%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV716-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 21:53:01 EDT 2023

% Result   : Unsatisfiable 1.60s 1.83s
% Output   : Proof 1.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.28  % Problem    : SWV716-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.29  % Command    : do_cvc5 %s %d
% 0.28/0.50  % Computer : n008.cluster.edu
% 0.28/0.50  % Model    : x86_64 x86_64
% 0.28/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.50  % Memory   : 8042.1875MB
% 0.28/0.50  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.28/0.50  % CPULimit   : 300
% 0.28/0.50  % WCLimit    : 300
% 0.28/0.50  % DateTime   : Tue Aug 29 04:33:47 EDT 2023
% 0.28/0.50  % CPUTime    : 
% 0.46/0.79  %----Proving TF0_NAR, FOF, or CNF
% 0.46/0.80  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.fYFPq2TkhA/cvc5---1.0.5_2195.p...
% 0.63/1.06  ------- get file name : TPTP file name is SWV716-1
% 0.63/1.06  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2195.smt2...
% 0.63/1.06  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.60/1.83  % SZS status Unsatisfiable for SWV716-1
% 1.60/1.83  % SZS output start Proof for SWV716-1
% 1.67/1.87  (
% 1.67/1.87  (let ((_let_1 (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) (let ((_let_3 (tptp.c_Int_OBit0 _let_2))) (let ((_let_4 (tptp.c_Int_Onumber__class_Onumber__of _let_3 tptp.tc_nat))) (let ((_let_5 (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) _let_4))) (let ((_let_6 (tptp.hAPP _let_5 tptp.v_ka____))) (let ((_let_7 (tptp.c_HOL_Ominus__class_Ominus tptp.v_i____ _let_6 tptp.tc_nat))) (let ((_let_8 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_9 (tptp.hAPP _let_8 _let_4))) (let ((_let_10 (tptp.c_COMBB tptp.v_a____ (tptp.c_COMBB tptp.c_Suc _let_9 tptp.tc_nat tptp.tc_nat tptp.tc_nat) tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_nat))) (let ((_let_11 (tptp.hAPP (tptp.c_FFT__Mirabelle_OIFFT tptp.v_ka____ _let_10) _let_7))) (let ((_let_12 (tptp.hAPP _let_9 _let_6))) (let ((_let_13 (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (let ((_let_14 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_Complex_Ocomplex))) (let ((_let_15 (tptp.hAPP _let_14 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Odivide _let_13 (tptp.c_FFT__Mirabelle_Oroot _let_12) tptp.tc_Complex_Ocomplex)) _let_7)))) (let ((_let_16 (tptp.hAPP _let_15 _let_11))) (let ((_let_17 (tptp.c_COMBB tptp.v_a____ _let_9 tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_nat))) (let ((_let_18 (tptp.hAPP (tptp.c_FFT__Mirabelle_OIFFT tptp.v_ka____ _let_17) _let_7))) (let ((_let_19 (tptp.c_HOL_Ominus__class_Ominus _let_18 _let_16 tptp.tc_Complex_Ocomplex))) (let ((_let_20 (tptp.c_FFT__Mirabelle_OIDFT _let_6 _let_10 _let_7))) (let ((_let_21 (tptp.hAPP _let_15 _let_20))) (let ((_let_22 (tptp.c_FFT__Mirabelle_OIDFT _let_6 _let_17 _let_7))) (let ((_let_23 (tptp.c_HOL_Ominus__class_Ominus _let_22 _let_21 tptp.tc_Complex_Ocomplex))) (let ((_let_24 (= _let_23 _let_19))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.c_HOL_Oord__class_Oless _let_7 _let_6 tptp.tc_nat))) (let ((_let_27 (tptp.c_Int_OBit0 tptp.c_Int_OPls))) (let ((_let_28 (forall ((V_a $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) tptp.v_ka____))) (or (= (tptp.c_FFT__Mirabelle_OIDFT _let_1 V_a V_i) (tptp.hAPP (tptp.c_FFT__Mirabelle_OIFFT tptp.v_ka____ V_a) V_i)) (not (tptp.c_HOL_Oord__class_Oless V_i _let_1 tptp.tc_nat))))))) (let ((_let_29 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_30 (tptp.hAPP tptp.c_Suc _let_29))) (let ((_let_31 (tptp.hAPP tptp.c_Suc _let_30))) (let ((_let_32 (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OPls tptp.tc_nat))) (let ((_let_33 (tptp.c_Int_OBit1 tptp.c_Int_OMin))) (let ((_let_34 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_35 (tptp.hAPP _let_34 _let_29))) (let ((_let_36 (tptp.hAPP _let_35 _let_30))) (let ((_let_37 (tptp.hAPP (tptp.hAPP _let_34 _let_30) _let_29))) (let ((_let_38 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))))))) (let ((_let_39 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_Complex_Ocomplex))) (let ((_let_40 (= _let_23 (tptp.hAPP (tptp.hAPP _let_39 _let_22) (tptp.c_HOL_Ouminus__class_Ouminus _let_21 tptp.tc_Complex_Ocomplex))))) (let ((_let_41 (= _let_19 (tptp.hAPP (tptp.hAPP _let_39 _let_18) (tptp.c_HOL_Ouminus__class_Ouminus _let_16 tptp.tc_Complex_Ocomplex))))) (let ((_let_42 (= _let_20 _let_11))) (let ((_let_43 (= _let_22 _let_18))) (let ((_let_44 (not _let_1))) (let ((_let_45 (or _let_44 _let_40))) (let ((_let_46 (_let_38))) (let ((_let_47 (ASSUME :args _let_46))) (let ((_let_48 ((tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a)))) (let ((_let_49 (ASSUME :args (_let_1)))) (let ((_let_50 (or _let_44 _let_41))) (let ((_let_51 (not _let_26))) (let ((_let_52 (or _let_42 _let_51))) (let ((_let_53 (_let_28))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 ((tptp.c_FFT__Mirabelle_OIDFT _let_6 V_a V_i)))) (let ((_let_56 (ASSUME :args (_let_26)))) (let ((_let_57 (or _let_43 _let_51))) (let ((_let_58 (and _let_40 _let_41 _let_42 _let_43))) (let ((_let_59 (ASSUME :args (_let_41)))) (let ((_let_60 (APPLY_UF tptp.hAPP))) (let ((_let_61 (ASSUME :args (_let_42)))) (let ((_let_62 (ASSUME :args (_let_43)))) (let ((_let_63 (ASSUME :args (_let_40)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_58)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_59 _let_62 _let_61 _let_63) (SCOPE (TRANS (SYMM (SYMM _let_63)) (CONG (CONG (REFL :args (_let_39)) (SYMM (SYMM _let_62)) :args _let_60) (CONG (CONG (REFL :args (_let_15)) (SYMM (SYMM _let_61)) :args _let_60) (REFL :args (tptp.tc_Complex_Ocomplex)) :args (APPLY_UF tptp.c_HOL_Ouminus__class_Ouminus)) :args _let_60) (SYMM _let_59)) :args (_let_41 _let_43 _let_42 _let_40))) :args (_let_40 _let_41 _let_42 _let_43))) :args (true _let_58)) :args ((or _let_24 (not _let_40) (not _let_41) (not _let_42) (not _let_43)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_51 _let_43 (not _let_57)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_17 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_53)) _let_54 :args (_let_57 false _let_28)) :args (_let_43 false _let_26 false _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_42 (not _let_52)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_10 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_55)) :args _let_53)) _let_54 :args (_let_52 false _let_28)) :args (_let_42 false _let_26 false _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_44 _let_41 (not _let_50)))) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.tc_Complex_Ocomplex _let_18 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_46)) _let_47 :args (_let_50 false _let_38)) :args (_let_41 false _let_1 false _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_44 _let_40 (not _let_45)))) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.tc_Complex_Ocomplex _let_22 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_46)) _let_47 :args (_let_45 false _let_38)) :args (_let_40 false _let_1 false _let_45)) (ASSUME :args (_let_25)) :args (false false _let_43 false _let_42 false _let_41 false _let_40 true _let_24)) :args ((forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a) V_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv V_m (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat) V_m)) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_r1 $$unsorted) (V_add $$unsorted) (V_mul $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_pwr V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_r1) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a))))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_P $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k) V_i)) V_j) V_k tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_j)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) T_a)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a))) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) V_b)) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) V_b)) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) (tptp.hAPP tptp.c_Suc _let_1))) (= V_m _let_1) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a)) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 V_b) V_c T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_x) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_n) T_a) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) _let_1 T_a) (not (tptp.c_lessequals V_x _let_1 T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) _let_1)) (= V_y _let_1))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv V_a V_c tptp.tc_nat)) (tptp.c_Divides_Odiv__class_Odiv V_b V_c tptp.tc_nat))) (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c tptp.tc_nat)) (tptp.c_Divides_Odiv__class_Omod V_b V_c tptp.tc_nat)) V_c tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) V_y) tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) V_y) tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)) (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) V_y) tptp.tc_nat)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat)) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) V_y) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven V_m tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_m tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)) (tptp.c_Parity_Oeven__odd__class_Oeven V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven V_m tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_m tptp.tc_nat)) (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (or (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP tptp.c_Suc V_x) _let_1 tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.c_Divides_Odiv__class_Odiv V_x _let_1 tptp.tc_nat))) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_b T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.c_Divides_Odiv__class_Omod V_x (tptp.hAPP tptp.c_Suc _let_1) tptp.tc_nat) _let_1)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (= (tptp.c_Divides_Odiv__class_Omod V_x (tptp.hAPP tptp.c_Suc _let_1) tptp.tc_nat) _let_1) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_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))))))) _let_38 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_Divides_Odiv__class_Odiv V_m V_k tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_add $$unsorted) (V_mul $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP (tptp.hAPP V_mul V_a) V_m)) (tptp.hAPP (tptp.hAPP V_mul V_b) V_m)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_a) V_b)) V_m)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_mul $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_r1 $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP (tptp.hAPP V_mul V_a) V_m)) V_m) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_a) V_r1)) V_m)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_m $$unsorted) (V_mul $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_m) (tptp.hAPP (tptp.hAPP V_mul V_a) V_m)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_a) V_r1)) V_m)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_m $$unsorted) (V_mul $$unsorted) (V_r1 $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_m) V_m) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_r1) V_r1)) V_m)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_r0 $$unsorted) (V_a $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_r0) V_a) V_a) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_r0 $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_a) V_r0) V_a) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_a) V_b) (tptp.hAPP (tptp.hAPP V_mul V_b) V_a)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_add $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_add V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP (tptp.hAPP V_mul V_a) V_c)) (tptp.hAPP (tptp.hAPP V_mul V_b) V_c))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_r0 $$unsorted) (V_a $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_r0) V_a) V_r0) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_a $$unsorted) (V_r0 $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_a) V_r0) V_r0) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_r1 $$unsorted) (V_a $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_r1) V_a) V_a) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_a) V_r1) V_a) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_ly)) (tptp.hAPP (tptp.hAPP V_mul V_rx) V_ry)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_rx)) (tptp.hAPP (tptp.hAPP V_mul V_ly) V_ry))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP V_mul V_rx) V_ry))) (let ((_let_2 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_2 V_ly)) _let_1) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP V_mul V_ly) _let_1))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_mul V_lx) V_ly)))) (let ((_let_2 (tptp.hAPP V_mul V_rx))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ry)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_ry))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_ly)) V_rx) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_rx)) V_ly)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_ly)) V_rx) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_mul V_ly) V_rx))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_mul V_rx) V_ry)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_rx)) V_ry)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_lx))) (let ((_let_2 (tptp.hAPP V_mul V_rx))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ry)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_ry))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_b)) (tptp.hAPP (tptp.hAPP V_add V_c) V_d)) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_c)) (tptp.hAPP (tptp.hAPP V_add V_b) V_d))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_b)) V_c) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_add V_b) V_c))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (let ((_let_2 (tptp.hAPP V_add V_c))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_d)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_d))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (or (= (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_b)) V_c) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_c)) V_b)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_a) V_c) (tptp.hAPP (tptp.hAPP V_add V_c) V_a)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_a))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_add V_c) V_d)) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_c)) V_d)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_add $$unsorted) (V_r0 $$unsorted) (V_x $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_r0) V_x) V_x) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_add $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_add V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_add V_y) V_z)) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_y)) V_z)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_add $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_mul $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_add V_x) V_y) (tptp.hAPP (tptp.hAPP V_add V_y) V_x)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_r0 $$unsorted) (V_x $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_r0) V_x) V_r0) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_r1 $$unsorted) (V_x $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_r1) V_x) V_x) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_mul V_y) V_z)) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_y)) V_z)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_add $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_x) V_y) (tptp.hAPP (tptp.hAPP V_mul V_y) V_x)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_mul $$unsorted) (V_x $$unsorted) (V_add $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_pwr $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_mul V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP V_add V_y) V_z)) (tptp.hAPP (tptp.hAPP V_add (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_pwr $$unsorted) (V_mul $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_pwr (tptp.hAPP (tptp.hAPP V_mul V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP (tptp.hAPP V_pwr V_x) V_q)) (tptp.hAPP (tptp.hAPP V_pwr V_y) V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_m V_n)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x))) (or (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_n _let_2) (= V_n _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_m _let_1) (= V_m _let_2))))) (= _let_30 _let_36) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) T_a) (not (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 V_u))) (= (tptp.hAPP _let_2 V_z) V_u)))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (or (= (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_1) (tptp.c_Divides_Odiv__class_Odiv V_x _let_1 tptp.tc_nat))) V_x) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin tptp.tc_nat) _let_29) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) V_n) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l) tptp.tc_nat) (not (tptp.c_lessequals V_k V_l tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP tptp.c_Suc V_a) V_c tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Divides_Odiv__class_Odiv V_a V_c tptp.tc_nat)) (tptp.c_Divides_Odiv__class_Odiv _let_1 V_c tptp.tc_nat))) (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Divides_Odiv__class_Omod V_a V_c tptp.tc_nat)) (tptp.c_Divides_Odiv__class_Omod _let_1 V_c tptp.tc_nat)) V_c tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (not (tptp.c_Parity_Oeven__odd__class_Oeven _let_2 tptp.tc_nat)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_2) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) _let_1)) (= V_x _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_c)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_d)))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_r))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x))) (or (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_c)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_d)))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((V_b $$unsorted) (V_q $$unsorted) (V_c $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_b))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_q V_c tptp.tc_nat))) V_r) (tptp.hAPP _let_1 V_c) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_r V_b tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_c tptp.tc_nat))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_b))) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.hAPP _let_1 V_c) tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod (tptp.c_Divides_Odiv__class_Odiv V_a V_b tptp.tc_nat) V_c tptp.tc_nat))) (tptp.c_Divides_Odiv__class_Omod V_a V_b tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b)) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b) V_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP _let_2 V_a) (tptp.hAPP _let_2 V_b) T_a) _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_1))) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP _let_2 V_m) (tptp.hAPP _let_2 V_n) tptp.tc_nat) _let_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.c_Divides_Odiv__class_Omod V_x (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc _let_1)) tptp.tc_nat) _let_1) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_Divides_Odiv__class_Omod V_x (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc _let_1)) tptp.tc_nat) _let_1)) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_a))) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP _let_1 V_b) V_c tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Odiv V_b V_c tptp.tc_nat))) (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_b V_c tptp.tc_nat)) V_c tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) (tptp.c_HOL_Oabs__class_Oabs V_b T_a))) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) (tptp.c_HOL_Oabs__class_Oabs V_b T_a))) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) (tptp.c_HOL_Oabs__class_Oabs V_b T_a))) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) (tptp.c_HOL_Oabs__class_Oabs V_b T_a))) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_x) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_n) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_x T_a) (tptp.c_HOL_Oabs__class_Oabs V_y T_a) T_a)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y V_x tptp.tc_Int_Oint) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_Int_Oint))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_lessequals V_n _let_1 tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_HOL_Oabs__class_Oabs V_b T_a)) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= V_a _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_j) V_k tptp.tc_nat) (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat))) (not (tptp.c_lessequals V_k V_j tptp.tc_nat))))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_j) V_i) V_k tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) V_i)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat))))) (= (tptp.c_Fact_Ofact__class_Ofact _let_30 tptp.tc_nat) _let_30) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1)) (= V_a _let_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.c_Complex_Oii))) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_x)) (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_Complex_Ocomplex)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oabs__if T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (or (not (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) V_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) V_m)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) T_a) (not (tptp.c_lessequals _let_2 V_x T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_2 V_x T_a) (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat) (not (tptp.c_lessequals _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) T_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_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)) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat) (not (tptp.c_lessequals V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_1) (tptp.c_Divides_Odiv__class_Odiv V_x _let_1 tptp.tc_nat)) V_x) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin tptp.c_Int_OPls tptp.tc_Int_Oint) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d) T_a) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) T_a)) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) T_a)) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a)) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_n)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) V_b)) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a))) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (= V_a _let_1)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin V_k tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin (tptp.c_Int_OBit0 V_k) tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin (tptp.c_Int_OBit0 V_k) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin V_k tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin V_k tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin (tptp.c_Int_OBit1 V_k) tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin (tptp.c_Int_OBit1 V_k) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin V_k tptp.tc_Int_Oint)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_N) (tptp.hAPP _let_1 V_n) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_n V_N tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_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_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_Divides_Odiv__class_Odiv V_k V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv V_k V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_b T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a_H T_a) V_b T_a)))) (forall ((V_mul $$unsorted) (V_pwr $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_p)) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_p) V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)) V_b T_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)) V_b T_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H) V_c T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP tptp.c_Suc _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_m _let_1) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) V_i tptp.tc_nat) (not (tptp.c_lessequals V_j (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_j (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) V_i tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_P $$unsorted) (V_i $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k) V_i)) V_j) V_k tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_i)))) (tptp.c_Parity_Oeven__odd__class_Oeven _let_29 tptp.tc_nat) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_n) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) T_a))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Omod V_m (tptp.hAPP tptp.c_Suc _let_1) tptp.tc_nat) _let_1))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oabs__class_Oabs V_y T_a)) V_x) (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a))))) (= _let_30 _let_37) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_Int_Oint))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) V_i))) (or (not (tptp.c_lessequals V_i _let_1 tptp.tc_nat)) (= (tptp.c_HOL_Ominus__class_Ominus _let_1 V_i tptp.tc_nat) V_k)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_k $$unsorted) (V_x $$unsorted)) (tptp.c_lessequals V_k (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) V_x) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.c_lessequals V_m (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_x) tptp.tc_nat)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_lessequals V_n (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_lessequals V_n (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) tptp.tc_nat)) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) V_y)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) _let_1 T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) V_n) V_m) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) V_m) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (= V_j (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat)) V_i)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a))))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) V_i) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_j) V_i) V_k tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i))) (or (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_j) V_k tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat))))) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls tptp.c_Int_OMin tptp.tc_Int_Oint)) (forall ((V_x $$unsorted) (V_n $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_xb $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_n))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) (tptp.hAPP _let_1 V_xa)) (tptp.hAPP (tptp.hAPP _let_2 V_y) (tptp.hAPP _let_1 V_xb)))) (= (tptp.c_Divides_Odiv__class_Omod V_x V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod V_y V_n tptp.tc_nat)))))) (forall ((V_P $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Odiv V_m _let_1 tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP V_P _let_1)))))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP V_P _let_1))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Odiv V_n _let_1 tptp.tc_nat)))))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Odiv V_n _let_1 tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) (tptp.c_HOL_Oabs__class_Oabs V_b T_a)) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a)) V_n) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP (tptp.hAPP _let_1 V_x) V_n) T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Fact_Ofact__class_Ofact V_m tptp.tc_nat) (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_m tptp.tc_nat)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (or (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP tptp.c_Suc V_x) _let_1 tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv V_x _let_1 tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oabs__if T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (tptp.c_lessequals _let_29 _let_29 tptp.tc_nat) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) (tptp.c_HOL_Oabs__class_Oabs V_b T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Olordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) (tptp.c_HOL_Oabs__class_Oabs V_b T_a)) T_a)))) (forall ((V_n $$unsorted)) (= (tptp.c_Fact_Ofact__class_Ofact (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n) tptp.tc_nat) (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_Fact_Ofact__class_Ofact V_m tptp.tc_nat) (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a))))) (= _let_37 _let_30) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_x T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.c_lessequals _let_1 _let_1 T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1))))) (= (tptp.hAPP _let_35 _let_29) _let_29) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a)) V_c T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_m))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_n)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_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 ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_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 ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Ring__and__Field_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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_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_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) (tptp.c_HOL_Oabs__class_Oabs V_b T_a)) T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z) tptp.tc_nat) (not (tptp.c_lessequals V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z) tptp.tc_nat) (not (tptp.c_lessequals V_x V_z tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_k) V_n tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_k V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_k) V_n tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_m) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_j) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a)) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) V_b) V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) _let_1 T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) T_a) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_y _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_x _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) _let_2 T_a) (not (tptp.c_lessequals V_x _let_2 T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oabs__class_Oabs V_x T_a)) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_n)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat))))) (forall ((V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven _let_2 tptp.tc_nat) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_2) _let_1 T_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Suc (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat)) V_n)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_2)) (= V_m _let_1) (= V_m _let_2))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_2)) (= V_n _let_2) (= V_n _let_1))))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k) tptp.c_Int_OMin tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_k tptp.c_Int_OMin tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_k tptp.c_Int_OMin tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k) tptp.c_Int_OMin tptp.tc_Int_Oint)))) (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_n))) (= V_a V_b) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) V_y)) (= V_x (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a))))) (= (tptp.c_Fact_Ofact__class_Ofact _let_29 tptp.tc_nat) _let_30) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_c)) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_b)) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k) V_n)) V_m) V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven__odd__class_Oeven _let_2 tptp.tc_nat)) (= _let_2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) _let_2) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((V_x $$unsorted)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_m)) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n) V_n)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OMin tptp.c_Int_OMin tptp.tc_Int_Oint)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) T_a))))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P V_n))) (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))))) (forall ((V_P $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_n)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_x $$unsorted)) (tptp.c_lessequals V_x V_x tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_nat) (not (tptp.c_lessequals V_j V_k tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))) (forall ((V_n $$unsorted)) (tptp.c_lessequals V_n V_n tptp.tc_nat)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_d) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a (tptp.hAPP _let_1 V_c) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (= _let_36 _let_30) (forall ((V_d $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_d) V_x) V_d tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) V_b)) V_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) _let_1))))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a) (not (tptp.c_lessequals _let_1 V_x T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 V_x T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a) (not (tptp.c_lessequals _let_1 V_x T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 V_x T_a) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_n) (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a)) V_n) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a)) V_x) (tptp.c_HOL_Oone__class_Oone T_a)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless V_x _let_2 T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= _let_2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) _let_2) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_x T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) T_a) (= V_x _let_2) (not (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a) V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) _let_1) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((V_v $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls V_v tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat) tptp.tc_nat)))) (forall ((V_v $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls V_v tptp.tc_Int_Oint)))) (forall ((V_P $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_n))) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP V_P V_x))) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_x)) tptp.tc_nat)) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_x) V_m tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_n) (tptp.hAPP tptp.c_Suc (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat))) tptp.tc_nat))) (forall ((V_v $$unsorted) (V_v_H $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v_H tptp.tc_nat)) V_k)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_v tptp.c_Int_OPls tptp.tc_Int_Oint))))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat)) (tptp.c_Int_Onumber__class_Onumber__of V_v_H tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_v tptp.c_Int_OPls tptp.tc_Int_Oint)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_n tptp.tc_nat))) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) T_a)) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) T_a) (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat)) V_u)) V_m) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat)) V_u)) V_m) V_n tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat)))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat)) V_u)) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat)) V_u)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))))) (forall ((V_a $$unsorted)) (= (tptp.c_FFT__Mirabelle_OIFFT (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_a) V_a)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1)) T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2)) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2)) _let_1 T_a))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_y _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2)) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2)) _let_1 T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) 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(tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_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_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) T_a) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) T_a) (= V_x _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_x T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_r) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_r) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_r T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)) V_c))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_b) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_b) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_y) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b_H) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 _let_2) _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_w))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_y)) (tptp.hAPP _let_2 V_z)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_2 V_y)))) (= V_y V_z) (= V_w V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_2 V_d)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_2 V_c)))) (= V_c V_d) (= V_a V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a)) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 _let_2) _let_2) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_b)))))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_xa))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a)) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP _let_1 V_x) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP _let_1 V_b) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a)) V_y) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_m)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_a_H)) V_b) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_ya) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ya)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_ya))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_b_H)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_b_H))))))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_xa))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP _let_1 V_b) T_a) (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_b))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of V_v T_a)))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_a) V_b)) _let_1) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus V_y V_b T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (let ((_let_4 (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a)))) (let ((_let_5 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y) (tptp.hAPP _let_3 V_b) T_a) (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP _let_4 _let_1)) (tptp.hAPP _let_4 V_b))) (tptp.hAPP _let_3 _let_1)))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c) V_d))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (= V_c (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a)) V_x)))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 V_m) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP _let_2 _let_1) _let_1)) V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_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_HOL_Oone__class_Oone T_a))) V_m)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Oone__class_Oone T_a))) V_m)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a))))) (forall 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(tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals _let_2 V_a T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_lessequals V_a _let_2 T_a)) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_lessequals _let_2 _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_lessequals _let_1 _let_2 T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not 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(tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_p)) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_p) V_q)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_c T_a) V_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_c T_a) V_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) V_c)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)) V_c) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))) (= V_z _let_2) (= V_y _let_2) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_2 V_w) V_y))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) V_c T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OPls T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OPls T_a)) V_a) V_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OPls T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OPls T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 _let_2)) (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_2 _let_1)) (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (= _let_2 _let_1))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 _let_2)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_2)) (= _let_2 _let_1))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_2 _let_1)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_k tptp.c_Int_OPls tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k) tptp.c_Int_OPls tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k) tptp.c_Int_OPls tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_k tptp.c_Int_OPls tptp.tc_Int_Oint)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.hAPP tptp.c_Suc V_n)) _let_1)))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l) tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_Int_Oint)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) (tptp.c_HOL_Oabs__class_Oabs V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1)) (= V_a _let_1) (= V_b _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_b))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (= V_a V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (let ((_let_3 (tptp.hAPP _let_1 V_z))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (let ((_let_3 (tptp.hAPP _let_1 V_d))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_e)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_e)) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a)) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a)) V_b) V_c T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a)) V_z) (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a)) (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d) T_a) (not (tptp.c_lessequals V_c (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d) T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals V_c (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d) T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c) V_d T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c) V_d T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d) T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_x) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_b) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) (tptp.c_HOL_Ominus__class_Ominus V_c V_d T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a) (= V_x _let_1) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a)) (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n) T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_1 T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_x T_a) V_y T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Groebner__Basis_Ogb__semiring (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a)) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_2 V_w) V_y)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z) T_a)) (= V_z _let_1) (= V_y _let_1)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_z) (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y)) V_y T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) V_z) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y)) V_y T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_2) _let_1) T_a)) (not (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_x T_a) (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a))) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_x) _let_1) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 V_w) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ozero__class_Ozero T_a)) _let_1)) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_x) _let_1) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.hAPP _let_1 V_n) (tptp.hAPP _let_1 V_N) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (not (tptp.c_lessequals V_n V_N tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a)) V_x) _let_1) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (= _let_33 tptp.c_Int_OMin) (forall ((V_k $$unsorted)) (or (not (= (tptp.c_Int_OBit1 V_k) tptp.c_Int_OMin)) (= V_k tptp.c_Int_OMin))) (forall ((V_l $$unsorted)) (or (not (= tptp.c_Int_OMin (tptp.c_Int_OBit1 V_l))) (= tptp.c_Int_OMin V_l))) (forall ((V_k1 $$unsorted) (V_k2 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k1) (tptp.c_Int_OBit1 V_k2) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_k1 V_k2 tptp.tc_Int_Oint)))) (forall ((V_k1 $$unsorted) (V_k2 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_k1 V_k2 tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k1) (tptp.c_Int_OBit1 V_k2) tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit1 V_l) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit1 V_l) tptp.tc_Int_Oint)))) (= tptp.c_Int_OMin _let_33) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP tptp.c_Suc (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat)) V_n tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_k1 $$unsorted) (V_k2 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_k1 V_k2 tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k1) (tptp.c_Int_OBit0 V_k2) tptp.tc_Int_Oint)))) (forall ((V_k1 $$unsorted) (V_k2 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 V_k1) (tptp.c_Int_OBit0 V_k2) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_k1 V_k2 tptp.tc_Int_Oint)))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (= V_x _let_2) (= V_x _let_1) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP tptp.c_Suc _let_2) tptp.tc_nat)))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.hAPP tptp.c_Suc _let_1) tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_x)) tptp.tc_nat)) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_i (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_i)) tptp.tc_nat)) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_i (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_m)) tptp.tc_nat)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_x $$unsorted)) (or (not (tptp.c_lessequals V_x V_x tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP tptp.c_Suc V_x) tptp.tc_nat))) (tptp.c_HOL_Oord__class_Oless _let_29 _let_30 tptp.tc_nat) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat)) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_k tptp.c_Int_OPls tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit0 V_k) tptp.c_Int_OPls tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit0 V_k) tptp.c_Int_OPls tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_k tptp.c_Int_OPls tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls V_k tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls (tptp.c_Int_OBit0 V_k) tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls (tptp.c_Int_OBit0 V_k) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls V_k tptp.tc_Int_Oint)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_m))) V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_m) V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv V_m (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_n))) tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv V_m (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_m))) V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_m) V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod V_m (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_n))) tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod V_m (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_m))) _let_1 tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_m) _let_1 tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_m))) _let_1 tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_m) _let_1 tptp.tc_nat)))) (forall ((V_n $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) tptp.tc_nat) tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat)))) (forall ((V_n $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven V_n tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_Divides_Odiv__class_Omod V_n (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) tptp.tc_nat) tptp.tc_nat) tptp.tc_nat)))) (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_m) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat) tptp.tc_nat) V_m)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) V_n) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a))))) (= _let_32 _let_29) (= _let_29 _let_32) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) _let_1)) (= V_a _let_1)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_v V_v_H tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP _let_2 V_m) (tptp.hAPP _let_2 V_n) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat))) (tptp.c_lessequals V_n V_m tptp.tc_nat) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m))) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) (tptp.hAPP _let_1 V_n))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_x))) (= (tptp.c_Fact_Ofact__class_Ofact _let_1 tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_1) (tptp.c_Fact_Ofact__class_Ofact V_x tptp.tc_nat))))) (= (tptp.hAPP (tptp.hAPP _let_8 _let_30) _let_30) _let_30) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_i) (tptp.hAPP _let_1 V_j) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (= V_m V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_c tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_b V_c tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_c V_a tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_n tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) V_j tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus V_a V_b tptp.tc_nat)))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat)) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_nat) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)) (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_nat) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) V_m) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) _let_1) (tptp.hAPP tptp.c_Suc _let_1)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) _let_1) V_n) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) _let_1) V_m) _let_1))) (forall ((V_x $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) V_m) _let_2)) (= V_x _let_2) (= V_m _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_i))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_i tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_nat) (= V_n _let_1) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) V_n) tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) V_n) tptp.tc_nat))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) _let_1) tptp.tc_nat))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2))) (= V_x V_y) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2)) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2)) _let_1)) (= V_x _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2)) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2)) _let_1)) (= V_y _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1) T_a)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) _let_1))))) (= (tptp.c_FFT__Mirabelle_Oroot _let_29) _let_13) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c) V_d T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) V_e)) V_c) V_d T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)) V_e)) V_d) T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y) V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted)) (not (= (tptp.hAPP tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m))) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP tptp.c_Suc (tptp.hAPP _let_1 V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)) V_n) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.hAPP tptp.c_Suc V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_n))) (or (= V_m _let_1) (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m _let_1 tptp.tc_nat))))) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_mul $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP V_mul V_x) (tptp.hAPP _let_1 V_n))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_q $$unsorted) (V_mul $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q)) (tptp.hAPP (tptp.hAPP V_mul V_x) (tptp.hAPP _let_1 V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_pwr $$unsorted) (V_x $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP (tptp.hAPP V_mul (tptp.hAPP _let_1 V_q)) V_x) (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_mul $$unsorted) (V_x $$unsorted) (V_pwr $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP (tptp.hAPP V_mul V_x) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_N $$unsorted)) (tptp.c_Fun_Oinj__on tptp.c_Suc V_N tptp.tc_nat tptp.tc_nat)) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_nat_H)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_m)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat)))) (or (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat) _let_1) (= _let_1 V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) V_m tptp.tc_nat) (tptp.c_lessequals V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) V_m tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_n))) (tptp.c_lessequals _let_1 _let_1 tptp.tc_nat))) (forall ((V_x $$unsorted)) (or (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP tptp.c_Suc V_x) tptp.tc_nat)))) (forall ((V_x $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP tptp.c_Suc V_x) tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat))) (not (= tptp.c_Int_OPls tptp.c_Int_OMin)) (not (= tptp.c_Int_OMin tptp.c_Int_OPls)) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls tptp.c_Int_OPls tptp.tc_Int_Oint)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_n))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP tptp.c_Suc V_n))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_3 V_a) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_b) _let_2))) (= V_a V_b) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) V_n))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat))))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_j) V_i tptp.tc_nat))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_i) V_i tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless _let_29 _let_29 tptp.tc_nat)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= V_n _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_l) (tptp.hAPP (tptp.hAPP _let_1 V_k) V_n))) (not (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) V_m) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_z tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_j) V_k tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_m) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_j) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_l $$unsorted)) (not (= tptp.c_Int_OMin (tptp.c_Int_OBit0 V_l)))) (forall ((V_k $$unsorted)) (not (= (tptp.c_Int_OBit0 V_k) tptp.c_Int_OMin))) (forall ((V_k1 $$unsorted) (V_k2 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit0 V_k1) (tptp.c_Int_OBit0 V_k2) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_k1 V_k2 tptp.tc_Int_Oint)))) (forall ((V_k1 $$unsorted) (V_k2 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_k1 V_k2 tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit0 V_k1) (tptp.c_Int_OBit0 V_k2) tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit0 V_l) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_k V_l tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit0 V_l) tptp.tc_Int_Oint)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) _let_1) (tptp.c_Int_Onumber__class_Onumber__of V_v_H tptp.tc_nat)) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_v_H tptp.c_Int_OPls tptp.tc_Int_Oint)) (tptp.c_HOL_Oord__class_Oless V_v tptp.c_Int_OPls tptp.tc_Int_Oint)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v_H tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat)) _let_1) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_v tptp.c_Int_OPls tptp.tc_Int_Oint))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oabs__class_Oabs V_x T_a)) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1)) (not (tptp.c_Parity_Oeven__odd__class_Oeven _let_1 tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_2) _let_1) _let_2) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_2) _let_1) _let_2) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_c T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) V_ya T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a)))))) (forall ((V_q $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_n))) (or (= V_q (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q)) tptp.tc_nat)) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_q) V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) tptp.tc_nat) (not (tptp.c_lessequals _let_1 V_n tptp.tc_nat)) (not (tptp.c_lessequals _let_1 V_m tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k) V_n)) V_m)) V_n tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_lessequals _let_1 V_m tptp.tc_nat) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_lessequals _let_1 V_n tptp.tc_nat) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) tptp.tc_nat))))) (forall ((V_xa $$unsorted)) (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) V_xa) tptp.tc_nat)) (forall ((V_xa $$unsorted)) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) V_xa)) tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_n) V_m) V_n tptp.tc_nat) V_m) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) V_n tptp.tc_nat) V_m) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_n tptp.tc_nat))) (not (tptp.c_lessequals V_n V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_k) (tptp.hAPP tptp.c_Suc V_j) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_j V_k tptp.tc_nat)) V_m tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.c_Suc V_j) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) V_m) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_j tptp.tc_nat)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_x) V_y) tptp.tc_nat)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_b) V_c) tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Divides_Odiv__class_Odiv V_a V_b tptp.tc_nat) V_c tptp.tc_nat))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_1) V_n) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) _let_1) _let_1))) (forall ((V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_w))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_y)) (tptp.hAPP _let_2 V_z)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_2 V_y)))) (= V_y V_z) (= V_w V_x))))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_2 V_d)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_2 V_c)))) (= V_c V_d) (= V_a V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) 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_let_2 _let_1) _let_1) T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_2 _let_1) _let_1) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a)) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) _let_1) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1 T_a) V_a) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1 T_a)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) V_c T_a) _let_1)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a)) _let_1)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a)) _let_1) V_b) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) V_c T_a) _let_1) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_2) _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1)) (= V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_2 V_w) V_y) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z) T_a)) (= V_z _let_1) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_RealVector_Oreal__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_b) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d) T_a) V_h T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) V_h T_a))) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) V_h T_a)) V_d))))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 V_w) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oone__class_Oone T_a)) _let_1)) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1)) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2)) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2)) T_a) (= V_x _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_3 V_x) _let_2)) (tptp.hAPP (tptp.hAPP _let_3 V_y) _let_2)) T_a) (= V_y _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_y) _let_1) T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OPls T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls V_v_H tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless V_v V_v_H tptp.tc_Int_Oint)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_v V_v_H tptp.tc_Int_Oint)) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Int_OPls V_v_H tptp.tc_Int_Oint)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_a _let_1) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_k)) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n)) T_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_n) V_m) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_i) V_j)) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_k) V_i)) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP _let_2 V_j) (tptp.hAPP _let_2 V_k) T_a)) V_i)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.hAPP tptp.c_Suc _let_1) tptp.tc_nat)) V_n) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.hAPP tptp.c_Suc V_i) tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((V_v $$unsorted) (V_v_H $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_nat))) (or (= (tptp.c_HOL_Ominus__class_Ominus _let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v_H tptp.tc_nat) tptp.tc_nat) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_v_H tptp.c_Int_OPls tptp.tc_Int_Oint))))) (forall ((V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= _let_1 _let_2)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) _let_1) tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_2 V_x tptp.tc_nat) (= _let_1 _let_2) (not (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) _let_1) tptp.tc_nat)))))) (forall ((V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n))) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_a T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not 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(tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1)) (tptp.c_Int_Onumber__class_Onumber__of V_w T_a)) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 V_w) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Suc V_n)) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_m V_n) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_x) V_y) tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_x) V_y) tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat)))) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_add $$unsorted) (V_mul $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (or (= (tptp.hAPP (tptp.hAPP V_pwr (tptp.hAPP _let_1 V_p)) V_q) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_p) V_q))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m))) (tptp.c_lessequals V_m (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_m)) tptp.tc_nat))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l) tptp.tc_nat) (not (tptp.c_lessequals V_k V_l tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (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_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_lessequals (tptp.hAPP _let_1 V_i) (tptp.hAPP _let_1 V_j) tptp.tc_nat) (not (tptp.c_lessequals V_i V_j tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_lessequals (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_2 V_m) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_n) _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (let ((_let_3 (tptp.hAPP _let_1 V_z))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2))))))) (forall ((V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (let ((_let_3 (tptp.hAPP _let_1 V_d))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2))))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (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_m $$unsorted)) (tptp.c_lessequals V_m (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_m) tptp.tc_nat)) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat)) V_k) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (= (tptp.hAPP _let_1 (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat)) (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_n) (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) V_n) (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) tptp.tc_nat))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat) (not (tptp.c_lessequals V_m (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat)) V_u)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals V_m (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat)) V_u)) V_n) tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat)) V_u)) V_m) V_n tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat)) V_u)) V_m) V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat)) V_u)) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod V_m V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Divides_Odiv__class_Odiv V_m V_n tptp.tc_nat)) V_n) tptp.tc_nat))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat)) V_u)) V_n) tptp.tc_nat)) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat)) V_u)) V_m) V_n tptp.tc_nat)) (not (tptp.c_lessequals V_j V_i tptp.tc_nat)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n))) (not (tptp.c_lessequals V_i V_j tptp.tc_nat)) (= V_m (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_j V_i tptp.tc_nat)) V_u)) V_n)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n))) (not (tptp.c_lessequals V_j V_i tptp.tc_nat)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat)) V_u)) V_m) V_n))))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (tptp.c_lessequals V_j V_i tptp.tc_nat)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat)) V_u)) V_m))))))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_b) V_d) V_b tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_d)))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_b) V_x) V_b tptp.tc_nat)))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_HOL_Ominus__class_Ominus V_n V_i tptp.tc_nat) tptp.tc_nat) V_i) (not (tptp.c_lessequals V_i V_n tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_n V_m tptp.tc_nat) _let_1)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) _let_1)) (= V_m V_n)))) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m V_m tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_m)) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_lessequals V_m V_n tptp.tc_nat) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_n $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_l tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_l tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_l V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_l V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_lessequals V_m V_n tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_i (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_k) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat))) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)) (= V_m V_n))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Ominus__class_Ominus _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_nat) tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat) (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_nat) tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_y tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_m tptp.tc_nat)) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_n V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_n tptp.tc_nat)) (not (tptp.c_lessequals V_k V_m tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m) V_n tptp.tc_nat) V_m)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) V_n tptp.tc_nat) V_m)) (forall ((V_i $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_i) V_n) tptp.tc_nat) (not (tptp.c_lessequals _let_1 V_i tptp.tc_nat))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) V_y) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_y tptp.tc_nat)) (not (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_y tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) V_y) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_Parity_Oeven__odd__class_Oeven V_x tptp.tc_nat) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_nat) V_x) V_y) tptp.tc_nat)))) (= (tptp.hAPP (tptp.hAPP _let_14 tptp.c_Complex_Oii) tptp.c_Complex_Oii) (tptp.c_HOL_Ouminus__class_Ouminus _let_13 tptp.tc_Complex_Ocomplex)) (not (= tptp.c_Complex_Oii _let_13)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) 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(tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_N) (tptp.hAPP _let_1 V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_n $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.c_Suc V_n) V_p tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_n V_p tptp.tc_nat))) V_y)) (not (tptp.c_lessequals V_p V_n tptp.tc_nat))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_n))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n))) (= (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 _let_2) tptp.tc_nat) (tptp.hAPP tptp.c_Suc _let_31)) (= (tptp.c_Int_Onumber__class_Onumber__of _let_2 tptp.tc_nat) _let_30) (forall ((V_mul $$unsorted) (V_x $$unsorted) (V_pwr $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP V_mul V_x) V_x) (tptp.hAPP (tptp.hAPP V_pwr V_x) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_m))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus _let_1 V_n tptp.tc_nat))) (or (= (tptp.c_Fact_Ofact__class_Ofact _let_2 tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_2) (tptp.c_Fact_Ofact__class_Ofact (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless V_n _let_1 tptp.tc_nat)))))) (forall ((V_d $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_d))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_FFT__Mirabelle_Oroot (tptp.hAPP _let_2 V_n))) (tptp.hAPP _let_2 V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_FFT__Mirabelle_Oroot V_n)) V_k)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_d tptp.tc_nat)))))) (forall ((V_n $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_FFT__Mirabelle_Oroot (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n))) V_n) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_y tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_y tptp.tc_Int_Oint)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Int_OBit1 tptp.c_Int_OPls) tptp.tc_Int_Oint) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_Onumber__class_Onumber__of V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_Onumber__class_Onumber__of V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Int_OBit1 tptp.c_Int_OPls) tptp.tc_Int_Oint)))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_z) V_z)))) (forall ((T_a $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) T_a)) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_z) V_z)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) T_a))))) (= _let_31 _let_4) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_m)) _let_1 tptp.tc_nat) (tptp.c_Divides_Odiv__class_Omod V_m _let_1 tptp.tc_nat)))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_n)))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n) (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_n)))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc V_m)) _let_1 tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.c_Divides_Odiv__class_Odiv V_m _let_1 tptp.tc_nat))))) (= _let_4 _let_31) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oabs__class_Oabs V_a T_a)) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) _let_1)))) (tptp.c_HOL_Oord__class_Oless _let_29 _let_4 tptp.tc_nat) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_z) V_z))) (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_z) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_z) V_z))) (forall ((V_x $$unsorted)) (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_x) tptp.tc_nat)) (forall ((V_A $$unsorted)) (tptp.c_Fun_Oinj__on (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_A tptp.tc_nat tptp.tc_nat)) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_mul $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_n))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n)) (tptp.hAPP (tptp.hAPP V_mul _let_2) _let_2)) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (= (tptp.c_FFT__Mirabelle_Oroot (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 _let_3) tptp.tc_nat)) tptp.c_Complex_Oii) (forall ((T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_r T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_r (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) T_a) T_a) T_a))))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_r (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_r T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) T_a) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n (tptp.hAPP tptp.c_Suc _let_1)) (= V_n _let_1) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat) tptp.tc_nat))))) (forall ((V_pwr $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_mul $$unsorted) (V_add $$unsorted) (V_r0 $$unsorted) (V_r1 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_pwr V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_n))) (or (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n))) (tptp.hAPP (tptp.hAPP V_mul V_x) (tptp.hAPP (tptp.hAPP V_mul _let_2) _let_2))) (not (tptp.c_Groebner__Basis_Ogb__semiring V_add V_mul V_pwr V_r0 V_r1 T_a)))))) (forall ((V_x $$unsorted)) (not (tptp.c_Parity_Oeven__odd__class_Oeven (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_x)) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_Int_Onumber__class_Onumber__of _let_1 tptp.tc_nat))) (let ((_let_4 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_5 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_5 V_x) V_y)) _let_3) (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_4 V_x) _let_3)) (tptp.hAPP (tptp.hAPP _let_4 V_y) _let_3))) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Int_Onumber__class_Onumber__of _let_1 T_a)) V_x)) V_y)))))))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n)) _let_1)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 _let_1) tptp.tc_nat)) V_n))) (or (= (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus _let_2 (tptp.c_Int_Onumber__class_Onumber__of _let_1 tptp.tc_nat) tptp.tc_nat))) _let_2) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_1) V_n))) (or (= (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ominus__class_Ominus _let_2 _let_1 tptp.tc_nat))) _let_2) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((V_A $$unsorted)) (tptp.c_Fun_Oinj__on (tptp.c_COMBB tptp.c_Suc (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_A tptp.tc_nat tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_Int_Onumber__class_Onumber__of _let_1 tptp.tc_nat))) (let ((_let_4 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a)) _let_3) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_4 V_x) _let_3)) (tptp.hAPP (tptp.hAPP _let_4 V_y) _let_3)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Int_Onumber__class_Onumber__of _let_1 T_a)) V_x)) V_y) T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n))) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n)) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OMin T_a))) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n))) _let_1)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n))) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_1) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_n)) _let_1))))))) _let_28 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_3 (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_1) V_n))) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_n)) _let_1)))))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 tptp.c_Int_OPls) T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 tptp.c_Int_OPls) T_a) T_a) V_x))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (or (not (= (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit0 V_l))) (= V_k V_l))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat)) (forall ((V_k $$unsorted)) (or (not (= (tptp.c_Int_OBit0 V_k) tptp.c_Int_OPls)) (= V_k tptp.c_Int_OPls))) (forall ((V_k $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) tptp.c_Int_OPls))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)) _let_1) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1) T_a)))))) (forall ((V_m $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_i))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex))) (let ((_let_4 (tptp.hAPP _let_1 (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)))) (= (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_FFT__Mirabelle_Oroot (tptp.hAPP _let_4 V_m))) (tptp.hAPP _let_2 (tptp.hAPP _let_4 V_j))) (tptp.hAPP (tptp.hAPP _let_3 (tptp.c_FFT__Mirabelle_Oroot V_m)) (tptp.hAPP _let_2 V_j)))))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_1))))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_l V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_l V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_l tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_l $$unsorted)) (not (= tptp.c_Int_OPls (tptp.c_Int_OBit1 V_l)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a) (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Suc V_nat) (tptp.hAPP tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.hAPP tptp.c_Suc V_x) (tptp.hAPP tptp.c_Suc V_y))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_n))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n))) (tptp.hAPP (tptp.hAPP _let_3 V_x) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_2)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.c_Suc V_m) (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_j $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_j V_n tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n V_n tptp.tc_nat))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Suc V_n)) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (= _let_27 tptp.c_Int_OPls) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_m V_n)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_q)) V_x) (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_n) (tptp.hAPP _let_1 V_N) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m)) V_n)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat) V_k tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus V_m (tptp.c_HOL_Ominus__class_Ominus V_n (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 tptp.c_Int_OPls) tptp.tc_nat) tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_Onumber__class_Onumber__of tptp.c_Int_OPls tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 tptp.c_Int_OPls) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b) T_a))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)))) (= tptp.c_Int_OPls _let_27) (tptp.c_HOL_Oord__class_Oless tptp.v_i____ (tptp.hAPP _let_5 (tptp.hAPP tptp.c_Suc tptp.v_ka____)) tptp.tc_nat) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (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 ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_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 ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_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 ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_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 ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_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 ((T_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 tptp.c_Int_OPls) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_q)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_q))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_m V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x) V_x))) (forall ((V_n $$unsorted)) (not (= (tptp.hAPP tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.hAPP tptp.c_Suc V_n)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) (tptp.c_HOL_Oinverse__class_Odivide V_z V_w T_a)) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_w) T_a))))) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat)) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.hAPP tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_i) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) V_n) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n) T_a))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_FFT__Mirabelle_Oroot V_n)) V_n) (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_lx) V_ly)))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_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))) (or (not (tptp.class_Ring__and__Field_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 ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_ry))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 tptp.c_Int_OPls) T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 tptp.c_Int_OPls) T_a)) V_a))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of V_v T_a)))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_c T_a)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c) T_a))))) (forall ((V_l $$unsorted)) (or (not (= tptp.c_Int_OPls (tptp.c_Int_OBit0 V_l))) (= tptp.c_Int_OPls V_l))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a)) V_n)))))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (or (not (= (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit1 V_l))) (= V_k V_l))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_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_HOL_Otimes__class_Otimes tptp.tc_nat) V_p) V_q))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_n)) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_q)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_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 ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_a)) V_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Oring__char__0 T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_Int_Onumber__class_Onumber__of V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_xa))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_b_H T_a)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_b_H) T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) V_k) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (= (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_m V_n tptp.tc_nat)) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_a V_a_H T_a)) V_b) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a)) V_ya) (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ya) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_ya) T_a))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_j tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ominus__class_Ominus V_i V_k tptp.tc_nat) V_j tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_n))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_Int_Onumber__class_Onumber__of (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)) tptp.tc_nat)) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) _let_2)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_m))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= _let_1 V_n) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_l $$unsorted)) (not (= (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit1 V_l)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a)) V_z) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z) V_y T_a))))) (not (tptp.c_HOL_Oord__class_Oless tptp.v_i____ _let_6 tptp.tc_nat)) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_m) V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_m) (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_m) (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_x) (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_n tptp.tc_nat)))) (tptp.c_HOL_Oord__class_Oless tptp.v_i____ _let_12 tptp.tc_nat) _let_26 _let_25 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oboolean__algebra (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Oboolean__algebra T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Divides_Osemiring__div tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_Int_Onumber tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add__abs tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add__abs tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__ring__strict tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__ring__abs tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__ring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Olordered__ring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oabs__if tptp.tc_Int_Oint) (tptp.class_Divides_Osemiring__div tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oidom tptp.tc_Int_Oint) (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint) (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint) (tptp.class_Divides_Oring__div tptp.tc_Int_Oint) (tptp.class_Orderings_Oorder tptp.tc_Int_Oint) (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint) (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint) (tptp.class_Power_Opower tptp.tc_Int_Oint) (tptp.class_Int_Onumber tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Complex_Ocomplex) _let_1 (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__field tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ofield tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oidom tptp.tc_Complex_Ocomplex) (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex) (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber tptp.tc_Complex_Ocomplex) (forall ((V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted)) (= (tptp.c_COMBC V_P V_Q V_R T_b T_c T_a) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBB V_P V_Q T_b T_a T_c) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.67/1.87  )
% 1.69/1.88  % SZS output end Proof for SWV716-1
% 1.69/1.88  % cvc5---1.0.5 exiting
% 1.69/1.89  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------