Rings_Oidom T_a)) (= (= (tptp.c_Polynomial_Opoly T_a V_pb_2) (tptp.c_Polynomial_Opoly T_a _let_1)) (= V_pb_2 _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a _let_1) _let_1)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_j $$unsorted)) (and (= V_m_2 (tptp.hAPP tptp.c_Nat_OSuc B_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) B_j) V_n_2))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP tptp.c_Nat_OSuc _let_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x) (tptp.hAPP tptp.c_Nat_OSuc _let_2))) (or (= V_x _let_1) (= V_x _let_2)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a _let_2)) (=> (not (= V_b _let_2)) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP _let_2 V_a)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) _let_1)) (=> (not (= V_a _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) _let_1))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) _let_1))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))) (=> (not (= V_a _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_a_2)))))) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_pa____)) (not _let_39) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) _let_1) V_n) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) _let_1) _let_1))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) _let_1) (or (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP _let_1 V_n_2) V_k_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_k_2)))) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (= V_m_2 V_n_2)))) (forall ((V_q $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero _let_1))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes _let_1) _let_2) V_q) _let_2))))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero _let_1))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes _let_1) V_p) _let_2) _let_2))))) (forall ((V_q $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP _let_1 (tptp.c_Polynomial_Osmult T_a V_a V_q)) (tptp.c_Polynomial_Osmult T_a V_a (tptp.hAPP _let_1 V_q)))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Polynomial_Osmult T_a V_a V_p)) V_q) (tptp.c_Polynomial_Osmult T_a V_a (tptp.hAPP (tptp.hAPP _let_1 V_p) V_q)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2))) (and (tptp.hBOOL (tptp.hAPP _let_1 V_m_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_n_2)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m_2)) (tptp.hAPP _let_2 V_n_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2))))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m_2) V_k_2)) (tptp.hAPP (tptp.hAPP _let_2 V_n_2) V_k_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2))))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)))))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_i)) (tptp.hAPP _let_1 V_j)))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_k_2)))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m_2)) (tptp.hAPP _let_2 V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_n)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_n)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_m)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b_2)) (= V_a_2 V_b_2)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (= V_a V_b)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2) _let_1) (or (= V_a_2 _let_1) (= V_b_2 _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a _let_1)) (=> (not (= V_b _let_1)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) _let_1))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) _let_1) (or (= V_a _let_1) (= V_b _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a _let_1) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a _let_1) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2) _let_1) (= V_a_2 _let_1))))) _let_41 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) _let_1) (= V_a _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (=> (not (= V_a _let_1)) (=> (not (= V_b _let_1)) (= V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 V_a_2) V_ca_2)) (tptp.hAPP (tptp.hAPP _let_3 V_b_2) V_ca_2))) (or (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_ca_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_b_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_ca_2) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_a_2)))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_a_2)) (tptp.hAPP _let_3 V_b_2))) (or (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_ca_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_b_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_ca_2) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_a_2)))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_ca_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a_2)) (tptp.hAPP _let_2 V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_b_2)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)) _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_ca_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a_2)) (tptp.hAPP _let_2 V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_a_2)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__comm__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))))))))) (= _let_38 _let_3) (forall ((B_x $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) B_x) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) tptp.v_c____) B_x)))) (forall ((V_P_2 $$unsorted) (V_k_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Owellorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_k_2) (tptp.c_Orderings_Oord__class_OLeast T_a V_P_2))) (not (tptp.hBOOL (tptp.hAPP V_P_2 V_k_2)))))) _let_40 (forall ((V_pb_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex V_pb_2)) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_pa____))) (=> (not (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_pb_2))) (exists ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_pb_2) B_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (= V_m_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m_2)) (tptp.hAPP _let_2 V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (forall ((V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_b) _let_1)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP _let_1 V_m))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_n)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_c))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_d)))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_d)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_b)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))) (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b_2) V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((V_p $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_p) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Osmult T_a V_b V_p))))) (forall ((V_n $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_q) V_n))))) (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_b_H)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_b_H))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y))))))) (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b_2))) (let ((_let_3 (tptp.hAPP _let_1 V_a_2))) (let ((_let_4 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (and (not (= V_a_2 V_b_2)) (not (= V_ca_2 V_d_2))) (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_ca_2)) (tptp.hAPP _let_2 V_d_2)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_d_2)) (tptp.hAPP _let_2 V_ca_2))))))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_a_H)) V_b) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b))))))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_ya) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ya)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_ya))))))) (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_m)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_m)))))) (forall ((V_z_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x_2))) (let ((_let_3 (tptp.hAPP _let_1 V_w_2))) (let ((_let_4 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_y_2)) (tptp.hAPP _let_2 V_z_2)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_z_2)) (tptp.hAPP _let_2 V_y_2))) (or (= V_w_2 V_x_2) (= V_y_2 V_z_2))))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Osemiring T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_e)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_e)) V_c)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x_2) V_x_2)) (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_y_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (=> (not (= V_r (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (= V_a V_b) (not (= V_c V_d))) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.hAPP _let_1 V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) (tptp.hAPP _let_1 V_d)))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x_2) V_x_2)) (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_y_2)))) (or (not (= V_x_2 _let_1)) (not (= V_y_2 _let_1)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y))) (tptp.c_Groups_Ozero__class_Ozero T_a))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_c)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (let ((_let_2 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_5 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a _let_5)) (=> (not (= V_b _let_5)) (= (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_1) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_a) V_b)) _let_2)) _let_1))))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_5 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a _let_5)) (=> (not (= V_b _let_5)) (= (tptp.hAPP (tptp.hAPP _let_2 _let_3) _let_1) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_4 _let_3) (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b))) _let_1))))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (=> (not (= V_x V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_z))) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_y)) (tptp.hBOOL (tptp.hAPP _let_2 V_x)))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hBOOL (tptp.hAPP _let_2 V_z)))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)) (=> (= V_b V_c) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a))) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (=> (= V_b V_c) (tptp.hBOOL (tptp.hAPP _let_1 V_c))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c))) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (tptp.hBOOL (tptp.hAPP _let_1 V_a))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (not (= V_y V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (not (= V_x V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (not (= V_x V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x V_y)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2))) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2))) (= V_x_2 V_y_2)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2)) (= V_x_2 V_y_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_x_2))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_x))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ry)))))) (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_rx))))))) (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ly)))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry))) (let ((_let_3 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_ly)) _let_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ly) _let_2)))))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_lx) V_ly)))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_ry))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m_2 V_n_2))))) (forall ((V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Owellorder T_a) (=> (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x1))) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Orderings_Oord__class_OLeast T_a V_P_2)))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_a V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))) (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Owellorder T_a) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_k_2)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Orderings_Oord__class_OLeast T_a V_P_2)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) _let_1) V_y) _let_1)))) (exists ((B_q $$unsorted)) (and (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex B_q) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_pa____)) (forall ((B_x $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex B_q) B_x) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) tptp.v_c____) B_x)))))) (=> _let_39 (exists ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) B_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_a_2)))))) (not (forall ((B_q $$unsorted)) (=> (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex B_q) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_pa____)) (not (forall ((B_x $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex B_q) B_x) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) tptp.v_c____) B_x)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) V_n)) (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m))) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP _let_1 V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n))))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_j)) V_i)))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_i)) V_i)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m_2)) (tptp.hAPP _let_2 V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2)))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_j)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_m)))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_j)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_j)))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))))))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_k) V_l)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l)))))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k) V_l)) (=> (= (tptp.hAPP (tptp.hAPP _let_2 V_m) V_l) (tptp.hAPP (tptp.hAPP _let_2 V_k) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_j)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_i) V_u)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_u)) V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)) V_u)) V_k))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n)))))) (forall ((V_q $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus _let_1) (tptp.c_Groups_Ozero__class_Ozero _let_1)) V_q) V_q)))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus _let_1) V_p) (tptp.c_Groups_Ozero__class_Ozero _let_1)) V_p)))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.hAPP (tptp.hAPP _let_1 V_p) V_q)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Osmult T_a V_a V_q)))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes _let_1))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus _let_1))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_p) V_q)) V_r) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_p) V_r)) (tptp.hAPP (tptp.hAPP _let_2 V_q) V_r)))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP tptp.c_Nat_OSuc _let_1))) (= (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) V_n_2)) (or (and (= V_m_2 _let_2) (= V_n_2 _let_1)) (and (= V_m_2 _let_1) (= V_n_2 _let_2))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP tptp.c_Nat_OSuc _let_1))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) V_n_2) _let_2) (or (and (= V_m_2 _let_2) (= V_n_2 _let_1)) (and (= V_m_2 _let_1) (= V_n_2 _let_2))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) V_n_2))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_m_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_n_2)))))) (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_m))))) (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_i))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) B_k)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m))) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) (tptp.hAPP _let_1 V_n))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ozero T_a) (= (= _let_1 V_x_2) (= V_x_2 _let_1))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a)) (= V_b V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a))) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c)) (= V_b V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a))) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c)) (= V_b V_c))))) (forall ((V_ca_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_a_2) (tptp.hAPP (tptp.hAPP _let_1 V_ca_2) V_a_2)) (= V_b_2 V_ca_2))))) (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2))) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.hAPP _let_1 V_b_2) (tptp.hAPP _let_1 V_ca_2)) (= V_b_2 V_ca_2))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2)) (= V_a_2 _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a_2) V_ca_2)) (tptp.hAPP (tptp.hAPP _let_2 V_b_2) V_ca_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_b_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_ca_2))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a_2)) (tptp.hAPP _let_2 V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_b_2))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))))) (forall ((B_w $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 tptp.v_c____))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 B_w)))))) (forall ((V_qa_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_pb_2) V_qa_2) (tptp.c_Polynomial_OAbs__poly T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.tc_Nat_Onat T_a T_a) (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus T_a)) (tptp.c_Polynomial_Ocoeff T_a V_pb_2))) (tptp.c_Polynomial_Ocoeff T_a V_qa_2)))))) (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Polynomial_OAbs__poly T_a (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2)) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)))))) _let_36 (forall ((V_a $$unsorted) (V_p $$unsorted)) (exists ((B_q $$unsorted)) (and (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex B_q) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex V_p)) (forall ((B_x $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex B_q) B_x) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_p) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) V_a) B_x))))))) (forall ((B_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) B_w))))) (forall ((V_m_2 $$unsorted) (V_Q_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2)) (=> (tptp.hBOOL (tptp.hAPP V_Q_2 V_m_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (forall ((B_k $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP tptp.c_Nat_OSuc B_k))) (tptp.hBOOL (tptp.hAPP V_Q_2 B_k)))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat V_P_2) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat V_Q_2)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_x)))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_w)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) V_w) V_z))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP _let_1 V_n_2) V_k_2)) (= V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2))) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (= V_m_2 V_n_2)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP _let_1 V_m))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_n)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2)))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z))) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 V_x))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (= V_x V_y))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x))) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_z)) (tptp.hBOOL (tptp.hAPP _let_1 V_z))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (= V_x V_y))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (=> (= V_b V_c) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_a)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a))) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (=> (= V_b V_c) (tptp.hBOOL (tptp.hAPP _let_1 V_c))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c))) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (tptp.hBOOL (tptp.hAPP _let_1 V_a))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_c)))))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (= V_x_2 V_y_2))))) (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_x_2 V_y_2) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2) V_x_2)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x))))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_g_2 B_x))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (= (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2))) (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))) (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)) V_s)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) V_s)))))))) (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)) V_s)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_r) V_s)))))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_z))) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 V_x))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z))))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_z) V_x))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x))) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_z)) (tptp.hBOOL (tptp.hAPP _let_1 V_z))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (=> (not (= V_a V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (not (= V_a V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2))) (= V_x_2 V_y_2))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (= V_x_2 V_y_2))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2)) (= V_x_2 V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2) V_x_2))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (not (= V_x_2 V_y_2)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y_2) V_x_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2) V_x_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (tptp.class_Rings_Odivision__ring__inverse__zero T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_ca_2))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a_2)) (tptp.hAPP _let_1 V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_b_2)))))) (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_ca_2)) (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_ca_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_b_2)))))) (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Owellorder T_a) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Orderings_Oord__class_OLeast T_a V_P_2)) V_k_2))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_OAbs__poly T_a (tptp.c_Polynomial_Ocoeff T_a V_x_2)) V_x_2))) (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2))) (or (and (tptp.hBOOL (tptp.hAPP _let_2 V_a_2)) (tptp.hBOOL (tptp.hAPP _let_2 V_b_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2) _let_1))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2)) _let_1)) (or (and (tptp.hBOOL (tptp.hAPP _let_2 V_a_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2) _let_1))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b_2))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) _let_1))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)) _let_1))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) _let_1))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Oordered__comm__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b)))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (or (and (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_b))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) _let_1)))) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (or (and (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) _let_1))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) _let_1))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_c)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_y_2)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x_2) V_y_2) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) _let_1)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_a_2)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))))) (forall ((V_q $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Polynomial_Odegree T_a V_p)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Polynomial_Odegree T_a V_q)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q))) V_n))))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Odegree T_a V_q))) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) _let_1)) (= (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) _let_1))))) (forall ((V_p $$unsorted) (V_q $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Odegree T_a V_p))) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_q)) _let_1)) (= (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) _let_1)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2))) (tptp.hBOOL (tptp.hAPP _let_1 V_a_2)))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero _let_1))) (=> (tptp.class_Rings_Oidom T_a) (=> (not (= V_p _let_2)) (=> (not (= V_q _let_2)) (= (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes _let_1) V_p) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) (tptp.c_Polynomial_Odegree T_a V_q))))))))) _let_35 (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) V_n)) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (not (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (not (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) (tptp.c_Polynomial_Odegree T_a V_p)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_pb_2) (tptp.c_Polynomial_Odegree T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b))))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_3) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_3) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_3) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)))))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_ca_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a_2)) (tptp.hAPP _let_1 V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2) V_a_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_ca_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_a_2)) (tptp.hAPP _let_1 V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_b_2))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) _let_1)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_c)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) _let_1))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1) V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) _let_1))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1) V_b)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x_2) V_x_2)) (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_y_2))) _let_1)) (and (= V_x_2 _let_1) (= V_y_2 _let_1))))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Odegree T_a V_q))) (let ((_let_2 (tptp.c_Polynomial_Odegree T_a V_p))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) _let_2) _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) _let_2)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_q) _let_1))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OAbs__poly T_a (tptp.c_COMBK T_a tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_a V_p))) (let ((_let_2 (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (=> (tptp.class_Groups_Ozero T_a) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not _let_2) (= _let_1 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree T_a V_p))))))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_r) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x))) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_r))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)))) (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_r_2 $$unsorted) (V_qa_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero _let_1))) (let ((_let_3 (= V_y_2 _let_2))) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opdivmod__rel T_a V_x_2 V_y_2 V_qa_2 V_r_2) (and (= V_x_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes _let_1) V_qa_2) V_y_2)) V_r_2)) (=> _let_3 (= V_qa_2 _let_2)) (=> (not _let_3) (or (= V_r_2 _let_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_r_2)) (tptp.c_Polynomial_Odegree T_a V_y_2)))))))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z)))))) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z)))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Polynomial_Opos__poly T_a V_pb_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_pb_2) (tptp.c_Polynomial_Odegree T_a V_pb_2))))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_l_2)) (exists ((B_n $$unsorted)) (= V_l_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) B_n))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z)))))) (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) V_y)))) (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_b))) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless _let_1) V_f_2) V_g_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_f_2) V_g_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq _let_1 V_g_2) V_f_2)))))))) (forall ((V_r2 $$unsorted) (V_q2 $$unsorted) (V_r1 $$unsorted) (V_q1 $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q1 V_r1) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q2 V_r2) (= V_q1 V_q2))))) (forall ((V_r2 $$unsorted) (V_q2 $$unsorted) (V_r1 $$unsorted) (V_q1 $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q1 V_r1) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q2 V_r2) (= V_r1 V_r2))))) (forall ((V_r2 $$unsorted) (V_q2 $$unsorted) (V_r1 $$unsorted) (V_q1 $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q1 V_r1) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q2 V_r2) (and (= V_q1 V_q2) (= V_r1 V_r2)))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2) _let_1)) (= V_n_2 _let_1)))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n)) V_n)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n_2)) V_m_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2))) (= (tptp.hBOOL (tptp.hAPP _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP _let_2 V_n_2)) (= V_m_2 _let_1)))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n_2)) (tptp.hAPP tptp.c_Nat_OSuc V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2) V_m_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m))) (=> (tptp.hBOOL (tptp.hAPP _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 V_n))) (= V_m _let_1)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)) (not (= V_m_2 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)) (= V_m_2 V_n_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (=> (not (= V_m V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (= V_m V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) V_m)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) B_k))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2)) (tptp.hAPP _let_1 V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_j)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_m)))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_j)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_j)))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)))))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_l)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l))))))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_k)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_n)))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_k)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_k)) V_n)) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_n))))))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_l)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l))))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_i)) (tptp.hAPP _let_1 V_j)))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_m)))))) (forall ((V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_m)))) (forall ((V_r_2 $$unsorted) (V_qa_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opdivmod__rel T_a _let_1 V_y_2 V_qa_2 V_r_2) (and (= V_qa_2 _let_1) (= V_r_2 _let_1)))))) (forall ((V_r_2 $$unsorted) (V_qa_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opdivmod__rel T_a V_x_2 _let_1 V_qa_2 V_r_2) (and (= V_qa_2 _let_1) (= V_r_2 V_x_2)))))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Fields_Ofield T_a) (tptp.c_Polynomial_Opdivmod__rel T_a _let_1 V_y _let_1 _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Fields_Ofield T_a) (tptp.c_Polynomial_Opdivmod__rel T_a V_x _let_1 _let_1 V_x)))) (forall ((V_a $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (tptp.c_Polynomial_Opdivmod__rel T_a (tptp.c_Polynomial_Osmult T_a V_a V_x) V_y (tptp.c_Polynomial_Osmult T_a V_a V_q) (tptp.c_Polynomial_Osmult T_a V_a V_r))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n_2)) V_m_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m_2)) V_n_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) (tptp.hAPP tptp.c_Nat_OSuc V_m_2))) (= V_n_2 V_m_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_k_2)))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2)) (tptp.hAPP _let_1 V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Polynomial_Opos__poly T_a V_p) (=> (tptp.c_Polynomial_Opos__poly T_a V_q) (tptp.c_Polynomial_Opos__poly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Polynomial_Opos__poly T_a V_p) (=> (tptp.c_Polynomial_Opos__poly T_a V_q) (tptp.c_Polynomial_Opos__poly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)))))) (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p))) (tptp.c_Polynomial_Odegree T_a V_p))))) (forall ((V_q $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_q)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q))) V_n)))))) (forall ((V_n_2 $$unsorted)) (= (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2))) (and (tptp.hBOOL (tptp.hAPP _let_1 V_m_2)) (tptp.hBOOL (tptp.hAPP _let_1 V_n_2)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2)) (tptp.hAPP _let_1 V_n_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_k_2)) (tptp.hAPP (tptp.hAPP _let_1 V_n_2) V_k_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m_2)) (tptp.hAPP _let_1 V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_z $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes _let_1) V_y))) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_q V_z V_q_H V_r_H) (tptp.c_Polynomial_Opdivmod__rel T_a V_x (tptp.hAPP _let_2 V_z) V_q_H (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus _let_1) (tptp.hAPP _let_2 V_r_H)) V_r)))))))) (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (not (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) (tptp.c_Polynomial_Odegree T_a V_p)))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) (tptp.c_Polynomial_Odegree T_a V_q)))))) (forall ((V_a $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (=> (not (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Oorder T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (tptp.c_Polynomial_Opdivmod__rel T_a V_x (tptp.c_Polynomial_Osmult T_a V_a V_y) (tptp.c_Polynomial_Osmult T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) V_q) V_r))))) (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Odegree T_a V_p))) (=> (tptp.class_Groups_Ozero T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat _let_1) V_n)) (=> (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) _let_1) V_n)))))))) (forall ((V_u $$unsorted) (V_y $$unsorted) (V_x1 $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_x1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x1) V_y)) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_u))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x))) (tptp.hAPP (tptp.hAPP _let_1 V_u) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x1))))))))))) (forall ((V_u $$unsorted) (V_y $$unsorted) (V_x1 $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (let ((_let_3 (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_x1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x1) V_y)) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_u))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)) V_y)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x1)) V_u)))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_z_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_z_2)) (tptp.hAPP (tptp.hAPP _let_1 V_y_2) V_z_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_z_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_x_2)) (tptp.hAPP _let_1 V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP _let_2 V_x_2) V_x_2)) (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_y_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j) V_k)) (tptp.hBOOL (tptp.hAPP _let_1 V_k)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_n))) (forall ((V_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w) V_w))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z) V_w)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w) V_z)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_j) V_k)) (tptp.hBOOL (tptp.hAPP _let_1 V_k)))))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z) V_w)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w) V_z)) (= V_z V_w)))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.hAPP _let_1 V_z1))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z2)) V_z3) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_z2) V_z3)))))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (= (tptp.hAPP (tptp.hAPP _let_1 V_z) V_w) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_z)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x_2) V_y_2)) (= V_x_2 V_y_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x_2) V_y_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)) (not (= V_x_2 V_y_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_ca_2))) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP _let_1 V_a_2) (tptp.hAPP _let_1 V_b_2)) (= V_a_2 V_b_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_ca_2) (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_ca_2)) (= V_a_2 V_b_2))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_z))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y)))))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_z1) V_z2)) V_w) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_z1) V_w)) (tptp.hAPP (tptp.hAPP _let_1 V_z2) V_w)))))) (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal _let_27) _let_27) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_z)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_z_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x_2) V_z_2)) (tptp.hAPP (tptp.hAPP _let_2 V_y_2) V_z_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2))))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_x_2)))) (= V_x_2 _let_1)))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b))) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K))))))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Opcompose T_a V_p V_q))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) (tptp.c_Polynomial_Odegree T_a V_q)))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Odecseq T_a V_X_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n)) (tptp.hAPP V_X_2 B_m)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Polynomial_Osmult T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_x) (tptp.c_Polynomial_Odegree T_a V_x))) V_x)))) (forall ((V_p $$unsorted) (V_r $$unsorted)) (exists ((B_m $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_m)) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_p) B_z))) B_m))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a _let_1 _let_1) _let_1)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Fields_Ofield T_a) (= (= (tptp.c_Polynomial_Opoly__gcd T_a V_x_2 V_y_2) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a (tptp.c_Polynomial_Opoly__gcd T_a V_a V_b) V_c) (tptp.c_Polynomial_Opoly__gcd T_a V_a (tptp.c_Polynomial_Opoly__gcd T_a V_b V_c))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_b (tptp.c_Polynomial_Opoly__gcd T_a V_a V_c)) (tptp.c_Polynomial_Opoly__gcd T_a V_a (tptp.c_Polynomial_Opoly__gcd T_a V_b V_c))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_a V_b) (tptp.c_Polynomial_Opoly__gcd T_a V_b V_a)))) (forall ((V_q $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Opcompose T_a _let_1 V_q) _let_1)))) (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_Opcompose T_a V_p V_q)) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))) (forall ((V_p $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (forall ((B_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) B_i)) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) B_i) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p)) V_n))))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b))) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K))))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y))) (let ((_let_3 (= V_y (tptp.c_Groups_Ozero__class_Ozero _let_1)))) (=> (tptp.class_Fields_Ofield T_a) (and (=> _let_3 (= _let_2 (tptp.c_Polynomial_Osmult T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_x) (tptp.c_Polynomial_Odegree T_a V_x))) V_x))) (=> (not _let_3) (= _let_2 (tptp.c_Polynomial_Opoly__gcd T_a V_y (tptp.c_Divides_Odiv__class_Omod _let_1 V_x V_y)))))))))) (forall ((V_ca_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (= (tptp.c_Polynomial_Osynthetic__div T_a V_pb_2 V_ca_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) B_K)))))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Oincseq T_a V_X_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m)) (tptp.hAPP V_X_2 B_n)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Omod _let_1 (tptp.c_Polynomial_Osmult T_a V_a V_x) V_y) (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Divides_Odiv__class_Omod _let_1 V_x V_y)))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_r)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_x (tptp.c_Polynomial_Osmult T_a V_a V_y)) (tptp.c_Divides_Odiv__class_Omod _let_1 V_x V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_x)) (tptp.c_Polynomial_Odegree T_a V_y))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_x)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero _let_1))) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y) (tptp.c_Polynomial_Opoly__gcd T_a V_y (tptp.c_Divides_Odiv__class_Omod _let_1 V_x V_y))))))) (forall ((V_k_2 $$unsorted) (V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_SEQ_OBseq T_a V_X_2) (tptp.c_SEQ_OBseq T_a (tptp.hAPP (tptp.c_COMBB tptp.tc_Nat_Onat T_a tptp.tc_Nat_Onat V_X_2) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Nat_Onat tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2)))))) (forall ((V_k_2 $$unsorted) (V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_SEQ_OBseq T_a (tptp.hAPP (tptp.c_COMBB tptp.tc_Nat_Onat T_a tptp.tc_Nat_Onat V_X_2) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Nat_Onat tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2))) (tptp.c_SEQ_OBseq T_a V_X_2)))) (forall ((V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osynthetic__div T_a _let_1 V_c) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Divides_Odiv__class_Omod _let_1 V_x V_y))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero _let_1))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y _let_3)) (or (= _let_2 _let_3) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a _let_2)) (tptp.c_Polynomial_Odegree T_a V_y)))))))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (= (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) V_m) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n))) (forall ((V_d_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m_2 V_d_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_q $$unsorted)) (= V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_d_2) B_q))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m (tptp.hAPP tptp.c_Nat_OSuc _let_1)) _let_1))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))) (let ((_let_2 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m) V_n))) (let ((_let_3 (= _let_1 V_n))) (and (=> _let_3 (= _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_m))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_m))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) V_m)) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m) V_n))) (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (let ((_let_1 (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_n_2 V_k_2))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2))) (=> (not _let_1) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) B_j) V_k_2)) (=> (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) B_i)) B_j)) (tptp.hBOOL (tptp.hAPP V_P_2 B_j)))))))))) (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_r) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_q V_c))) V_r)) (tptp.hAPP _let_1 V_c)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a _let_1 V_b) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a _let_1 V_a) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H) V_c))))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP _let_1 V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c))))) (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H) V_c))))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP _let_1 V_b) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP _let_1 V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_a) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))) (forall ((V_X_2 $$unsorted) (V_K_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_K_2)) (=> (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) V_K_2))) (tptp.c_SEQ_OBseq T_a V_X_2))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) B_K)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y))) (let ((_let_2 (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a _let_1) (tptp.c_Polynomial_Odegree T_a _let_1)))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (let ((_let_4 (and (= V_x _let_3) (= V_y _let_3)))) (=> (tptp.class_Fields_Ofield T_a) (and (=> _let_4 (= _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not _let_4) (= _let_2 (tptp.c_Groups_Oone__class_Oone T_a)))))))))) (forall ((V_K_2 $$unsorted) (V_X_2 $$unsorted) (V_N_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (forall ((B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_N_2) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) V_K_2)))) (tptp.c_SEQ_OBseq T_a V_X_2)))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_n))) (let ((_let_2 (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not _let_2) (= _let_1 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a _let_1) _let_1)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2) _let_1) (= V_x_2 _let_1))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Groups_Oone T_a) (= (= _let_1 V_x_2) (= V_x_2 _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_x) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.c_Groups_Oone__class_Oone T_a) V_p) V_p))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n) V_n)) (not (= _let_27 _let_28)) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_z) V_z)) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a _let_1 V_y) _let_1)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)))) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x _let_1) _let_1)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_m)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) V_n)))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)))))) (forall ((V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_2 V_m) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP _let_2 _let_1) _let_1)) V_m)))))) (forall ((V_a $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Oone__class_Oone T_a)) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) V_b)))) (= _let_33 _let_32) (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) _let_34 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (or (= V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) V_x)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_x)) V_x)))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) _let_1) _let_1)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2)) _let_1)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1) V_x_2))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x_2) _let_1)))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_m $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) _let_1) V_k)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m)) V_k) _let_1)))) (forall ((V_x $$unsorted)) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__semiring__1 T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_u)) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_v)) (=> (= (tptp.hAPP (tptp.hAPP _let_2 V_u) V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_u) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_v) V_y))) V_a)))))))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2)) _let_1)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x_2)))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) _let_1))))))) (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__semiring__1__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_x) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_y) V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_4 V_u)) (=> (tptp.hBOOL (tptp.hAPP _let_4 V_v)) (=> (= (tptp.hAPP (tptp.hAPP _let_2 V_u) V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_u) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_v) V_y))) V_a))))))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (forall ((B_z $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero T_a)) B_z)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 B_z) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_z) V_x)) V_y)))))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y))))) (forall ((V_p $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.c_Polynomial_Odegree T_a V_p))) (exists ((B_i $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) B_i)) (not (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) B_i) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (forall ((V_y $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_x V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_y V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_y) V_x)) (exists ((B_q $$unsorted)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) B_q))))))) (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2)) (exists ((B_k $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) B_k) V_n_2)) (forall ((B_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i) B_k)) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) B_k) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))) (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatceiling (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))) (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))) (= (tptp.c_RComplete_Onatfloor _let_28) _let_33) (= (tptp.c_RComplete_Onatceiling _let_28) _let_33) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_RComplete_Onatfloor V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_RComplete_Onatfloor V_y))))) (= (tptp.c_RComplete_Onatfloor _let_27) _let_19) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)) (tptp.c_RComplete_Onatceiling V_y))))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_RComplete_Onatceiling V_x)))) (= (tptp.c_RComplete_Onatceiling _let_27) _let_19) (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_RComplete_Onatfloor V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x_2)))) (forall ((V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_a)) (tptp.c_RComplete_Onatfloor V_b))) (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_a) V_b)))))))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) _let_1) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) _let_1) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))) (forall ((V_i_2 $$unsorted) (V_P_2 $$unsorted) (V_pb_2 $$unsorted)) (=> (forall ((B_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) B_i) V_pb_2)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_i)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_i) V_pb_2)))))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_i_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i_2) V_pb_2)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))) (not (forall ((B_c $$unsorted)) (not (forall ((B_w $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 B_c))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 B_w))))))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))) (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)) (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (= V_n_2 V_m_2))) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_19) _let_27) (forall ((V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) V_m_2)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2) V_m_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_33) _let_28) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x))))) (forall ((V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n))))) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_32) _let_28) (forall ((V_n $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x))) V_x)))) (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) (tptp.c_RComplete_Onatfloor V_a))))) (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)) V_a)))) (forall ((V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n_2)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_a_2) (tptp.c_RComplete_Onatfloor V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2)) V_x_2))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_N))))))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_N))))))))) (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2)) V_a_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2)))))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n))) B_K))))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_N))))))))) (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n))) B_K))))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_N))))))))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) V_n))))) (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) V_a)))) (forall ((V_n $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_z) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) _let_1) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (= (tptp.c_RComplete_Onatfloor V_x) V_n))))) (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatceiling (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x)) V_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) _let_1) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1) V_x)) (exists ((B_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)) V_y)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_n))) V_y)))))))))) (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (exists ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_n)))) V_x))))) (forall ((V_r $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_r)) (exists ((B_n $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_r) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_n)))))))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_x)) _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1)) V_n))))))) (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (forall ((B_y $$unsorted)) (exists ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) B_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)) V_x))))))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))) (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_q)))))) (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_q)))))) (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_q)) V_x) (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_q)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_p)) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_p) V_q)))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_n))))) (forall ((V_x $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) V_p) V_n)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) V_n)))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_p)) V_q) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_p) V_q))))))) (forall ((V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_q)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_q))))))) (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_n)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_x))) (forall ((V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_SEQ_OBseq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x_2))))) (forall ((V_n $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_r) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_r) (tptp.hAPP tptp.c_Nat_OSuc V_n))) V_r)))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n)))))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n))))))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_i)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n)))))) (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2))) (or (= V_n_2 _let_1) (tptp.hBOOL (tptp.hAPP _let_2 V_x_2))))))) (forall ((V_m_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP tptp.c_Nat_OSuc _let_1))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_m_2) _let_2) (or (= V_m_2 _let_1) (= V_x_2 _let_2)))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) _let_1) V_n) _let_1))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_i)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m)) (tptp.hAPP _let_2 V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))))) (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2))) (or (tptp.hBOOL (tptp.hAPP _let_2 V_x_2)) (= V_n_2 _let_1)))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_y) V_z)))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) V_n) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) V_n))) (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) V_p) V_n))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) V_n))))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_RComplete_Onatfloor V_x))) (=> (= V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_1)) (= (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) _let_1) V_n))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (=> (not (= V_a _let_1)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) _let_1)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a) (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) _let_1)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m)) V_n)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_n))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_a))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n)))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))) (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Omult__zero T_a) (tptp.class_Rings_Ono__zero__divisors T_a) (tptp.class_Rings_Ozero__neq__one T_a)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_n_2) _let_1) (and (= V_a_2 _let_1) (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a_2)) (= (= (tptp.hAPP _let_1 V_m_2) (tptp.hAPP _let_1 V_n_2)) (= V_m_2 V_n_2)))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.hAPP tptp.c_Nat_OSuc V_n)) _let_1)))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_n)) V_a))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP _let_1 V_n)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n)))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_n)))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_n))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)))))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (let ((_let_2 (tptp.hAPP tptp.c_Nat_OSuc V_n))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP _let_3 V_a) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_b) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (= V_a V_b))))))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) _let_1)))))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n))) (let ((_let_3 (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (and (=> _let_3 (= _let_2 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Nat_OSuc V_n)))))))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_N)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_n)) (tptp.hAPP _let_1 V_N))))))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Oone__class_Oone T_a)) V_b_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_x_2)) (tptp.hAPP _let_1 V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x_2) V_y_2)))))))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_N)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_n)) (tptp.hAPP _let_1 V_N)))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) _let_1)) _let_1)))))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Nat_OSuc V_n))) _let_1)))))))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_N)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_N)) (tptp.hAPP _let_1 V_n)))))))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_n)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (= V_a V_b))))))))) (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_N)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_N)) (tptp.hAPP _let_1 V_n))))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_b_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP _let_1 V_x_2)) (tptp.hAPP _let_1 V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x_2) V_y_2))))))) (forall ((V_n $$unsorted) (V_b $$unsorted)) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (exists ((B_z $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) B_z) V_n))))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Power_Opower_Opower T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Otimes__class_Otimes T_a))))) (forall ((V_x $$unsorted) (V_p $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom T_a (tptp.c_Groups_Oone__class_Oone T_a) V_n)) V_p)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x))))) (forall ((V_y $$unsorted) (V_m $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_m)) V_y) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) V_m)))) (forall ((V_d_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m_2 V_d_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (exists ((B_q $$unsorted)) (= V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_d_2) B_q))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP _let_1 V_b) V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP _let_1 V_b) V_c)))) (forall ((V_y $$unsorted) (V_q_1 $$unsorted) (V_b_1 $$unsorted) (V_a_1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b_1)))) (=> (= V_a_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_1) V_q_1)) V_y)) (=> (and (=> _let_3 (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_y) V_b_1)))) (=> (not _let_3) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b_1) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y) _let_1))))) (=> (not (= V_b_1 _let_1)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a_1 V_b_1) V_y)))))))) (forall ((V_q $$unsorted) (V_r $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c))) V_r)) _let_1)))))))) (forall ((V_q $$unsorted) (V_r $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r) _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c))) V_r)))))))))) (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_3) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_r) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c))) V_r)) (tptp.hAPP _let_1 V_c)))))))))) (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 _let_1) V_c)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_r) V_b)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c))) V_r)))))))))) (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (and (=> (= V_k_2 _let_1) (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_k_2)) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) B_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) B_j) V_k_2)) (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i)) B_j))) (tptp.hBOOL (tptp.hAPP V_P_2 B_j))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_k_2) _let_1)) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) B_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i)) B_j))) (tptp.hBOOL (tptp.hAPP V_P_2 B_j)))))))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_i)) (tptp.hAPP _let_1 V_j)))))))) (forall ((V_b_2 $$unsorted) (V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Polynomial_Omonom T_a V_a_2 V_n_2) (tptp.c_Polynomial_Omonom T_a V_b_2 V_n_2)) (= V_a_2 V_b_2)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 V_z) V_w) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_z)))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (let ((_let_2 (tptp.hAPP _let_1 V_z1))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z2)) V_z3) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_z2) V_z3)))))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_z1) V_z2)) V_w) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_z1) V_w)) (tptp.hAPP (tptp.hAPP _let_1 V_z2) V_w)))))) (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_z1) V_z2)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_z1)) (tptp.hAPP _let_1 V_z2)))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_3 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (let ((_let_4 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (let ((_let_5 (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_b_H) V_q_H)) V_r_H))) (=> (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 V_b) V_q)) V_r) _let_5) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_5) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_r) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_r_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H) V_q)))))))))))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_q_H)) V_r_H)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_q)) V_r))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_r)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_r_H)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q) V_q_H)))))))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint))) (let ((_let_5 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (let ((_let_6 (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_b_H) V_q_H)) V_r_H))) (=> (= (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_b) V_q)) V_r) _let_6) (=> (tptp.hBOOL (tptp.hAPP _let_3 _let_6)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_r_H) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q) V_q_H))))))))))))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_q_H)) V_r_H)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_q)) V_r))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r_H) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H) V_q)))))))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H)) V_r_H)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_r_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b_H)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H) _let_1)))))))) (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H)) V_r_H))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_r_H) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 _let_1) V_b_H)) (tptp.hBOOL (tptp.hAPP _let_2 V_q_H))))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_m_2)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m_2) V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1)))))) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z) V_z)) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)) (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a)) (=> (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_r) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_q))))))) (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) _let_1) V_a)) (=> (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))) (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Omonom T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_n) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Polynomial_Omonom T_a V_a_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Omonom T_a V_a V_n)) V_n)))) (forall ((V_a $$unsorted) (V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_Omonom T_a V_a V_m)) V_n))) (let ((_let_2 (= V_m V_n))) (=> (tptp.class_Groups_Ozero T_a) (and (=> _let_2 (= _let_1 V_a)) (=> (not _let_2) (= _let_1 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Polynomial_Omonom T_a V_b V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_n)))) (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Omonom T_a V_a V_n))) V_n)))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom T_a V_a V_n)) (tptp.c_Polynomial_Omonom T_a V_b V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_n)))) (forall ((V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_one_2)) (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_a_2))) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_n_2)) (tptp.hAPP (tptp.hAPP V_times_2 V_a_2) (tptp.hAPP _let_1 V_n_2))))) (forall ((V_m_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a T_a))) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Omonom T_a V_a_2 V_m_2) (tptp.c_Polynomial_OAbs__poly T_a (tptp.c_COMBC tptp.tc_Nat_Onat T_a T_a (tptp.c_COMBC tptp.tc_Nat_Onat T_a _let_1 (tptp.hAPP (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun T_a _let_1) tptp.tc_Nat_Onat (tptp.c_If T_a)) (tptp.hAPP tptp.c_fequal V_m_2)) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))) (forall ((V_x $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_Omonom T_a V_a V_n)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))))) (forall ((V_n $$unsorted) (V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom T_a V_a V_m)) (tptp.c_Polynomial_Omonom T_a V_b V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n))))) (forall ((V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_SEQ_Omonoseq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x_2))))) (forall ((V_a $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_a)) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_x)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_x) V_n) V_a) (forall ((B_y $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_y)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_y) V_n) V_a)) (= B_y B_x)))))))) (forall ((V_z_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z_2)) V_z_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_z_2) _let_1))))))) (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)))))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_z)))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_w_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_z_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w_2) V_z_2)))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w_2))) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_z_2)) (= V_w_2 V_z_2))))) (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2) V_z_2)))) (forall ((V_z_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z_2)))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) _let_30) _let_29)) (not (= _let_30 _let_29)) (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (not (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 V_z) V_w) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_z)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z))))))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (let ((_let_2 (tptp.hAPP _let_1 V_z1))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_z2)) V_z3) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_z2) V_z3)))))) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z) V_z)) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_w_2 $$unsorted) (V_z_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_z_2) V_w_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_2) V_w_2)) (not (= V_z_2 V_w_2))))) (forall ((V_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w) V_w))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z) V_w)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w) V_z)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j) V_k)) (tptp.hBOOL (tptp.hAPP _let_1 V_k)))))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z) V_w)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w) V_z)) (= V_z V_w)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_k))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP _let_1 V_i)) (tptp.hAPP _let_1 V_j)))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))))))) (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_w_H) V_w)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_w_H) V_z_H)) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_z)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_a) V_b))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) _let_2) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) _let_2)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) _let_1)))))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_3) V_b)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_3) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_a) V_b)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))) (let ((_let_2 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP _let_2 _let_3)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) _let_3)) (tptp.hBOOL (tptp.hAPP _let_2 _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) V_a)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_a)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_y))))))) (forall ((V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_k)) V_m)))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) V_b))))) (forall ((V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (forall ((V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint _let_1 V_b) _let_1))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_SEQ_Oincseq T_a V_X_2) (tptp.c_SEQ_Omonoseq T_a V_X_2)))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_SEQ_Odecseq T_a V_X_2) (tptp.c_SEQ_Omonoseq T_a V_X_2)))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Omonoseq T_a V_X_2) (or (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n)) (tptp.hAPP V_X_2 (tptp.hAPP tptp.c_Nat_OSuc B_n))))) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 (tptp.hAPP tptp.c_Nat_OSuc B_n))) (tptp.hAPP V_X_2 B_n)))))))) (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Omonoseq T_a V_X_2) (or (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m)) (tptp.hAPP V_X_2 B_n))))) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n)) (tptp.hAPP V_X_2 B_m))))))))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y))))))) (tptp.hBOOL (tptp.hAPP _let_31 _let_30)) (tptp.hBOOL (tptp.hAPP _let_31 _let_29)) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_x) V_y))))))) (forall ((V_a $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_a)) (exists ((B_r $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_r)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_r) V_n) V_a)))))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Transcendental_Oln V_x))))) (= (tptp.c_Transcendental_Oln _let_28) _let_27) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_y_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Transcendental_Oln V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_2) V_y_2)))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y_2)) (= (= (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (= V_x_2 V_y_2)))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Transcendental_Oln V_x)) V_x))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Transcendental_Oln V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2))))))) (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x)))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_x_2)) (= (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transcendental_Oln V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x_2))))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) _let_1) V_x_2)) (= (= (tptp.c_Transcendental_Oln V_x_2) _let_1) (= V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 _let_2) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Transcendental_Oln V_x_2)) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Transcendental_Oln V_x)) _let_1))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Transcendental_Oln V_x))) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1) (tptp.c_Transcendental_Oln V_x))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) _let_1) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x)))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) _let_1) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1) (tptp.c_Transcendental_Oln V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x_2)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (= (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)) (tptp.c_Transcendental_Oln V_y))))))) (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))) V_x)))) (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) B_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i)) B_j))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_i) B_j))))))) (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_k_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) B_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) B_j) V_k_2)) (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i)) B_j))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_i) B_j))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) V_b) V_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) V_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b)))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_4 (= V_c _let_3))) (=> (tptp.class_Divides_Osemiring__div T_a) (and (=> _let_4 (= _let_2 _let_3)) (=> (not _let_4) (= _let_2 (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a $$unsorted)) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_y))))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) _let_1))))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b_2) _let_1)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a_2))))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2)) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a_2) _let_1))))))) (forall ((V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint _let_1 V_b) _let_1))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a _let_1 V_a) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a _let_1) _let_1)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (forall ((V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (and (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a _let_1) _let_1) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a _let_1) V_a)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_b V_c))) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_c)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c))))) (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) V_a_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_H V_b)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)))))) (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) V_a_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_H V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) V_a)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) _let_1))))) (forall ((V_b $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b_H)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b))))))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) _let_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) _let_1) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) _let_1)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b_2) _let_1)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a_2) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_a) V_b)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) _let_1)))))) (forall ((V_b $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) _let_1) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b_H)))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) _let_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_a_2)) (= (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_2) V_a_2)) (tptp.hBOOL (tptp.hAPP _let_2 V_b_2)))))))) (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 V_k_2)) (= (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_i_2 V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2) V_i_2)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) _let_1) V_b_2)) (= (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2))) (tptp.hBOOL (tptp.hAPP _let_2 V_a_2))))))) (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_i_2 V_k_2) _let_2) (or (= V_k_2 _let_2) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_2) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i_2) V_k_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i_2) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_k_2) V_i_2)))))))) (forall ((V_k $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_k)) V_x)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_c)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c)))) (forall ((V_k $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) V_b)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_k)))) (forall ((V_k $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b))) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_k)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP _let_1 V_b) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_b V_c))) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c))))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b))) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_b) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) (tptp.c_Groups_Oone__class_Oone T_a))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) (tptp.c_Groups_Oone__class_Oone T_a))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b)) V_a))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_a))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b))) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b))) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c))))) (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2))) (and (=> (= V_k_2 _let_1) (tptp.hBOOL (tptp.hAPP V_P_2 _let_1))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_k_2)) (forall ((B_i $$unsorted)) (=> (exists ((B_j $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) B_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) B_j) V_k_2)) (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i)) B_j)))) (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_k_2) _let_1)) (forall ((B_i $$unsorted)) (=> (exists ((B_j $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) B_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i)) B_j)))) (tptp.hBOOL (tptp.hAPP V_P_2 B_i)))))))))) (forall ((V_r_1 $$unsorted) (V_y $$unsorted) (V_b_1 $$unsorted) (V_a_1 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_b_1)))) (=> (= V_a_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_1) V_y)) V_r_1)) (=> (and (=> _let_3 (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1) V_r_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_r_1) V_b_1)))) (=> (not _let_3) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_b_1) V_r_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r_1) _let_1))))) (=> (not (= V_b_1 _let_1)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_1 V_b_1) V_y)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_c)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.hAPP _let_1 V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c))) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))) (forall ((V_k $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_k))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) _let_1) V_m)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_k)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP _let_2 V_m) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) (tptp.hAPP tptp.c_Nat_OSuc _let_1))))))))) (forall ((V_n $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_a)) (exists ((B_r $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_r)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_r) (tptp.hAPP tptp.c_Nat_OSuc V_n)) V_a))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (let ((_let_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n)))) (let ((_let_3 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_4 (= V_k _let_3))) (and (=> _let_4 (= _let_2 _let_3)) (=> (not _let_4) (= _let_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n))))))))) (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_m)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_m))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_k)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_n V_k))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)))) (let ((_let_4 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 _let_4) V_n)) (and (=> _let_3 (= _let_1 _let_4)) (=> (not _let_3) (= _let_1 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n))))))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_b V_c))) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a V_c)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_b V_c)) V_c))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Fields_Ofield T_a) (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y (tptp.c_Divides_Odiv__class_Odiv _let_1 V_x V_y) (tptp.c_Divides_Odiv__class_Omod _let_1 V_x V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Odiv _let_1 (tptp.c_Polynomial_Osmult T_a V_a V_x) V_y) (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Divides_Odiv__class_Odiv _let_1 V_x V_y)))))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_q)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_b) V_c))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Odiv _let_1 V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes _let_1) V_y) V_z)) (tptp.c_Divides_Odiv__class_Odiv _let_1 (tptp.c_Divides_Odiv__class_Odiv _let_1 V_x V_y) V_z))))) (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_e_2)) V_ca_2)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_e_2)) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_2) V_b_2)) V_e_2)) V_ca_2)) V_d_2))))))) (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_e_2)) V_ca_2)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_e_2)) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ca_2) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_b_2) V_a_2)) V_e_2)) V_d_2)))))))) (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_e_2)) V_ca_2)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_e_2)) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_2) V_b_2)) V_e_2)) V_ca_2)) V_d_2)))))))) (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_e_2)) V_ca_2)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b_2) V_e_2)) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_3 V_ca_2) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_b_2) V_a_2)) V_e_2)) V_d_2))))))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_k V_m)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus T_a))) (let ((_let_3 (tptp.c_Groups_Otimes__class_Otimes T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_x) V_x)) _let_1) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) V_n) V_m))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m) V_n) V_m))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_m)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus T_a))) (let ((_let_3 (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_5 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a _let_5)) (=> (not (= V_b _let_5)) (= (tptp.hAPP (tptp.hAPP _let_2 _let_3) _let_1) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_4 _let_3) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_a))) _let_1))))))))))) (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom T_a V_a V_n)) (tptp.c_Polynomial_Omonom T_a V_b V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_b) V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n)))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_b_H)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_b_H))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y))))))) (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_a_H)) V_b) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b))))))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_ya) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ya)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_ya))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus T_a))) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m)) (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)) (tptp.hAPP tptp.c_Nat_OSuc V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) V_k)))) (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus T_a))) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_b_2) (tptp.hAPP (tptp.hAPP _let_1 V_ca_2) V_d_2)) (= (= V_a_2 V_b_2) (= V_ca_2 V_d_2)))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP _let_1 V_i))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_j)) V_k) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_k)) V_j))))) (forall ((V_n $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_q) V_n))))) (forall ((V_p $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_b) V_p) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Osmult T_a V_b V_p))))) (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))) (forall ((V_qa_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a)) V_pb_2) V_qa_2) (tptp.c_Polynomial_OAbs__poly T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.tc_Nat_Onat T_a T_a) (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus T_a)) (tptp.c_Polynomial_Ocoeff T_a V_pb_2))) (tptp.c_Polynomial_Ocoeff T_a V_qa_2)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)))) (and (=> _let_2 (= _let_1 V_m)) (=> (not _let_2) (= _let_1 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_n)) (=> (tptp.hBOOL (tptp.hAPP _let_2 V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_m))))))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_n_2) V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP tptp.c_Nat_OSuc V_m)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) V_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))))) (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_i_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j_2) V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i_2) V_k_2)) V_j_2))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_m))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2))) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_m_2)) (=> (tptp.hBOOL (tptp.hAPP _let_3 V_n_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m_2) V_k_2)) (tptp.hAPP (tptp.hAPP _let_2 V_n_2) V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_m_2) V_n_2))))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_c) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_i)) V_k) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)) V_i)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_k)) V_i) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_i)) V_k)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_j)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))))))) (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2) V_j_2)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j_2) V_i_2) V_k_2) (= V_j_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) V_i_2))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_n) V_m))) (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_j_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j_2) V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i_2) V_k_2)) V_j_2))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_k)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_j)) V_k)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_m))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) V_m)) V_k))))) (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted) (V_j_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j_2) V_k_2)) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i_2) V_k_2))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP (tptp.hAPP _let_1 V_i) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_k)) V_j))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_b_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_2) V_b_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 V_a_2) V_b_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_2) V_b_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a))) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP _let_1 V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus T_a))) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus T_a))) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c))))) (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus T_a))) (=> (tptp.class_Divides_Oring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H) V_c))))))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))) (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Int_Oint) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint) (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Int_Oint) (tptp.class_Divides_Osemiring__div tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint) (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint) (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__ring tptp.tc_Int_Oint) (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint) (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint) (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Int_Oint) (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint) (tptp.class_Rings_Osemiring__0 tptp.tc_Int_Oint) (tptp.class_Divides_Oring__div tptp.tc_Int_Oint) (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__ring tptp.tc_Int_Oint) (tptp.class_Orderings_Oorder tptp.tc_Int_Oint) (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint) (tptp.class_Rings_Osemiring tptp.tc_Int_Oint) (tptp.class_Orderings_Oord tptp.tc_Int_Oint) (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint) (tptp.class_Power_Opower tptp.tc_Int_Oint) (tptp.class_Groups_Ozero tptp.tc_Int_Oint) (tptp.class_Rings_Oidom tptp.tc_Int_Oint) (tptp.class_Groups_Oone tptp.tc_Int_Oint) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Nat_Onat) (tptp.class_Divides_Osemiring__div tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat) (tptp.class_Orderings_Owellorder tptp.tc_Nat_Onat) (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat) (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat) (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat) (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring__0 tptp.tc_Nat_Onat) (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat) (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat) (tptp.class_Orderings_Oord tptp.tc_Nat_Onat) (tptp.class_Power_Opower tptp.tc_Nat_Onat) (tptp.class_Groups_Ozero tptp.tc_Nat_Onat) (tptp.class_Groups_Oone tptp.tc_Nat_Onat) (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool) (tptp.class_Orderings_Oord tptp.tc_HOL_Obool) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Fields_Olinordered__field__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Fields_Ofield__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Fields_Olinordered__field tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_RealDef_Oreal) (tptp.class_Rings_Odivision__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal) (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring__0 tptp.tc_RealDef_Oreal) (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__ring tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal) (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal) (tptp.class_Fields_Ofield tptp.tc_RealDef_Oreal) (tptp.class_Power_Opower tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oidom tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Fields_Ofield__inverse__zero tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Complex_Ocomplex) _let_26 (tptp.class_Rings_Ocomm__semiring tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__group__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Omonoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__ring tptp.tc_Complex_Ocomplex) (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Fields_Ofield tptp.tc_Complex_Ocomplex) (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex) _let_25 _let_24 (tptp.class_Groups_Oone tptp.tc_Complex_Ocomplex) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__1__strict (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Olinordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__1__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__cancel__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__comm__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semidom (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Groups_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__idom (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Fields_Ofield T_1) (tptp.class_Divides_Osemiring__div (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__ring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Opreorder (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring__0 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Fields_Ofield T_1) (tptp.class_Divides_Oring__div (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Omult__zero (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oorder (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Int_Oring__char__0 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oord (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Oring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Power_Opower (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ozero T_1) (tptp.class_Groups_Ozero (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oidom (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Oone (tptp.tc_Polynomial_Opoly T_1)))) (forall ((V_Q $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK T_a T_b V_P) V_Q) V_P)) (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c V_P_2) V_Q_2) V_R_2) (tptp.hAPP V_P_2 (tptp.hAPP V_Q_2 V_R_2)))) (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_COMBC T_b T_c T_a V_P_2 V_Q_2) V_R_2) (tptp.hAPP (tptp.hAPP V_P_2 V_R_2) V_Q_2))) (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b T_c T_a) V_P_2) V_Q_2) V_R_2) (tptp.hAPP (tptp.hAPP V_P_2 V_R_2) (tptp.hAPP V_Q_2 V_R_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fequal V_x_2) V_y_2))) (= V_x_2 V_y_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fequal V_x_2) V_y_2)))) (forall ((V_Q_2 $$unsorted) (V_P_2 $$unsorted)) (or (tptp.hBOOL V_P_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fimplies V_P_2) V_Q_2)))) (forall ((V_P_2 $$unsorted) (V_Q_2 $$unsorted)) (or (not (tptp.hBOOL V_Q_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fimplies V_P_2) V_Q_2)))) (forall ((V_Q_2 $$unsorted) (V_P_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fimplies V_P_2) V_Q_2))) (not (tptp.hBOOL V_P_2)) (tptp.hBOOL V_Q_2))) _let_23 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.18/1.60  )
% 1.18/1.60  % SZS output end Proof for SWW252+1
% 1.18/1.60  % cvc5---1.0.5 exiting
% 1.18/1.60  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------