TSTP Solution File: SWV621-1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 21:52:43 EDT 2023
% Result : Unsatisfiable 3.54s 3.74s
% Output : Proof 3.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.22 % Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.23 % Command : do_cvc5 %s %d
% 0.23/0.43 % Computer : n024.cluster.edu
% 0.23/0.43 % Model : x86_64 x86_64
% 0.23/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.43 % Memory : 8042.1875MB
% 0.23/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.23/0.43 % CPULimit : 300
% 0.23/0.43 % WCLimit : 300
% 0.23/0.43 % DateTime : Tue Aug 29 03:55:08 EDT 2023
% 0.23/0.44 % CPUTime :
% 0.30/0.67 %----Proving TF0_NAR, FOF, or CNF
% 0.46/0.67 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.OHzor8L5Qh/cvc5---1.0.5_8324.p...
% 0.54/0.84 ------- get file name : TPTP file name is SWV621-1
% 0.54/0.85 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8324.smt2...
% 0.54/0.85 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.54/3.74 % SZS status Unsatisfiable for SWV621-1
% 3.54/3.74 % SZS output start Proof for SWV621-1
% 3.65/3.81 (
% 3.65/3.81 (let ((_let_1 (tptp.class_SEQ_Obanach tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex))) (let ((_let_3 (tptp.class_Ring__and__Field_Ofield tptp.tc_Complex_Ocomplex))) (let ((_let_4 (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Complex_Ocomplex))) (let ((_let_5 (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Complex_Ocomplex))) (let ((_let_6 (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Complex_Ocomplex))) (let ((_let_7 (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Complex_Ocomplex))) (let ((_let_8 (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex))) (let ((_let_9 (tptp.class_Ring__and__Field_Odivision__ring tptp.tc_Complex_Ocomplex))) (let ((_let_10 (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Complex_Ocomplex))) (let ((_let_11 (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex))) (let ((_let_12 (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_Complex_Ocomplex))) (let ((_let_13 (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex))) (let ((_let_14 (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (let ((_let_15 (tptp.c_FFT__Mirabelle_Oroot tptp.v_n))) (let ((_let_16 (tptp.c_HOL_Oinverse__class_Odivide _let_14 _let_15 tptp.tc_Complex_Ocomplex))) (let ((_let_17 (tptp.c_Power_Opower__class_Opower _let_16 tptp.tc_Complex_Ocomplex))) (let ((_let_18 (tptp.hAPP _let_17 tptp.v_k))) (let ((_let_19 (tptp.c_HOL_Ominus__class_Ominus _let_18 _let_14 tptp.tc_Complex_Ocomplex))) (let ((_let_20 (tptp.c_Power_Opower__class_Opower _let_18 tptp.tc_Complex_Ocomplex))) (let ((_let_21 (tptp.hAPP _let_20 tptp.v_n))) (let ((_let_22 (tptp.c_HOL_Ominus__class_Ominus _let_21 _let_14 tptp.tc_Complex_Ocomplex))) (let ((_let_23 (tptp.c_HOL_Oinverse__class_Odivide _let_22 _let_19 tptp.tc_Complex_Ocomplex))) (let ((_let_24 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_25 (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_24 tptp.v_n tptp.tc_nat))) (let ((_let_26 (tptp.c_Finite__Set_Osetsum _let_20 _let_25 tptp.tc_nat tptp.tc_Complex_Ocomplex))) (let ((_let_27 (= _let_26 _let_23))) (let ((_let_28 (not _let_27))) (let ((_let_29 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower V_x T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Finite__Set_Osetsum _let_2 (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_n) _let_1 T_a) (tptp.c_HOL_Ominus__class_Ominus V_x _let_1 T_a) T_a)) (= V_x _let_1))))))) (let ((_let_30 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (let ((_let_31 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_FFT__Mirabelle_Oroot V_n) tptp.tc_Complex_Ocomplex) V_n) (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))))) (let ((_let_32 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) V_n) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n) T_a)))))) (let ((_let_33 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Oone__class_Oone T_a)))))) (let ((_let_34 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))))) (let ((_let_35 (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) V_n) _let_1)))))) (let ((_let_36 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Oone__class_Oone T_a)))))) (let ((_let_37 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) V_n) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (let ((_let_38 (forall ((V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.c_Finite__Set_Osetsum (tptp.c_Power_Opower__class_Opower (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_FFT__Mirabelle_Oroot V_n) tptp.tc_Complex_Ocomplex) V_k) tptp.tc_Complex_Ocomplex) (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_n tptp.tc_nat) tptp.tc_nat tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_k tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 tptp.tc_nat) V_k)))))))) (let ((_let_39 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (let ((_let_40 (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.v_k tptp.tc_nat) tptp.v_n)))) (let ((_let_41 (tptp.c_HOL_Oord__class_Oless _let_24 tptp.tc_nat))) (let ((_let_42 (tptp.hBOOL (tptp.hAPP _let_41 tptp.v_k)))) (let ((_let_43 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))))) (let ((_let_44 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_Transcendental_Oexp (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Transcendental_Oexp V_x T_a) (tptp.c_Transcendental_Oexp V_y T_a) T_a)))))) (let ((_let_45 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))))) (let ((_let_46 (tptp.c_Suc _let_24))) (let ((_let_47 (forall ((T_a $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_Transcendental_Oexp (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))))) (let ((_let_48 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))) (let ((_let_49 (forall ((V_n $$unsorted)) (not (= (tptp.c_FFT__Mirabelle_Oroot V_n) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (let ((_let_50 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) V_y T_a)))))) (let ((_let_51 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_a T_a)))))) (let ((_let_52 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_n)))))) (let ((_let_53 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))))))) (let ((_let_54 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat)) (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.hAPP _let_1 V_m) T_a) V_n))))))) (let ((_let_55 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))))) (let ((_let_56 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))))) (let ((_let_57 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))))) (let ((_let_58 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))))) (let ((_let_59 (tptp.c_Suc tptp.v_n))) (let ((_let_60 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))))) (let ((_let_61 (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))))) (let ((_let_62 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))))) (let ((_let_63 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a))))) (let ((_let_64 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP _let_1 V_n) V_a T_a))))))) (let ((_let_65 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_x T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.c_Suc V_q)) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.hAPP _let_1 V_q) T_a))))))) (let ((_let_66 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat))))) (let ((_let_67 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))))) (let ((_let_68 (tptp.c_Power_Opower__class_Opower _let_15 tptp.tc_Complex_Ocomplex))) (let ((_let_69 (tptp.hAPP _let_68 tptp.v_n))) (let ((_let_70 (= _let_14 _let_69))) (let ((_let_71 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_72 (tptp.c_HOL_Ouminus__class_Ouminus _let_71 tptp.tc_Complex_Ocomplex))) (let ((_let_73 (= _let_71 _let_72))) (let ((_let_74 (tptp.c_HOL_Oinverse__class_Oinverse _let_71 tptp.tc_Complex_Ocomplex))) (let ((_let_75 (= _let_71 _let_74))) (let ((_let_76 (tptp.c_HOL_Oinverse__class_Oinverse _let_14 tptp.tc_Complex_Ocomplex))) (let ((_let_77 (= _let_14 _let_76))) (let ((_let_78 (tptp.c_HOL_Otimes__class_Otimes tptp.v_k tptp.v_n tptp.tc_nat))) (let ((_let_79 (= _let_21 (tptp.hAPP _let_17 _let_78)))) (let ((_let_80 (= (tptp.c_HOL_Otimes__class_Otimes _let_16 _let_18 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes _let_18 _let_16 tptp.tc_Complex_Ocomplex)))) (let ((_let_81 (= (tptp.c_HOL_Otimes__class_Otimes _let_18 _let_21 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes _let_21 _let_18 tptp.tc_Complex_Ocomplex)))) (let ((_let_82 (tptp.c_HOL_Oinverse__class_Oinverse _let_15 tptp.tc_Complex_Ocomplex))) (let ((_let_83 (= _let_16 _let_82))) (let ((_let_84 (tptp.c_Transcendental_Oexp _let_71 tptp.tc_Complex_Ocomplex))) (let ((_let_85 (= _let_14 _let_84))) (let ((_let_86 (= _let_16 (tptp.c_HOL_Otimes__class_Otimes _let_14 _let_82 tptp.tc_Complex_Ocomplex)))) (let ((_let_87 (tptp.c_HOL_Oinverse__class_Oinverse _let_19 tptp.tc_Complex_Ocomplex))) (let ((_let_88 (tptp.c_HOL_Otimes__class_Otimes _let_22 _let_87 tptp.tc_Complex_Ocomplex))) (let ((_let_89 (= _let_23 _let_88))) (let ((_let_90 (= _let_71 (tptp.c_Finite__Set_Osetsum (tptp.c_Power_Opower__class_Opower (tptp.hAPP _let_68 tptp.v_k) tptp.tc_Complex_Ocomplex) _let_25 tptp.tc_nat tptp.tc_Complex_Ocomplex)))) (let ((_let_91 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_71 tptp.tc_Complex_Ocomplex) _let_24))) (let ((_let_92 (= _let_14 _let_91))) (let ((_let_93 (tptp.c_HOL_Oinverse__class_Odivide _let_71 _let_71 tptp.tc_Complex_Ocomplex))) (let ((_let_94 (= _let_71 _let_93))) (let ((_let_95 (tptp.hAPP _let_17 _let_24))) (let ((_let_96 (= _let_14 _let_95))) (let ((_let_97 (= _let_14 _let_18))) (let ((_let_98 (tptp.c_HOL_Otimes__class_Otimes tptp.v_n tptp.v_k tptp.tc_nat))) (let ((_let_99 (= _let_78 _let_98))) (let ((_let_100 (tptp.c_Power_Opower__class_Opower _let_14 tptp.tc_Complex_Ocomplex))) (let ((_let_101 (tptp.hAPP _let_100 _let_59))) (let ((_let_102 (= _let_101 (tptp.c_HOL_Otimes__class_Otimes _let_14 (tptp.hAPP _let_100 tptp.v_n) tptp.tc_Complex_Ocomplex)))) (let ((_let_103 (tptp.hAPP _let_17 _let_46))) (let ((_let_104 (= _let_103 (tptp.c_HOL_Otimes__class_Otimes _let_16 _let_95 tptp.tc_Complex_Ocomplex)))) (let ((_let_105 (tptp.hAPP _let_20 _let_78))) (let ((_let_106 (tptp.c_Suc _let_78))) (let ((_let_107 (= (tptp.hAPP _let_20 _let_106) (tptp.c_HOL_Otimes__class_Otimes _let_105 _let_18 tptp.tc_Complex_Ocomplex)))) (let ((_let_108 (= (tptp.c_HOL_Otimes__class_Otimes _let_88 _let_19 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes _let_22 (tptp.c_HOL_Otimes__class_Otimes _let_87 _let_19 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_109 (tptp.c_HOL_Ominus__class_Ominus _let_71 _let_71 tptp.tc_Complex_Ocomplex))) (let ((_let_110 (= _let_72 _let_109))) (let ((_let_111 (= _let_93 (tptp.c_HOL_Otimes__class_Otimes _let_71 _let_74 tptp.tc_Complex_Ocomplex)))) (let ((_let_112 (= (tptp.c_Transcendental_Oexp _let_109 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Odivide _let_84 _let_84 tptp.tc_Complex_Ocomplex)))) (let ((_let_113 (= _let_74 (tptp.c_HOL_Oinverse__class_Odivide _let_14 _let_71 tptp.tc_Complex_Ocomplex)))) (let ((_let_114 (= _let_87 (tptp.c_HOL_Oinverse__class_Odivide _let_14 _let_19 tptp.tc_Complex_Ocomplex)))) (let ((_let_115 (tptp.hAPP _let_68 _let_46))) (let ((_let_116 (tptp.hAPP _let_100 _let_46))) (let ((_let_117 (= _let_103 (tptp.c_HOL_Oinverse__class_Odivide _let_116 _let_115 tptp.tc_Complex_Ocomplex)))) (let ((_let_118 (= _let_14 _let_101))) (let ((_let_119 (= _let_14 _let_116))) (let ((_let_120 (= _let_71 (tptp.c_HOL_Ominus__class_Ominus _let_14 _let_14 tptp.tc_Complex_Ocomplex)))) (let ((_let_121 (tptp.c_HOL_Otimes__class_Otimes _let_14 _let_15 tptp.tc_Complex_Ocomplex))) (let ((_let_122 (= _let_121 (tptp.c_HOL_Otimes__class_Otimes _let_15 _let_14 tptp.tc_Complex_Ocomplex)))) (let ((_let_123 (tptp.c_HOL_Oinverse__class_Oinverse _let_21 tptp.tc_Complex_Ocomplex))) (let ((_let_124 (tptp.c_HOL_Otimes__class_Otimes _let_123 _let_16 tptp.tc_Complex_Ocomplex))) (let ((_let_125 (= _let_124 (tptp.c_HOL_Otimes__class_Otimes _let_16 _let_123 tptp.tc_Complex_Ocomplex)))) (let ((_let_126 (= _let_15 (tptp.c_HOL_Oinverse__class_Oinverse _let_82 tptp.tc_Complex_Ocomplex)))) (let ((_let_127 (= _let_71 (tptp.c_HOL_Otimes__class_Otimes _let_23 _let_71 tptp.tc_Complex_Ocomplex)))) (let ((_let_128 (= _let_21 (tptp.c_HOL_Otimes__class_Otimes _let_21 _let_14 tptp.tc_Complex_Ocomplex)))) (let ((_let_129 (= _let_105 (tptp.c_HOL_Otimes__class_Otimes _let_105 _let_14 tptp.tc_Complex_Ocomplex)))) (let ((_let_130 (= _let_15 _let_121))) (let ((_let_131 (= (tptp.hAPP _let_17 _let_98) (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.hAPP _let_17 tptp.v_n) tptp.tc_Complex_Ocomplex) tptp.v_k)))) (let ((_let_132 (= (tptp.hAPP _let_20 _let_98) (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_21 tptp.tc_Complex_Ocomplex) tptp.v_k)))) (let ((_let_133 (= (tptp.c_HOL_Oinverse__class_Oinverse _let_69 tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_82 tptp.tc_Complex_Ocomplex) tptp.v_n)))) (let ((_let_134 (tptp.c_HOL_Oinverse__class_Odivide _let_18 _let_16 tptp.tc_Complex_Ocomplex))) (let ((_let_135 (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Odivide _let_16 _let_18 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) _let_134))) (let ((_let_136 (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide _let_123 _let_76 tptp.tc_Complex_Ocomplex) _let_16 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Odivide _let_124 _let_76 tptp.tc_Complex_Ocomplex)))) (let ((_let_137 (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_134 tptp.tc_Complex_Ocomplex) tptp.v_k) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP _let_20 tptp.v_k) _let_18 tptp.tc_Complex_Ocomplex)))) (let ((_let_138 (ASSUME :args (_let_28)))) (let ((_let_139 (_let_31))) (let ((_let_140 (ASSUME :args _let_139))) (let ((_let_141 (not _let_4))) (let ((_let_142 (or _let_141 _let_73))) (let ((_let_143 (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))))))) (let ((_let_144 (EQ_RESOLVE (ASSUME :args (_let_62)) (MACRO_SR_EQ_INTRO :args (_let_62 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_145 (ASSUME :args (_let_4)))) (let ((_let_146 (not _let_12))) (let ((_let_147 (or _let_146 _let_75))) (let ((_let_148 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a))))))) (let ((_let_149 (EQ_RESOLVE (ASSUME :args (_let_60)) (MACRO_SR_EQ_INTRO :args (_let_60 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_150 (ASSUME :args (_let_12)))) (let ((_let_151 (not _let_9))) (let ((_let_152 (or _let_151 _let_77))) (let ((_let_153 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a))))))) (let ((_let_154 (EQ_RESOLVE (ASSUME :args (_let_58)) (MACRO_SR_EQ_INTRO :args (_let_58 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_155 (ASSUME :args (_let_9)))) (let ((_let_156 (not _let_5))) (let ((_let_157 (or _let_156 _let_79))) (let ((_let_158 (_let_54))) (let ((_let_159 (ASSUME :args _let_158))) (let ((_let_160 (tptp.c_Power_Opower__class_Opower V_a T_a))) (let ((_let_161 ((tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.hAPP _let_160 V_m) T_a) V_n)))) (let ((_let_162 (ASSUME :args (_let_5)))) (let ((_let_163 (or _let_156 _let_80))) (let ((_let_164 (_let_53))) (let ((_let_165 (ASSUME :args _let_164))) (let ((_let_166 ((tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n)))) (let ((_let_167 (or _let_156 _let_81))) (let ((_let_168 (= _let_71 _let_15))) (let ((_let_169 (not _let_3))) (let ((_let_170 (or _let_169 _let_83 _let_168))) (let ((_let_171 (_let_39))) (let ((_let_172 (ASSUME :args _let_171))) (let ((_let_173 (_let_49))) (let ((_let_174 (ASSUME :args _let_173))) (let ((_let_175 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_174 :args (tptp.v_n QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_FFT__Mirabelle_Oroot V_n)))) :args _let_173))) _let_174 :args ((not _let_168) false _let_49)))) (let ((_let_176 (ASSUME :args (_let_3)))) (let ((_let_177 (not _let_8))) (let ((_let_178 (not _let_1))) (let ((_let_179 (or _let_178 _let_177 _let_85))) (let ((_let_180 (_let_47))) (let ((_let_181 (ASSUME :args _let_180))) (let ((_let_182 (ASSUME :args (_let_1)))) (let ((_let_183 (ASSUME :args (_let_8)))) (let ((_let_184 (or _let_169 _let_86))) (let ((_let_185 (_let_45))) (let ((_let_186 (ASSUME :args _let_185))) (let ((_let_187 ((tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))) (let ((_let_188 (or _let_169 _let_89))) (let ((_let_189 (not _let_42))) (let ((_let_190 (not _let_40))) (let ((_let_191 (or _let_90 _let_190 _let_189))) (let ((_let_192 (forall ((V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Finite__Set_Osetsum (tptp.c_Power_Opower__class_Opower (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_FFT__Mirabelle_Oroot V_n) tptp.tc_Complex_Ocomplex) V_k) tptp.tc_Complex_Ocomplex) (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_n tptp.tc_nat) tptp.tc_nat tptp.tc_Complex_Ocomplex)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_k tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 tptp.tc_nat) V_k)))))))) (let ((_let_193 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_194 (not _let_2))) (let ((_let_195 (not _let_7))) (let ((_let_196 (or _let_195 _let_194 _let_92))) (let ((_let_197 (_let_36))) (let ((_let_198 (ASSUME :args _let_197))) (let ((_let_199 (or _let_169 _let_146 _let_94))) (let ((_let_200 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a))))))) (let ((_let_201 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_202 (not _let_11))) (let ((_let_203 (or _let_202 _let_96))) (let ((_let_204 (_let_33))) (let ((_let_205 (ASSUME :args _let_204))) (let ((_let_206 (ASSUME :args (_let_11)))) (let ((_let_207 (or _let_169 _let_27 _let_97))) (let ((_let_208 (_let_29))) (let ((_let_209 (ASSUME :args _let_208))) (let ((_let_210 (_let_66))) (let ((_let_211 (ASSUME :args _let_210))) (let ((_let_212 (or _let_202 _let_102))) (let ((_let_213 (_let_65))) (let ((_let_214 (ASSUME :args _let_213))) (let ((_let_215 ((tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_Suc V_q))))) (let ((_let_216 (or _let_202 _let_104))) (let ((_let_217 (or _let_156 _let_107))) (let ((_let_218 (_let_64))) (let ((_let_219 (ASSUME :args _let_218))) (let ((_let_220 (not _let_10))) (let ((_let_221 (or _let_220 _let_108))) (let ((_let_222 (_let_55))) (let ((_let_223 (ASSUME :args _let_222))) (let ((_let_224 (or _let_141 _let_110))) (let ((_let_225 (_let_48))) (let ((_let_226 (ASSUME :args _let_225))) (let ((_let_227 (or _let_169 _let_111))) (let ((_let_228 (or _let_178 _let_177 _let_112))) (let ((_let_229 (_let_44))) (let ((_let_230 (ASSUME :args _let_229))) (let ((_let_231 (or _let_169 _let_113))) (let ((_let_232 (_let_43))) (let ((_let_233 (ASSUME :args _let_232))) (let ((_let_234 ((tptp.c_HOL_Oinverse__class_Oinverse V_a T_a)))) (let ((_let_235 (or _let_169 _let_114))) (let ((_let_236 (or _let_169 _let_117 _let_168))) (let ((_let_237 (_let_37))) (let ((_let_238 (ASSUME :args _let_237))) (let ((_let_239 (or _let_156 _let_118))) (let ((_let_240 (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) V_n))))))) (let ((_let_241 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_242 (_let_240))) (let ((_let_243 ((tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_n)))) (let ((_let_244 (or _let_156 _let_119))) (let ((_let_245 (not _let_6))) (let ((_let_246 (or _let_245 _let_120))) (let ((_let_247 (_let_30))) (let ((_let_248 (ASSUME :args _let_247))) (let ((_let_249 (or _let_202 _let_122))) (let ((_let_250 (_let_67))) (let ((_let_251 (ASSUME :args _let_250))) (let ((_let_252 ((tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (let ((_let_253 (or _let_202 _let_125))) (let ((_let_254 (or _let_151 _let_146 _let_126))) (let ((_let_255 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)))))) (let ((_let_256 (EQ_RESOLVE (ASSUME :args (_let_63)) (MACRO_SR_EQ_INTRO :args (_let_63 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_257 (not _let_13))) (let ((_let_258 (or _let_257 _let_127))) (let ((_let_259 (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))))))) (let ((_let_260 (EQ_RESOLVE (ASSUME :args (_let_61)) (MACRO_SR_EQ_INTRO :args (_let_61 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_261 (or _let_156 _let_128))) (let ((_let_262 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= V_a (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)))))) (let ((_let_263 (EQ_RESOLVE (ASSUME :args (_let_57)) (MACRO_SR_EQ_INTRO :args (_let_57 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_264 (_let_262))) (let ((_let_265 ((tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)))) (let ((_let_266 (or _let_156 _let_129))) (let ((_let_267 (or _let_156 _let_130))) (let ((_let_268 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= V_a (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))))) (let ((_let_269 (EQ_RESOLVE (ASSUME :args (_let_56)) (MACRO_SR_EQ_INTRO :args (_let_56 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_270 (or _let_156 _let_131))) (let ((_let_271 (or _let_156 _let_132))) (let ((_let_272 (or _let_151 _let_146 _let_133))) (let ((_let_273 (_let_52))) (let ((_let_274 (ASSUME :args _let_273))) (let ((_let_275 (or _let_169 _let_146 _let_135))) (let ((_let_276 (_let_51))) (let ((_let_277 (ASSUME :args _let_276))) (let ((_let_278 (or _let_169 _let_146 _let_136))) (let ((_let_279 (_let_50))) (let ((_let_280 (ASSUME :args _let_279))) (let ((_let_281 (or _let_169 _let_146 _let_137))) (let ((_let_282 (_let_32))) (let ((_let_283 (ASSUME :args _let_282))) (let ((_let_284 (= _let_71 _let_88))) (let ((_let_285 (= _let_71 _let_26))) (let ((_let_286 (ASSUME :args (_let_73)))) (let ((_let_287 (SYMM _let_286))) (let ((_let_288 (SYMM _let_287))) (let ((_let_289 (ASSUME :args (_let_89)))) (let ((_let_290 (SYMM (SYMM _let_289)))) (let ((_let_291 (APPLY_UF tptp.c_HOL_Otimes__class_Otimes))) (let ((_let_292 (REFL :args (tptp.tc_Complex_Ocomplex)))) (let ((_let_293 (ASSUME :args (_let_114)))) (let ((_let_294 (APPLY_UF tptp.c_HOL_Oinverse__class_Odivide))) (let ((_let_295 (REFL :args (_let_19)))) (let ((_let_296 (ASSUME :args (_let_97)))) (let ((_let_297 (SYMM _let_296))) (let ((_let_298 (SYMM _let_297))) (let ((_let_299 (CONG (SYMM _let_298) _let_295 _let_292 :args _let_294))) (let ((_let_300 (CONG _let_298 (REFL :args (_let_14)) _let_292 :args (APPLY_UF tptp.c_HOL_Ominus__class_Ominus)))) (let ((_let_301 (ASSUME :args (_let_120)))) (let ((_let_302 (SYMM _let_301))) (let ((_let_303 (SYMM _let_302))) (let ((_let_304 (TRANS _let_303 _let_300))) (let ((_let_305 (CONG _let_298 _let_304 _let_292 :args _let_294))) (let ((_let_306 (ASSUME :args (_let_113)))) (let ((_let_307 (SYMM _let_306))) (let ((_let_308 (ASSUME :args (_let_75)))) (let ((_let_309 (SYMM _let_308))) (let ((_let_310 (SYMM _let_309))) (let ((_let_311 (ASSUME :args (_let_94)))) (let ((_let_312 (ASSUME :args (_let_111)))) (let ((_let_313 (SYMM _let_304))) (let ((_let_314 (ASSUME :args (_let_108)))) (let ((_let_315 (ASSUME :args (_let_127)))) (let ((_let_316 (APPLY_UF tptp.c_Finite__Set_Osetsum))) (let ((_let_317 (REFL :args (tptp.tc_nat)))) (let ((_let_318 (REFL :args (_let_25)))) (let ((_let_319 (APPLY_UF tptp.c_Power_Opower__class_Opower))) (let ((_let_320 (ASSUME :args (_let_118)))) (let ((_let_321 (SYMM _let_320))) (let ((_let_322 (ASSUME :args (_let_102)))) (let ((_let_323 (SYMM _let_322))) (let ((_let_324 (APPLY_UF tptp.hAPP))) (let ((_let_325 (REFL :args (tptp.v_n)))) (let ((_let_326 (CONG _let_297 _let_292 :args _let_319))) (let ((_let_327 (CONG _let_326 _let_325 :args _let_324))) (let ((_let_328 (CONG _let_297 _let_327 _let_292 :args _let_291))) (let ((_let_329 (ASSUME :args (_let_81)))) (let ((_let_330 (SYMM _let_329))) (let ((_let_331 (CONG (REFL :args (_let_21)) _let_298 _let_292 :args _let_291))) (let ((_let_332 (ASSUME :args (_let_128)))) (let ((_let_333 (SYMM (SYMM _let_332)))) (let ((_let_334 (TRANS _let_333 _let_331 _let_330 _let_328 _let_323 _let_321))) (let ((_let_335 (CONG (TRANS _let_334 _let_298) _let_292 :args _let_319))) (let ((_let_336 (ASSUME :args (_let_79)))) (let ((_let_337 (SYMM _let_336))) (let ((_let_338 (TRANS (CONG _let_337 _let_292 :args _let_319) _let_335))) (let ((_let_339 (ASSUME :args (_let_85)))) (let ((_let_340 (ASSUME :args (_let_110)))) (let ((_let_341 (CONG (TRANS (SYMM _let_340) _let_287) _let_292 :args (APPLY_UF tptp.c_Transcendental_Oexp)))) (let ((_let_342 (ASSUME :args (_let_112)))) (let ((_let_343 (ASSUME :args (_let_92)))) (let ((_let_344 (SYMM _let_343))) (let ((_let_345 (ASSUME :args (_let_96)))) (let ((_let_346 (SYMM _let_345))) (let ((_let_347 (CONG (TRANS _let_346 _let_339) (TRANS _let_344 _let_339) _let_292 :args _let_294))) (let ((_let_348 (ASSUME :args (_let_99)))) (let ((_let_349 (ASSUME :args (_let_131)))) (let ((_let_350 (REFL :args (tptp.v_k)))) (let ((_let_351 (ASSUME :args (_let_86)))) (let ((_let_352 (SYMM _let_351))) (let ((_let_353 (ASSUME :args (_let_83)))) (let ((_let_354 (SYMM _let_353))) (let ((_let_355 (CONG _let_297 (SYMM _let_354) _let_292 :args _let_291))) (let ((_let_356 (ASSUME :args (_let_80)))) (let ((_let_357 (SYMM (SYMM _let_356)))) (let ((_let_358 (TRANS _let_357 _let_355 _let_352))) (let ((_let_359 (SYMM _let_358))) (let ((_let_360 (ASSUME :args (_let_133)))) (let ((_let_361 (APPLY_UF tptp.c_HOL_Oinverse__class_Oinverse))) (let ((_let_362 (ASSUME :args (_let_70)))) (let ((_let_363 (CONG _let_298 _let_292 :args _let_361))) (let ((_let_364 (ASSUME :args (_let_77)))) (let ((_let_365 (SYMM _let_364))) (let ((_let_366 (SYMM _let_365))) (let ((_let_367 (ASSUME :args (_let_132)))) (let ((_let_368 (SYMM _let_326))) (let ((_let_369 (CONG _let_368 (REFL :args (_let_78)) :args _let_324))) (let ((_let_370 (TRANS _let_369 (CONG (REFL :args (_let_20)) _let_348 :args _let_324) (SYMM (SYMM _let_367)) (CONG _let_335 _let_350 :args _let_324)))) (let ((_let_371 (ASSUME :args (_let_129)))) (let ((_let_372 (ASSUME :args (_let_107)))) (let ((_let_373 (SYMM _let_372))) (let ((_let_374 (CONG _let_368 (REFL :args (_let_106)) :args _let_324))) (let ((_let_375 (TRANS _let_374 (SYMM _let_373) (CONG (REFL :args (_let_105)) _let_297 _let_292 :args _let_291) (SYMM _let_371) (SYMM _let_369)))) (let ((_let_376 (TRANS _let_373 (SYMM _let_374)))) (let ((_let_377 (REFL :args (_let_18)))) (let ((_let_378 (ASSUME :args (_let_137)))) (let ((_let_379 (REFL :args (_let_16)))) (let ((_let_380 (CONG _let_298 _let_379 _let_292 :args _let_294))) (let ((_let_381 (CONG _let_380 _let_292 :args _let_319))) (let ((_let_382 (ASSUME :args (_let_135)))) (let ((_let_383 (CONG _let_358 _let_377 _let_292 :args _let_291))) (let ((_let_384 (CONG (TRANS (SYMM _let_327) _let_334 _let_298) _let_292 :args _let_361))) (let ((_let_385 (CONG _let_327 _let_292 :args _let_361))) (let ((_let_386 (ASSUME :args (_let_125)))) (let ((_let_387 (ASSUME :args (_let_136)))) (let ((_let_388 (ASSUME :args (_let_104)))) (let ((_let_389 (ASSUME :args (_let_117)))) (let ((_let_390 (ASSUME :args (_let_119)))) (let ((_let_391 (TRANS (CONG (SYMM (SYMM _let_390)) (REFL :args (_let_115)) _let_292 :args _let_294) (SYMM _let_389) (SYMM (SYMM _let_388)) (CONG _let_359 (TRANS _let_346 _let_298) _let_292 :args _let_291) _let_383 _let_357 _let_355 _let_352))) (let ((_let_392 (SYMM _let_391))) (let ((_let_393 (CONG (TRANS _let_354 _let_392) _let_292 :args _let_361))) (let ((_let_394 (ASSUME :args (_let_126)))) (let ((_let_395 (SYMM _let_394))) (let ((_let_396 (SYMM _let_395))) (let ((_let_397 (ASSUME :args (_let_130)))) (let ((_let_398 (REFL :args (_let_15)))) (let ((_let_399 (CONG _let_297 _let_398 _let_292 :args _let_291))) (let ((_let_400 (SYMM _let_399))) (let ((_let_401 (ASSUME :args (_let_122)))) (let ((_let_402 (TRANS (CONG _let_398 _let_297 _let_292 :args _let_291) (SYMM _let_401) _let_400))) (let ((_let_403 (SYMM _let_402))) (let ((_let_404 (CONG _let_403 _let_292 :args _let_319))) (let ((_let_405 (CONG _let_392 _let_292 :args _let_361))) (let ((_let_406 (TRANS _let_396 _let_393 (SYMM _let_405)))) (let ((_let_407 (CONG (SYMM _let_406) _let_292 :args _let_319))) (let ((_let_408 (ASSUME :args (_let_90)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_286 (MODUS_PONENS (AND_INTRO _let_296 _let_320 _let_322 _let_329 _let_343 _let_332 _let_336 _let_339 _let_286 _let_340 _let_342 _let_345 _let_348 _let_349 _let_351 _let_353 _let_356 _let_360 _let_362 _let_364 _let_367 _let_371 _let_372 _let_378 _let_382 _let_386 _let_387 _let_388 _let_389 _let_390 _let_394 _let_397 _let_401 _let_408) (SCOPE (TRANS (SYMM (SYMM _let_408)) (CONG (TRANS (CONG (TRANS (TRANS (CONG (TRANS (SYMM _let_407) (TRANS _let_407 (CONG (TRANS _let_406 (TRANS _let_405 (SYMM _let_393) _let_395 _let_397 _let_400) _let_403) _let_292 :args _let_319) (SYMM _let_404)) (TRANS _let_404 (CONG (TRANS _let_402 (TRANS _let_399 (SYMM _let_397) _let_396 _let_393 (CONG (TRANS _let_391 (TRANS _let_351 (CONG (TRANS _let_339 (SYMM _let_341) _let_342 (SYMM _let_347) (CONG (TRANS _let_346 (TRANS _let_366 _let_363 (SYMM _let_384) (SYMM _let_385))) (REFL :args (_let_91)) _let_292 :args _let_294) (CONG (REFL :args (_let_123)) (TRANS _let_344 _let_366) _let_292 :args _let_294)) _let_354 _let_292 :args _let_291) (SYMM (SYMM _let_387)) (CONG (TRANS (SYMM (SYMM _let_386)) (CONG _let_359 (TRANS _let_385 _let_384 (SYMM _let_363) _let_365 _let_298) _let_292 :args _let_291) _let_383 _let_357 _let_355 _let_352) _let_365 _let_292 :args _let_294) (CONG _let_379 _let_298 _let_292 :args _let_294))) _let_292 :args _let_361) (SYMM (SYMM _let_382)) (SYMM _let_380)) _let_380) _let_292 :args _let_319) (SYMM _let_381)) _let_381) _let_350 :args _let_324) (SYMM (SYMM _let_378)) (CONG (TRANS (SYMM _let_370) (SYMM _let_375) (SYMM _let_376)) _let_377 _let_292 :args _let_294) (CONG (TRANS _let_376 _let_375 _let_370 (TRANS (CONG (CONG (TRANS _let_297 (TRANS _let_366 _let_363 (CONG (TRANS _let_297 (SYMM (SYMM _let_362))) _let_292 :args _let_361) (SYMM (SYMM _let_360)) (CONG (TRANS (CONG (TRANS _let_354 _let_359) _let_292 :args _let_319) (CONG _let_358 _let_292 :args _let_319)) _let_325 :args _let_324))) _let_292 :args _let_319) _let_350 :args _let_324) (SYMM _let_349) (CONG (REFL :args (_let_17)) (SYMM _let_348) :args _let_324) _let_337 _let_333 _let_331 _let_330 _let_328 _let_323 _let_321) _let_345) (SYMM (TRANS _let_344 _let_298)) _let_292 :args _let_294) _let_347 (SYMM _let_342) _let_341 (SYMM _let_339)) _let_298) _let_292 :args _let_319) (SYMM _let_338)) _let_318 _let_317 _let_292 :args _let_316) (CONG _let_338 _let_318 _let_317 _let_292 :args _let_316)) :args (_let_97 _let_118 _let_102 _let_81 _let_92 _let_128 _let_79 _let_85 _let_73 _let_110 _let_112 _let_96 _let_99 _let_131 _let_86 _let_83 _let_80 _let_133 _let_70 _let_77 _let_132 _let_129 _let_107 _let_137 _let_135 _let_125 _let_136 _let_104 _let_117 _let_119 _let_126 _let_130 _let_122 _let_90))) (MODUS_PONENS (AND_INTRO _let_315 _let_314 _let_308 _let_306 _let_301 _let_293 _let_312 _let_296 _let_289 _let_311) (SCOPE (TRANS (SYMM (SYMM _let_315)) (CONG (REFL :args (_let_23)) _let_304 _let_292 :args _let_291) (CONG _let_290 _let_295 _let_292 :args _let_291) (SYMM (SYMM _let_314)) (CONG (REFL :args (_let_22)) (TRANS (TRANS (CONG _let_293 _let_295 _let_292 :args _let_291) (CONG (TRANS (TRANS (SYMM _let_299) (SYMM _let_305) _let_307 _let_309 _let_303 _let_300) _let_313) _let_313 _let_292 :args _let_291) (CONG (REFL :args (_let_71)) _let_310 _let_292 :args _let_291) (SYMM _let_312) (SYMM _let_311) _let_303 _let_300) (TRANS (SYMM _let_300) _let_302 _let_310 (SYMM _let_307) _let_305 _let_299 (SYMM _let_293))) _let_292 :args _let_291)) :args (_let_127 _let_108 _let_75 _let_113 _let_120 _let_114 _let_111 _let_97 _let_89 _let_94))) _let_289 _let_138) :args (_let_28 _let_73 _let_75 _let_77 _let_79 _let_80 _let_81 _let_85 _let_86 _let_89 _let_83 _let_90 _let_92 _let_94 _let_96 _let_70 _let_97 _let_99 _let_102 _let_104 _let_107 _let_108 _let_110 _let_111 _let_112 _let_113 _let_114 _let_117 _let_118 _let_119 _let_120 _let_122 _let_125 _let_126 _let_127 _let_128 _let_129 _let_130 _let_131 _let_132 _let_133 _let_135 _let_136 _let_137)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_138)) (TRUE_INTRO (TRANS (SYMM (ASSUME :args (_let_285))) _let_288 (SYMM (TRANS _let_290 (SYMM (ASSUME :args (_let_284))) _let_288)))))) :args (_let_73 _let_285 _let_284 _let_89 _let_28)) :args ((not (and _let_28 _let_73 _let_75 _let_77 _let_79 _let_80 _let_81 _let_85 _let_86 _let_89 _let_83 _let_90 _let_92 _let_94 _let_96 _let_70 _let_97 _let_99 _let_102 _let_104 _let_107 _let_108 _let_110 _let_111 _let_112 _let_113 _let_114 _let_117 _let_118 _let_119 _let_120 _let_122 _let_125 _let_126 _let_127 _let_128 _let_129 _let_130 _let_131 _let_132 _let_133 _let_135 _let_136 _let_137)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) (REFL :args ((not _let_73))) (REFL :args ((not _let_75))) (REFL :args ((not _let_77))) (REFL :args ((not _let_79))) (REFL :args ((not _let_80))) (REFL :args ((not _let_81))) (REFL :args ((not _let_85))) (REFL :args ((not _let_86))) (REFL :args ((not _let_89))) (REFL :args ((not _let_83))) (REFL :args ((not _let_90))) (REFL :args ((not _let_92))) (REFL :args ((not _let_94))) (REFL :args ((not _let_96))) (REFL :args ((not _let_70))) (REFL :args ((not _let_97))) (REFL :args ((not _let_99))) (REFL :args ((not _let_102))) (REFL :args ((not _let_104))) (REFL :args ((not _let_107))) (REFL :args ((not _let_108))) (REFL :args ((not _let_110))) (REFL :args ((not _let_111))) (REFL :args ((not _let_112))) (REFL :args ((not _let_113))) (REFL :args ((not _let_114))) (REFL :args ((not _let_117))) (REFL :args ((not _let_118))) (REFL :args ((not _let_119))) (REFL :args ((not _let_120))) (REFL :args ((not _let_122))) (REFL :args ((not _let_125))) (REFL :args ((not _let_126))) (REFL :args ((not _let_127))) (REFL :args ((not _let_128))) (REFL :args ((not _let_129))) (REFL :args ((not _let_130))) (REFL :args ((not _let_131))) (REFL :args ((not _let_132))) (REFL :args ((not _let_133))) (REFL :args ((not _let_135))) (REFL :args ((not _let_136))) (REFL :args ((not _let_137))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_281)) :args ((or _let_146 _let_169 _let_137 (not _let_281)))) _let_150 _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_283 :args (tptp.tc_Complex_Ocomplex _let_18 _let_16 tptp.v_k QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n) T_a)))) :args _let_282)) _let_283 :args (_let_281 false _let_32)) :args (_let_137 false _let_12 false _let_3 false _let_281)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_278)) :args ((or _let_146 _let_169 _let_136 (not _let_278)))) _let_150 _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_280 :args (tptp.tc_Complex_Ocomplex _let_123 _let_76 _let_16 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a)))) :args _let_279)) _let_280 :args (_let_278 false _let_50)) :args (_let_136 false _let_12 false _let_3 false _let_278)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_275)) :args ((or _let_146 _let_169 _let_135 (not _let_275)))) _let_150 _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_277 :args (tptp.tc_Complex_Ocomplex _let_16 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))) :args _let_276)) _let_277 :args (_let_275 false _let_51)) :args (_let_135 false _let_12 false _let_3 false _let_275)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_272)) :args ((or _let_146 _let_151 _let_133 (not _let_272)))) _let_150 _let_155 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_274 :args (tptp.tc_Complex_Ocomplex _let_15 tptp.v_n QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_n)))) :args _let_273)) _let_274 :args (_let_272 false _let_52)) :args (_let_133 false _let_12 false _let_9 false _let_272)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_271)) :args ((or _let_156 _let_132 (not _let_271)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_159 :args (tptp.tc_Complex_Ocomplex _let_18 tptp.v_n tptp.v_k QUANTIFIERS_INST_E_MATCHING _let_161)) :args _let_158)) _let_159 :args (_let_271 false _let_54)) :args (_let_132 false _let_5 false _let_271)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_270)) :args ((or _let_156 _let_131 (not _let_270)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_159 :args (tptp.tc_Complex_Ocomplex _let_16 tptp.v_n tptp.v_k QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP _let_160 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))))) :args _let_158)) _let_159 :args (_let_270 false _let_54)) :args (_let_131 false _let_5 false _let_270)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_267)) :args ((or _let_156 _let_130 (not _let_267)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_269 :args (tptp.tc_Complex_Ocomplex _let_15 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) :args (_let_268))) _let_269 :args (_let_267 false _let_268)) :args (_let_130 false _let_5 false _let_267)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_266)) :args ((or _let_156 _let_129 (not _let_266)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_263 :args (tptp.tc_Complex_Ocomplex _let_105 QUANTIFIERS_INST_E_MATCHING _let_265)) :args _let_264)) _let_263 :args (_let_266 false _let_262)) :args (_let_129 false _let_5 false _let_266)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_261)) :args ((or _let_156 _let_128 (not _let_261)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_263 :args (tptp.tc_Complex_Ocomplex _let_21 QUANTIFIERS_INST_E_MATCHING _let_265)) :args _let_264)) _let_263 :args (_let_261 false _let_262)) :args (_let_128 false _let_5 false _let_261)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_258)) :args ((or _let_257 _let_127 (not _let_258)))) (ASSUME :args (_let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_260 :args (tptp.tc_Complex_Ocomplex _let_23 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) :args (_let_259))) _let_260 :args (_let_258 false _let_259)) :args (_let_127 false _let_13 false _let_258)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_254)) :args ((or _let_146 _let_151 _let_126 (not _let_254)))) _let_150 _let_155 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_256 :args (tptp.tc_Complex_Ocomplex _let_15 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)))) :args (_let_255))) _let_256 :args (_let_254 false _let_255)) :args (_let_126 false _let_12 false _let_9 false _let_254)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_253)) :args ((or _let_202 _let_125 (not _let_253)))) _let_206 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_251 :args (tptp.tc_Complex_Ocomplex _let_123 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_252)) :args _let_250)) _let_251 :args (_let_253 false _let_67)) :args (_let_125 false _let_11 false _let_253)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_249)) :args ((or _let_202 _let_122 (not _let_249)))) _let_206 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_251 :args (tptp.tc_Complex_Ocomplex _let_14 _let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_252)) :args _let_250)) _let_251 :args (_let_249 false _let_67)) :args (_let_122 false _let_11 false _let_249)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_246)) :args ((or _let_245 _let_120 (not _let_246)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_248 :args (tptp.tc_Complex_Ocomplex _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a)))) :args _let_247))) _let_248 :args (_let_246 false _let_30)) :args (_let_120 false _let_6 false _let_246)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_244)) :args ((or _let_156 _let_119 (not _let_244)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_241 :args (tptp.tc_Complex_Ocomplex _let_46 QUANTIFIERS_INST_E_MATCHING _let_243)) :args _let_242)) _let_241 :args (_let_244 false _let_240)) :args (_let_119 false _let_5 false _let_244)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_239)) :args ((or _let_156 _let_118 (not _let_239)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_241 :args (tptp.tc_Complex_Ocomplex _let_59 QUANTIFIERS_INST_E_MATCHING _let_243)) :args _let_242)) _let_241 :args (_let_239 false _let_240)) :args (_let_118 false _let_5 false _let_239)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_236)) :args ((or _let_169 _let_168 _let_117 (not _let_236)))) _let_176 _let_175 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_238 :args (tptp.tc_Complex_Ocomplex _let_14 _let_15 _let_46 QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) V_n)))) :args _let_237))) _let_238 :args (_let_236 false _let_37)) :args (_let_117 false _let_3 true _let_168 false _let_236)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_235)) :args ((or _let_169 _let_114 (not _let_235)))) _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_233 :args (tptp.tc_Complex_Ocomplex _let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_234)) :args _let_232)) _let_233 :args (_let_235 false _let_43)) :args (_let_114 false _let_3 false _let_235)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_231)) :args ((or _let_169 _let_113 (not _let_231)))) _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_233 :args (tptp.tc_Complex_Ocomplex _let_71 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_234)) :args _let_232)) _let_233 :args (_let_231 false _let_43)) :args (_let_113 false _let_3 false _let_231)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_228)) :args ((or _let_177 _let_178 _let_112 (not _let_228)))) _let_183 _let_182 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_230 :args (tptp.tc_Complex_Ocomplex _let_71 _let_71 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Transcendental_Oexp V_x T_a) (tptp.c_Transcendental_Oexp V_y T_a) T_a)))) :args _let_229)) _let_230 :args (_let_228 false _let_44)) :args (_let_112 false _let_8 false _let_1 false _let_228)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_227)) :args ((or _let_169 _let_111 (not _let_227)))) _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_186 :args (tptp.tc_Complex_Ocomplex _let_71 _let_71 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_187)) :args _let_185)) _let_186 :args (_let_227 false _let_45)) :args (_let_111 false _let_3 false _let_227)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_224)) :args ((or _let_141 _let_110 (not _let_224)))) _let_145 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_226 :args (tptp.tc_Complex_Ocomplex _let_71 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))) :args _let_225))) _let_226 :args (_let_224 false _let_48)) :args (_let_110 false _let_4 false _let_224)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_221)) :args ((or _let_220 _let_108 (not _let_221)))) (ASSUME :args (_let_10)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_223 :args (tptp.tc_Complex_Ocomplex _let_22 _let_87 _let_19 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) :args _let_222)) _let_223 :args (_let_221 false _let_55)) :args (_let_108 false _let_10 false _let_221)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_217)) :args ((or _let_156 _let_107 (not _let_217)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_219 :args (tptp.tc_Complex_Ocomplex _let_18 _let_78 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) V_a T_a)))) :args _let_218)) _let_219 :args (_let_217 false _let_64)) :args (_let_107 false _let_5 false _let_217)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_216)) :args ((or _let_202 _let_104 (not _let_216)))) _let_206 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_214 :args (tptp.tc_Complex_Ocomplex _let_16 _let_24 QUANTIFIERS_INST_E_MATCHING _let_215)) :args _let_213)) _let_214 :args (_let_216 false _let_65)) :args (_let_104 false _let_11 false _let_216)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_212)) :args ((or _let_202 _let_102 (not _let_212)))) _let_206 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_214 :args (tptp.tc_Complex_Ocomplex _let_14 tptp.v_n QUANTIFIERS_INST_E_MATCHING _let_215)) :args _let_213)) _let_214 :args (_let_212 false _let_65)) :args (_let_102 false _let_11 false _let_212)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_211 :args (tptp.v_k tptp.v_n QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat)))) :args _let_210)) _let_211 :args (_let_99 false _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_207)) :args ((or _let_27 _let_169 _let_97 (not _let_207)))) _let_138 _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_209 :args (tptp.tc_Complex_Ocomplex _let_18 tptp.v_n QUANTIFIERS_INST_E_MATCHING ((tptp.c_Finite__Set_Osetsum (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_24 V_n tptp.tc_nat) tptp.tc_nat T_a)))) :args _let_208))) _let_209 :args (_let_207 false _let_29)) :args (_let_97 true _let_27 false _let_3 false _let_207)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_203)) :args ((or _let_202 _let_96 (not _let_203)))) _let_206 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_205 :args (tptp.tc_Complex_Ocomplex _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Power_Opower__class_Opower V_x T_a)))) :args _let_204))) _let_205 :args (_let_203 false _let_33)) :args (_let_96 false _let_11 false _let_203)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_199)) :args ((or _let_146 _let_169 _let_94 (not _let_199)))) _let_150 _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_201 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Ofield T_a) false))))) :args (_let_200))) _let_201 :args (_let_199 false _let_200)) :args (_let_94 false _let_12 false _let_3 false _let_199)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_196)) :args ((or _let_195 _let_194 _let_92 (not _let_196)))) (ASSUME :args (_let_7)) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_198 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Osemiring__0 T_a) false))))) :args _let_197))) _let_198 :args (_let_196 false _let_36)) :args (_let_92 false _let_7 false _let_2 false _let_196)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_191)) :args ((or _let_189 _let_190 _let_90 (not _let_191)))) (ASSUME :args (_let_42)) (ASSUME :args (_let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_193 :args (tptp.v_n tptp.v_k QUANTIFIERS_INST_E_MATCHING ((tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_k tptp.tc_nat) V_n)))) :args (_let_192))) _let_193 :args (_let_191 false _let_192)) :args (_let_90 false _let_42 false _let_40 false _let_191)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_188)) :args ((or _let_169 _let_89 (not _let_188)))) _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_186 :args (tptp.tc_Complex_Ocomplex _let_22 _let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_187)) :args _let_185)) _let_186 :args (_let_188 false _let_45)) :args (_let_89 false _let_3 false _let_188)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_184)) :args ((or _let_169 _let_86 (not _let_184)))) _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_186 :args (tptp.tc_Complex_Ocomplex _let_14 _let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_187)) :args _let_185)) _let_186 :args (_let_184 false _let_45)) :args (_let_86 false _let_3 false _let_184)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_179)) :args ((or _let_177 _let_178 _let_85 (not _let_179)))) _let_183 _let_182 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_181 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_SEQ_Obanach T_a) false))))) :args _let_180))) _let_181 :args (_let_179 false _let_47)) :args (_let_85 false _let_8 false _let_1 false _let_179)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_170)) :args ((or _let_169 _let_168 _let_83 (not _let_170)))) _let_176 _let_175 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_172 :args (tptp.tc_Complex_Ocomplex _let_15 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) :args _let_171))) _let_172 :args (_let_170 false _let_39)) :args (_let_83 false _let_3 true _let_168 false _let_170)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_167)) :args ((or _let_156 _let_81 (not _let_167)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_165 :args (tptp.tc_Complex_Ocomplex _let_18 tptp.v_n QUANTIFIERS_INST_E_MATCHING _let_166)) :args _let_164))) _let_165 :args (_let_167 false _let_53)) :args (_let_81 false _let_5 false _let_167)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_163)) :args ((or _let_156 _let_80 (not _let_163)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_165 :args (tptp.tc_Complex_Ocomplex _let_16 tptp.v_k QUANTIFIERS_INST_E_MATCHING _let_166)) :args _let_164))) _let_165 :args (_let_163 false _let_53)) :args (_let_80 false _let_5 false _let_163)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_157)) :args ((or _let_156 _let_79 (not _let_157)))) _let_162 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_159 :args (tptp.tc_Complex_Ocomplex _let_16 tptp.v_k tptp.v_n QUANTIFIERS_INST_E_MATCHING _let_161)) :args _let_158))) _let_159 :args (_let_157 false _let_54)) :args (_let_79 false _let_5 false _let_157)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_152)) :args ((or _let_151 _let_77 (not _let_152)))) _let_155 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_154 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Odivision__ring T_a) false))))) :args (_let_153))) _let_154 :args (_let_152 false _let_153)) :args (_let_77 false _let_9 false _let_152)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_147)) :args ((or _let_146 _let_75 (not _let_147)))) _let_150 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_149 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Odivision__by__zero T_a) false))))) :args (_let_148))) _let_149 :args (_let_147 false _let_148)) :args (_let_75 false _let_12 false _let_147)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_142)) :args ((or _let_141 _let_73 (not _let_142)))) _let_145 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_144 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_OrderedGroup_Ogroup__add T_a) false))))) :args (_let_143))) _let_144 :args (_let_142 false _let_143)) :args (_let_73 false _let_4 false _let_142)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_140 :args (tptp.v_n QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_FFT__Mirabelle_Oroot V_n)))) :args _let_139))) _let_140 :args (_let_70 false _let_31)) _let_138 :args (false false _let_137 false _let_136 false _let_135 false _let_133 false _let_132 false _let_131 false _let_130 false _let_129 false _let_128 false _let_127 false _let_126 false _let_125 false _let_122 false _let_120 false _let_119 false _let_118 false _let_117 false _let_114 false _let_113 false _let_112 false _let_111 false _let_110 false _let_108 false _let_107 false _let_104 false _let_102 false _let_99 false _let_97 false _let_96 false _let_94 false _let_92 false _let_90 false _let_89 false _let_86 false _let_85 false _let_83 false _let_81 false _let_80 false _let_79 false _let_77 false _let_75 false _let_73 false _let_70 true _let_27)) :args ((forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.c_Suc V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Oring__char__0 T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_Int_Onumber__class_Onumber__of V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_y T_a))) (= V_x V_y))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Suc _let_1))) (or (= V_x _let_2) (= V_x _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) (tptp.c_Suc _let_2)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))))) (forall ((V_P $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_Q $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK V_P T_a T_b) V_Q) V_P)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_z T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1))))))) _let_67 _let_66 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a)))) _let_65 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.hAPP _let_1 V_n) T_a))))) _let_64 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_x T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.c_Suc V_n)) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.hAPP _let_1 V_n) 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_Otimes__class_Otimes V_a _let_1 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))))))) (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_Otimes__class_Otimes V_a _let_1 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)))) _let_63 (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes 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))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless V_a 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.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b)))))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.c_Suc _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odvd T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b (tptp.c_HOL_Otimes__class_Otimes V_b V_k T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (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_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))))))) (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_Otimes__class_Otimes V_a _let_1 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))))))) (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_Otimes__class_Otimes V_a _let_1 T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless V_a 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.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b)))))))) (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 (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1))))))) (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_n) tptp.tc_nat) V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_n) tptp.tc_nat) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_m) tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_m) tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_c T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_m _let_1)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))))))) (forall ((T_a $$unsorted)) (tptp.c_Finite__Set_Ofinite (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) 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.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes 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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b))))) (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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_y))))) (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.hBOOL (tptp.hAPP (tptp.c_lessequals V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (= V_a V_b))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.c_Suc V_n)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OlessThan V_x T_a) (tptp.c_SetInterval_Oord__class_OlessThan V_y T_a))) (= V_x V_y))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_m)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) _let_1)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_m))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 tptp.tc_nat) V_n)) (= _let_1 V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_n) tptp.tc_nat) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_n) tptp.tc_nat) V_m))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) _let_1)))))) (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b)))))) (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) 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.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) 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.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 tptp.tc_nat) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)))))) (forall ((V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_m V_m tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Finite__Set_Ofinite_Ofinite T_a)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_i V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_j V_k tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) V_j))))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_i tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_j tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) V_j))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_Suc V_n)))))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_x) tptp.tc_nat) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) _let_62 (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a))))) _let_61 (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= V_a _let_1) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) _let_60 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_a _let_1) (= V_b _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (not (= (tptp.c_Transcendental_Oexp V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_ly V_ry T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes _let_1 V_ry T_a) T_a))))) (= (tptp.c_SetInterval_Oord__class_OlessThan _let_24 tptp.tc_nat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (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))) (= (tptp.c_HOL_Oord__class_Oless tptp.v_n tptp.tc_nat) (tptp.c_lessequals _let_59 tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y tptp.tc_nat) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_y)) (= V_x V_y))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m)) (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (= V_m V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b _let_1 T_a) T_a)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_i) tptp.tc_nat) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_j tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) V_j))))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) (tptp.c_Suc V_x)))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.c_Suc V_n)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_lessequals V_a T_a))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_2 _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_3 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (= V_a _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Suc V_n)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Suc V_n) V_n))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_k V_i tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_j tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_i V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_j V_k tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) V_b)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat))) (= V_m V_n)))) (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_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) V_b)))))) (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))) (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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b 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.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_lessequals _let_1 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.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) V_b)))))))) (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))) (let ((_let_3 (tptp.c_lessequals _let_2 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.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$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_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) _let_1) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) _let_1))))))) (forall ((T_a $$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)) (= V_x _let_1) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) _let_2) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) _let_2))) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y_H T_a) V_x_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y_H T_a) V_x_H))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x_H T_a) V_y_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x_H T_a) V_y_H))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_xa V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ominus__class_Ominus V_b V_b_H T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_a_H T_a) V_b T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_ya T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) V_h T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_h T_a) T_a) _let_2 T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1)) (= V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_2 T_a) _let_2 T_a) _let_1))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_w T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_x)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$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)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1 T_a) V_b) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= V_b (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1 T_a)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_Onumber__class_Onumber__of V_w T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_Int_Onumber__class_Onumber__of V_w T_a) T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)))))))) (forall ((T_a $$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)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a)) (= V_c (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_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a 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.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a 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.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes 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_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP _let_1 V_c))))) (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_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_HOL_Oord__class_Oless _let_1 T_a))) (let ((_let_3 (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_3)) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_3))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_c))))))) (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))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_2 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.hBOOL (tptp.hAPP _let_3 _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP _let_3 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)))))))) (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))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless V_a 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.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))))))) (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))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (let ((_let_3 (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.hBOOL (tptp.hAPP _let_2 _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_3 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 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))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_2 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP _let_3 _let_1))))))) (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))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_2 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.hBOOL (tptp.hAPP _let_3 V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP _let_3 _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)))))) (forall ((T_a $$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)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$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.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_w T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_x)))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a))))) (forall ((T_a $$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.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1 T_a)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1 T_a) V_a) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_2 _let_1 T_a) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_w T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (let ((_let_2 (tptp.c_lessequals V_a 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.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals V_a 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.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_a 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)) (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)))))) (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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (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.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) _let_58 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))) _let_57 _let_56 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1)) (= V_x _let_1)))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_24 tptp.tc_nat) _let_24)) (not (tptp.hBOOL (tptp.hAPP _let_41 _let_24))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 tptp.tc_nat) V_n)) (= V_n _let_1)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes V_m _let_1 tptp.tc_nat) _let_1))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (= V_m V_n) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_b $$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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes 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))) (let ((_let_3 (tptp.c_lessequals V_a 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.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b)))))))) _let_55 (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ly T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly V_rx T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ry T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_m (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) T_a) (tptp.hAPP _let_1 V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_x) T_a) (tptp.hAPP _let_1 V_y)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_x) T_a) (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_i V_k tptp.tc_nat) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_j V_l tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))))) (forall ((V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_m (tptp.c_HOL_Otimes__class_Otimes V_m V_m tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_x)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.c_Suc V_m)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.c_Suc V_m))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (let ((_let_2 (tptp.c_lessequals V_m tptp.tc_nat))) (or (= V_m _let_1) (tptp.hBOOL (tptp.hAPP _let_2 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) _let_2 T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_b $$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_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) 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_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c 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_Otimes__class_Otimes V_a _let_1 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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))))))) (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_Otimes__class_Otimes V_a _let_1 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.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))))))) (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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals V_a 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.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals V_a 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.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (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.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Ouminus__class_Ouminus 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.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (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))) (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (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))) (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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (= V_a _let_1) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a)))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_m)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) (tptp.c_Suc V_n)))))) (forall ((V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_x))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) (tptp.c_Suc V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) _let_1 T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP _let_1 V_c)))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_m $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.c_HOL_Otimes__class_Otimes V_m _let_1 tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n _let_1 tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) _let_1)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_nat_H)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_m)))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_x) T_a) (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_x) T_a) (tptp.hAPP _let_1 V_y)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_n) T_a) (tptp.hAPP _let_1 V_N))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_N)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) T_a) (tptp.hAPP _let_1 V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) (tptp.c_Suc V_n)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_n) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a) T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_n) T_a) (tptp.hAPP _let_1 V_N))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_N)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) V_n) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))))) (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_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) _let_1 T_a))))) _let_54 _let_53 _let_52 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) V_n) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) V_q) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) V_q) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_y T_a) V_q) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_x T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.hAPP _let_1 V_p) T_a) V_q) (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_p V_q tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_y T_a) V_n) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_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)))) _let_51 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_z V_w T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_w T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_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 $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a)))) _let_50 (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_xa V_x T_a))) (or (not (tptp.class_HOL_Oord T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f _let_1 T_a T_b) (tptp.c_Finite__Set_Osetsum V_g _let_1 T_a T_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 V_xa V_x V_f V_g T_a T_b) T_a) V_x))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_xa V_x T_a))) (or (not (tptp.class_HOL_Oord T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f _let_1 T_a T_b) (tptp.c_Finite__Set_Osetsum V_g _let_1 T_a T_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_xa T_a) (tptp.c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 V_xa V_x V_f V_g T_a T_b)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osums V_f (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat T_a) T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) (tptp.c_Series_Osko__Series__Xseries__zero__1__1 V_f V_n T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_N) T_a) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_N)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_N) T_a) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_N)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) (tptp.c_Suc V_n)) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (let ((_let_3 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= _let_3 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) _let_3)))) (tptp.hBOOL (tptp.hAPP _let_2 _let_1))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) _let_1)))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) _let_1) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n))) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_Suc V_n) tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m))))) _let_49 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) _let_48 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) _let_47 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_n)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) (tptp.c_Suc V_n)) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) V_n) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) V_n) T_a) _let_1)))))) (forall ((T_a $$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.c_Power_Opower__class_Opower V_a T_a) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_x)))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _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 $$unsorted) (V_b $$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.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_b (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$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.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 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.hBOOL (tptp.hAPP _let_2 V_b)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) 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.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a 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.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_a 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)) (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b 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))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 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.hBOOL (tptp.hAPP _let_2 V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP _let_2 _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_x)))))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Suc V_nat) (tptp.c_Suc V_nat_H))) (= V_nat V_nat_H))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Suc V_x) (tptp.c_Suc V_y))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_2 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) V_b)))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b)))))))) (tptp.hBOOL (tptp.hAPP _let_41 _let_46)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat))) (or (= V_n V_m) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat))) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat))) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)))))))) (= (tptp.c_HOL_Otimes__class_Otimes _let_46 _let_46 tptp.tc_nat) _let_46) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_n)))) (forall ((V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_x T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.hAPP _let_1 V_q) T_a) (tptp.hAPP _let_1 (tptp.c_Suc V_q)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_x T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP _let_1 V_q) V_x T_a) (tptp.hAPP _let_1 (tptp.c_Suc V_q)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_y T_a) V_m) T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_m tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_m) tptp.tc_nat) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) _let_45 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oinverse__class_Oinverse V_y T_a) T_a)))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_n) tptp.tc_nat) V_n)))) (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.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (let ((_let_3 (tptp.c_lessequals _let_1 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.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b)))))))) (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_lessequals (tptp.c_Int_Onumber__class_Onumber__of V_w T_a) 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.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_Int_Onumber__class_Onumber__of V_w T_a) 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.hBOOL (tptp.hAPP _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_c V_d T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_x)))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_x))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_i tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP _let_1 V_m) V_b T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd (tptp.hAPP _let_1 V_n) V_b T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_z T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_z T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_z T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_z T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_x)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_Transcendental_Oexp (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Transcendental_Oexp V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (let ((_let_3 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b)))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.c_Suc V_m)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Suc V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Suc V_m)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))))))) (forall ((T_a $$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)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_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 $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 _let_2)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_2 _let_1)) (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 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.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 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.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))))))) (forall ((T_a $$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__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 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.hBOOL (tptp.hAPP _let_2 V_b)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_d $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_FFT__Mirabelle_Oroot (tptp.c_HOL_Otimes__class_Otimes V_d V_n tptp.tc_nat)) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes V_d V_k tptp.tc_nat)) (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_FFT__Mirabelle_Oroot V_n) tptp.tc_Complex_Ocomplex) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_d))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum (tptp.c_COMBK _let_1 T_a T_b) V_A T_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (not (= (tptp.hAPP V_f (tptp.c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1 V_A V_f T_a T_b)) _let_1)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) _let_1)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_Finite__Set_Ofinite V_A T_b))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (= (tptp.c_Finite__Set_Osetsum V_f V_A T_a T_b) (tptp.c_HOL_Ozero__class_Ozero T_b)) (tptp.c_Finite__Set_Ofinite V_A T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a T_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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (= V_m V_n)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) V_n) T_a)))) _let_44 _let_43 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (= (tptp.hAPP V_f (tptp.c_Series_Osko__Series__Xseries__zero__1__1 V_f V_n T_a)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.c_Series_Osums V_f (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat T_a) T_a))) (forall ((V_m $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool)))) (forall ((V_n $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) (tptp.c_SetInterval_Oord__class_OlessThan V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_g $$unsorted)) (let ((_let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_xa V_x T_a))) (let ((_let_2 (tptp.c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 V_xa V_x V_f V_g T_a T_b))) (or (not (tptp.class_HOL_Oord T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_b)) (not (= (tptp.hAPP V_f _let_2) (tptp.hAPP V_g _let_2))) (= (tptp.c_Finite__Set_Osetsum V_f _let_1 T_a T_b) (tptp.c_Finite__Set_Osetsum V_g _let_1 T_a T_b)))))) _let_42 _let_40 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (= V_z _let_1) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_2 T_a) _let_1) _let_2) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_2 T_a) _let_1) _let_2) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$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.c_Power_Opower__class_Opower V_a T_a) _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 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.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) V_n)))) (tptp.hBOOL (tptp.hAPP _let_2 _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) 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.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) 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.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b 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_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) _let_1)))))) _let_39 (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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b 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_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) 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.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) 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.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_p $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_p tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat) tptp.tc_nat T_a) T_a) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_n V_p tptp.tc_nat) tptp.tc_nat T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_p))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1) (tptp.c_HOL_Oone__class_Oone T_a))))) _let_38 (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (not (= (tptp.hAPP V_f _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_Suc _let_1) V_k tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_k tptp.tc_nat) tptp.tc_nat 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))))) _let_37 _let_36 _let_35 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) _let_34 (forall ((T_a $$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 $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_n $$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.c_Power_Opower__class_Opower _let_1 T_a) 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.c_Power_Opower__class_Opower _let_1 T_a) V_n) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) _let_33 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a 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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) _let_1)) (= V_a _let_1)))) (forall ((T_a $$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.c_Power_Opower__class_Opower V_a T_a) V_n) _let_1)) (= V_a _let_1)))) _let_32 _let_31 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (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 $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) _let_30 (forall ((T_a $$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 $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) T_a) V_n))))) (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.c_Power_Opower__class_Opower V_a T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (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)) (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 $$unsorted) (V_a $$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 $$unsorted) (V_x $$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) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_y T_a) _let_1)))) _let_29 _let_28 (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Finite__Set_Ofinite_Ofinite (tptp.tc_fun T_2 T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_1)) (not (tptp.class_Finite__Set_Ofinite_Ofinite T_2)))) (forall ((T_2 $$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 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Oorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Obot (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Obot T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_HOL_Oord (tptp.tc_fun T_2 T_1)) (not (tptp.class_HOL_Oord T_1)))) (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_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_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Odvd tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Orderings_Obot tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_Int_Onumber tptp.tc_nat) (tptp.class_HOL_Oord tptp.tc_nat) (tptp.class_Lattices_Oboolean__algebra tptp.tc_bool) (tptp.class_Finite__Set_Ofinite_Ofinite tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_HOL_Oord tptp.tc_bool) (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_Ring__and__Field_Oring__no__zero__divisors 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_Ring__and__Field_Opordered__semiring 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_Ring__and__Field_Opordered__ring 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__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_OrderedGroup_Ogroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1 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_Ring__and__Field_Odvd tptp.tc_Int_Oint) (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint) (tptp.class_Orderings_Olinorder 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_HOL_Oord tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) _let_13 (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Complex_Ocomplex) _let_12 _let_11 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) _let_10 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) _let_9 _let_8 (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) _let_7 _let_6 (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex) _let_5 _let_4 (tptp.class_Ring__and__Field_Oring__1 tptp.tc_Complex_Ocomplex) _let_3 (tptp.class_Ring__and__Field_Oring tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oidom tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odvd tptp.tc_Complex_Ocomplex) (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex) _let_2 _let_1 (tptp.class_Int_Onumber tptp.tc_Complex_Ocomplex) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 3.65/3.82 )
% 3.65/3.83 % SZS output end Proof for SWV621-1
% 3.65/3.83 % cvc5---1.0.5 exiting
% 3.65/3.83 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------