%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV618-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n007.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 21:52:42 EDT 2023

% Result   : Unsatisfiable 33.60s 34.26s
% Output   : Proof 33.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.21  % Problem    : SWV618-1 : TPTP v8.1.2. Released v4.1.0.
% 0.21/0.22  % Command    : do_cvc5 %s %d
% 0.22/0.43  % Computer : n007.cluster.edu
% 0.22/0.43  % Model    : x86_64 x86_64
% 0.22/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.43  % Memory   : 8042.1875MB
% 0.22/0.43  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.22/0.43  % CPULimit   : 300
% 0.22/0.43  % WCLimit    : 300
% 0.22/0.43  % DateTime   : Tue Aug 29 06:01:43 EDT 2023
% 0.22/0.43  % CPUTime    : 
% 0.40/0.64  %----Proving TF0_NAR, FOF, or CNF
% 0.40/0.65  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.q5Fo5qGdGE/cvc5---1.0.5_10631.p...
% 0.49/0.75  ------- get file name : TPTP file name is SWV618-1
% 0.49/0.75  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10631.smt2...
% 0.49/0.75  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.66/11.02  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.78/16.19  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.91/21.34  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.95/26.48  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.07/31.68  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 33.60/34.26  % SZS status Unsatisfiable for SWV618-1
% 33.60/34.26  % SZS output start Proof for SWV618-1
% 33.73/34.36  (
% 33.73/34.36  (let ((_let_1 (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex))) (let ((_let_3 (tptp.class_Ring__and__Field_Oidom tptp.tc_Complex_Ocomplex))) (let ((_let_4 (tptp.class_Ring__and__Field_Ofield tptp.tc_Complex_Ocomplex))) (let ((_let_5 (tptp.class_Ring__and__Field_Oring__1 tptp.tc_Complex_Ocomplex))) (let ((_let_6 (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Complex_Ocomplex))) (let ((_let_7 (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Complex_Ocomplex))) (let ((_let_8 (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex))) (let ((_let_9 (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Complex_Ocomplex))) (let ((_let_10 (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Complex_Ocomplex))) (let ((_let_11 (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Complex_Ocomplex))) (let ((_let_12 (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex))) (let ((_let_13 (tptp.class_Ring__and__Field_Odivision__ring tptp.tc_Complex_Ocomplex))) (let ((_let_14 (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex))) (let ((_let_15 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex))) (let ((_let_16 (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex))) (let ((_let_17 (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_Complex_Ocomplex))) (let ((_let_18 (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Complex_Ocomplex))) (let ((_let_19 (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex))) (let ((_let_20 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_21 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_22 (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_21 tptp.v_n tptp.tc_nat))) (let ((_let_23 (tptp.c_FFT__Mirabelle_Oroot tptp.v_n))) (let ((_let_24 (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (let ((_let_25 (tptp.c_HOL_Oinverse__class_Odivide _let_24 _let_23 tptp.tc_Complex_Ocomplex))) (let ((_let_26 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_25 tptp.tc_Complex_Ocomplex) tptp.v_k))) (let ((_let_27 (tptp.c_Power_Opower__class_Opower _let_26 tptp.tc_Complex_Ocomplex))) (let ((_let_28 (tptp.c_Finite__Set_Osetsum _let_27 _let_22 tptp.tc_nat tptp.tc_Complex_Ocomplex))) (let ((_let_29 (not (= _let_28 _let_20)))) (let ((_let_30 (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 ((_let_31 (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)))))) (let ((_let_32 (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))))))) (let ((_let_33 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) T_a) V_n))))))) (let ((_let_34 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) V_n) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n) T_a)))))) (let ((_let_35 (forall ((T_a $$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)))))) (let ((_let_36 (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)))))) (let ((_let_37 (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_38 (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))))) (let ((_let_39 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))))) (let ((_let_40 (forall ((T_a $$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 ((_let_41 (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_42 (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Oone__class_Oone T_a)))))) (let ((_let_43 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) V_n) (tptp.c_HOL_Oinverse__class_Odivide (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (let ((_let_44 (forall ((V_n $$unsorted)) (not (= (tptp.c_FFT__Mirabelle_Oroot V_n) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (let ((_let_45 (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.c_HOL_Oord__class_Oless V_k V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_k tptp.tc_nat))))))) (let ((_let_46 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower V_x T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Finite__Set_Osetsum _let_2 (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP _let_2 V_n) _let_1 T_a) (tptp.c_HOL_Ominus__class_Ominus V_x _let_1 T_a) T_a)) (= V_x _let_1))))))) (let ((_let_47 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (let ((_let_48 (tptp.c_HOL_Oord__class_Oless tptp.v_k tptp.v_n tptp.tc_nat))) (let ((_let_49 (tptp.c_HOL_Oord__class_Oless _let_21 tptp.v_k tptp.tc_nat))) (let ((_let_50 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a)))))) (let ((_let_51 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))))) (let ((_let_52 (forall ((T_a $$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)))))) (let ((_let_53 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oinverse__class_Oinverse V_y T_a) T_a)))))) (let ((_let_54 (forall ((T_a $$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_55 (tptp.c_Suc _let_21))) (let ((_let_56 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))))))) (let ((_let_57 (forall ((T_a $$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)))))) (let ((_let_58 (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_59 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))))) (let ((_let_60 (forall ((T_a $$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_61 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))))) (let ((_let_62 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) V_q) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) V_q) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_y T_a) V_q) T_a)))))) (let ((_let_63 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) V_n) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n) T_a)))))) (let ((_let_64 (forall ((T_a $$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_65 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_n) (tptp.c_HOL_Otimes__class_Otimes (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a) T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a)))))) (let ((_let_66 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))))) (let ((_let_67 (forall ((T_a $$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_68 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))))) (let ((_let_69 (forall ((T_a $$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)))))))) (let ((_let_70 (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)))))) (let ((_let_71 (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)))))) (let ((_let_72 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (= V_z _let_1) (= V_y _let_1)))))) (let ((_let_73 (forall ((T_a $$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))))) (let ((_let_74 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))))) (let ((_let_75 (forall ((T_a $$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_76 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b))))) (let ((_let_77 (forall ((T_a $$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))))) (let ((_let_78 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)))))) (let ((_let_79 (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))))) (let ((_let_80 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_a_H T_a) V_b T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b T_a) T_a)))))) (let ((_let_81 (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_xa V_y T_a) T_a)))))) (let ((_let_82 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a)))))) (let ((_let_83 (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_84 (= _let_20 _let_28))) (let ((_let_85 (tptp.c_HOL_Oinverse__class_Oinverse _let_24 tptp.tc_Complex_Ocomplex))) (let ((_let_86 (= _let_24 _let_85))) (let ((_let_87 (tptp.c_HOL_Oinverse__class_Oinverse _let_23 tptp.tc_Complex_Ocomplex))) (let ((_let_88 (= _let_25 _let_87))) (let ((_let_89 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_23 tptp.tc_Complex_Ocomplex) tptp.v_k))) (let ((_let_90 (tptp.c_Power_Opower__class_Opower _let_89 tptp.tc_Complex_Ocomplex))) (let ((_let_91 (tptp.c_Finite__Set_Osetsum _let_90 _let_22 tptp.tc_nat tptp.tc_Complex_Ocomplex))) (let ((_let_92 (= _let_20 _let_91))) (let ((_let_93 (tptp.c_HOL_Oinverse__class_Odivide _let_24 _let_89 tptp.tc_Complex_Ocomplex))) (let ((_let_94 (= _let_26 _let_93))) (let ((_let_95 (= _let_24 (tptp.hAPP _let_27 _let_21)))) (let ((_let_96 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_87 tptp.tc_Complex_Ocomplex) tptp.v_k))) (let ((_let_97 (tptp.c_HOL_Oinverse__class_Oinverse _let_89 tptp.tc_Complex_Ocomplex))) (let ((_let_98 (= _let_97 _let_96))) (let ((_let_99 (= _let_85 (tptp.c_HOL_Oinverse__class_Odivide _let_24 _let_24 tptp.tc_Complex_Ocomplex)))) (let ((_let_100 (= _let_89 (tptp.c_HOL_Oinverse__class_Oinverse _let_97 tptp.tc_Complex_Ocomplex)))) (let ((_let_101 (tptp.c_HOL_Oinverse__class_Oinverse _let_26 tptp.tc_Complex_Ocomplex))) (let ((_let_102 (= _let_101 (tptp.c_HOL_Oinverse__class_Odivide _let_24 _let_26 tptp.tc_Complex_Ocomplex)))) (let ((_let_103 (= _let_24 _let_26))) (let ((_let_104 (SYMM (ASSUME :args (_let_29))))) (let ((_let_105 (not _let_13))) (let ((_let_106 (or _let_105 _let_86))) (let ((_let_107 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a))))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO :args (_let_67 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (ASSUME :args (_let_13)))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_106)) :args ((or _let_105 _let_86 (not _let_106)))) _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Odivision__ring T_a) false))))) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_86 false _let_13 false _let_106)))) (let ((_let_111 (not _let_4))) (let ((_let_112 (or _let_111 _let_88))) (let ((_let_113 (_let_51))) (let ((_let_114 (ASSUME :args _let_113))) (let ((_let_115 (ASSUME :args (_let_4)))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_111 _let_88 (not _let_112)))) _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_114 :args (tptp.tc_Complex_Ocomplex _let_23 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) :args _let_113))) _let_114 :args (_let_112 false _let_51)) :args (_let_88 false _let_4 false _let_112)))) (let ((_let_117 (not _let_49))) (let ((_let_118 (not _let_48))) (let ((_let_119 (or _let_92 _let_118 _let_117))) (let ((_let_120 (forall ((V_n $$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.c_HOL_Oord__class_Oless V_k V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_k tptp.tc_nat))))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_45)) (MACRO_SR_EQ_INTRO :args (_let_45 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (tptp.v_n tptp.v_k QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_HOL_Oord__class_Oless V_k V_n tptp.tc_nat) false))))) :args (_let_120))))) (let ((_let_123 (ASSUME :args (_let_48)))) (let ((_let_124 (ASSUME :args (_let_49)))) (let ((_let_125 (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_117 _let_118 _let_92 (not _let_119)))))) (let ((_let_126 (MACRO_RESOLUTION_TRUST _let_125 _let_124 _let_123 (MACRO_RESOLUTION_TRUST _let_122 _let_121 :args (_let_119 false _let_120)) :args (_let_92 false _let_49 false _let_48 false _let_119)))) (let ((_let_127 (not _let_17))) (let ((_let_128 (or _let_111 _let_127 _let_94))) (let ((_let_129 (_let_33))) (let ((_let_130 (ASSUME :args _let_129))) (let ((_let_131 ((tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) T_a) V_n)))) (let ((_let_132 (ASSUME :args (_let_17)))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_128)) :args ((or _let_127 _let_111 _let_94 (not _let_128)))) _let_132 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_130 :args (tptp.tc_Complex_Ocomplex _let_23 tptp.v_k QUANTIFIERS_INST_E_MATCHING _let_131)) :args _let_129))) _let_130 :args (_let_128 false _let_33)) :args (_let_94 false _let_17 false _let_4 false _let_128)))) (let ((_let_134 (not _let_16))) (let ((_let_135 (or _let_134 _let_95))) (let ((_let_136 (_let_37))) (let ((_let_137 (ASSUME :args _let_136))) (let ((_let_138 (ASSUME :args (_let_16)))) (let ((_let_139 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_135)) :args ((or _let_134 _let_95 (not _let_135)))) _let_138 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_137 :args (tptp.tc_Complex_Ocomplex _let_26 QUANTIFIERS_INST_CBQI_PROP)) :args _let_136))) _let_137 :args (_let_135 false _let_37)) :args (_let_95 false _let_16 false _let_135)))) (let ((_let_140 (or _let_105 _let_127 _let_98))) (let ((_let_141 (_let_64))) (let ((_let_142 (ASSUME :args _let_141))) (let ((_let_143 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_140)) :args ((or _let_127 _let_105 _let_98 (not _let_140)))) _let_132 _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_142 :args (tptp.tc_Complex_Ocomplex _let_23 tptp.v_k 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_141)) _let_142 :args (_let_140 false _let_64)) :args (_let_98 false _let_17 false _let_13 false _let_140)))) (let ((_let_144 (or _let_111 _let_99))) (let ((_let_145 ((tptp.c_HOL_Oinverse__class_Oinverse V_a T_a)))) (let ((_let_146 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_144)) :args ((or _let_111 _let_99 (not _let_144)))) _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (tptp.tc_Complex_Ocomplex _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_145)) :args _let_113)) _let_114 :args (_let_144 false _let_51)) :args (_let_99 false _let_4 false _let_144)))) (let ((_let_147 (or _let_105 _let_127 _let_100))) (let ((_let_148 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)))))) (let ((_let_149 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_150 (_let_148))) (let ((_let_151 (tptp.tc_Complex_Ocomplex _let_89 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_152 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_147)) :args ((or _let_127 _let_105 _let_100 (not _let_147)))) _let_132 _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_149 :args _let_151) :args _let_150)) _let_149 :args (_let_147 false _let_148)) :args (_let_100 false _let_17 false _let_13 false _let_147)))) (let ((_let_153 (= _let_20 _let_26))) (let ((_let_154 (or _let_111 _let_102 _let_153))) (let ((_let_155 (_let_47))) (let ((_let_156 (ASSUME :args _let_155))) (let ((_let_157 (= _let_20 _let_25))) (let ((_let_158 (not _let_153))) (let ((_let_159 (not _let_19))) (let ((_let_160 (or _let_159 _let_158 _let_157))) (let ((_let_161 (forall ((T_a $$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 (= _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (= V_a _let_1)))))) (let ((_let_162 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_163 (_let_161))) (let ((_let_164 ((tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n)))) (let ((_let_165 (tptp.c_HOL_Oinverse__class_Oinverse _let_20 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(_let_170)))) (let ((_let_190 (=))) (let ((_let_191 (ASSUME :args (_let_88)))) (let ((_let_192 (SYMM _let_191))) (let ((_let_193 (SYMM _let_192))) (let ((_let_194 (ASSUME :args (_let_167)))) (let ((_let_195 (SYMM _let_194))) (let ((_let_196 (SYMM _let_195))) (let ((_let_197 (ASSUME :args (_let_19)))) (let ((_let_198 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_160)) :args ((or _let_159 _let_158 _let_157 (not _let_160)))) _let_197 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_188)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_189 _let_194 _let_191) (SCOPE (FALSE_ELIM (TRANS (CONG _let_196 _let_193 :args _let_190) (FALSE_INTRO _let_189))) :args (_let_170 _let_167 _let_88))) :args (_let_167 _let_88 _let_170))) :args (true _let_188)) (CONG _let_187 _let_186 (MACRO_SR_PRED_INTRO :args ((= (not _let_170) _let_166))) (REFL :args (_let_168)) :args _let_185)) :args ((or _let_184 _let_183 _let_168 _let_166))) _let_182 _let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_171)) :args ((or _let_127 _let_105 _let_169 _let_170 (not _let_171)))) _let_132 _let_109 _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_173 :args (tptp.tc_Complex_Ocomplex _let_23 _let_20 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a)))) :args _let_172))) _let_173 :args (_let_171 false _let_76)) :args (_let_170 false _let_17 false _let_13 true _let_169 false _let_171)) :args (_let_168 false _let_167 false _let_88 true _let_166)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_162 :args (tptp.tc_Complex_Ocomplex _let_25 tptp.v_k QUANTIFIERS_INST_E_MATCHING _let_164)) :args _let_163))) _let_162 :args (_let_160 false _let_161)) :args (_let_158 false _let_19 true _let_157 false _let_160)))) (let ((_let_199 (tptp.c_HOL_Ominus__class_Ominus _let_26 _let_24 tptp.tc_Complex_Ocomplex))) (let ((_let_200 (tptp.hAPP _let_27 tptp.v_n))) (let ((_let_201 (tptp.c_HOL_Ominus__class_Ominus _let_200 _let_24 tptp.tc_Complex_Ocomplex))) (let ((_let_202 (tptp.c_HOL_Oinverse__class_Odivide _let_201 _let_199 tptp.tc_Complex_Ocomplex))) (let ((_let_203 (= _let_28 _let_202))) (let ((_let_204 (or _let_111 _let_203 _let_103))) (let ((_let_205 (_let_46))) (let ((_let_206 (ASSUME :args _let_205))) (let ((_let_207 ((tptp.c_Finite__Set_Osetsum (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_21 V_n tptp.tc_nat) tptp.tc_nat T_a)))) (let ((_let_208 (tptp.hAPP _let_90 tptp.v_n))) (let ((_let_209 (tptp.c_HOL_Ominus__class_Ominus _let_208 _let_24 tptp.tc_Complex_Ocomplex))) (let ((_let_210 (= _let_20 _let_209))) (let ((_let_211 (= _let_24 _let_89))) (let ((_let_212 (tptp.c_HOL_Ouminus__class_Ouminus _let_20 tptp.tc_Complex_Ocomplex))) (let ((_let_213 (= _let_20 _let_212))) (let ((_let_214 (tptp.c_HOL_Otimes__class_Otimes _let_24 _let_87 tptp.tc_Complex_Ocomplex))) (let ((_let_215 (= _let_25 _let_214))) (let ((_let_216 (tptp.c_Power_Opower__class_Opower _let_24 tptp.tc_Complex_Ocomplex))) (let ((_let_217 (tptp.hAPP _let_216 tptp.v_k))) (let ((_let_218 (= _let_26 (tptp.c_HOL_Oinverse__class_Odivide _let_217 _let_89 tptp.tc_Complex_Ocomplex)))) (let ((_let_219 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_20 tptp.tc_Complex_Ocomplex) _let_21))) (let ((_let_220 (= _let_24 _let_219))) (let ((_let_221 (= _let_20 (tptp.c_HOL_Oinverse__class_Odivide _let_20 _let_20 tptp.tc_Complex_Ocomplex)))) (let ((_let_222 (= _let_24 _let_217))) (let ((_let_223 (tptp.c_HOL_Oinverse__class_Odivide _let_23 _let_24 tptp.tc_Complex_Ocomplex))) (let ((_let_224 (= _let_23 _let_223))) (let ((_let_225 (= _let_214 (tptp.c_HOL_Otimes__class_Otimes _let_87 _let_24 tptp.tc_Complex_Ocomplex)))) (let ((_let_226 (tptp.c_HOL_Ominus__class_Ominus _let_24 _let_26 tptp.tc_Complex_Ocomplex))) (let ((_let_227 (tptp.c_HOL_Ouminus__class_Ouminus _let_226 tptp.tc_Complex_Ocomplex))) (let ((_let_228 (= _let_199 _let_227))) (let ((_let_229 (tptp.c_HOL_Ominus__class_Ominus _let_24 _let_200 tptp.tc_Complex_Ocomplex))) (let ((_let_230 (= _let_201 (tptp.c_HOL_Ouminus__class_Ouminus _let_229 tptp.tc_Complex_Ocomplex)))) (let ((_let_231 (tptp.c_HOL_Otimes__class_Otimes _let_24 _let_23 tptp.tc_Complex_Ocomplex))) (let ((_let_232 (tptp.c_HOL_Oinverse__class_Oinverse _let_231 tptp.tc_Complex_Ocomplex))) (let ((_let_233 (= _let_232 (tptp.c_HOL_Otimes__class_Otimes _let_85 _let_87 tptp.tc_Complex_Ocomplex)))) (let ((_let_234 (tptp.c_HOL_Ouminus__class_Ouminus _let_24 tptp.tc_Complex_Ocomplex))) (let ((_let_235 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_234 tptp.tc_Complex_Ocomplex) _let_21))) (let ((_let_236 (tptp.c_HOL_Otimes__class_Otimes _let_235 _let_219 tptp.tc_Complex_Ocomplex))) (let ((_let_237 (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_212 tptp.tc_Complex_Ocomplex) _let_21) _let_236))) (let ((_let_238 (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_214 tptp.tc_Complex_Ocomplex) tptp.v_k) (tptp.c_HOL_Otimes__class_Otimes _let_217 _let_96 tptp.tc_Complex_Ocomplex)))) (let ((_let_239 (= _let_223 (tptp.c_HOL_Oinverse__class_Oinverse _let_25 tptp.tc_Complex_Ocomplex)))) (let ((_let_240 (tptp.c_HOL_Otimes__class_Otimes _let_23 _let_85 tptp.tc_Complex_Ocomplex))) (let ((_let_241 (= _let_223 _let_240))) (let ((_let_242 (tptp.c_HOL_Oinverse__class_Odivide _let_89 _let_217 tptp.tc_Complex_Ocomplex))) (let ((_let_243 (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_223 tptp.tc_Complex_Ocomplex) tptp.v_k) _let_242))) (let ((_let_244 (tptp.hAPP _let_90 _let_21))) (let ((_let_245 (tptp.c_HOL_Oinverse__class_Odivide _let_24 _let_244 tptp.tc_Complex_Ocomplex))) (let ((_let_246 (tptp.c_Power_Opower__class_Opower _let_93 tptp.tc_Complex_Ocomplex))) (let ((_let_247 (= (tptp.hAPP _let_246 _let_21) _let_245))) (let ((_let_248 (= _let_24 _let_235))) (let ((_let_249 (= _let_24 _let_244))) (let ((_let_250 (= _let_231 (tptp.c_HOL_Oinverse__class_Oinverse _let_232 tptp.tc_Complex_Ocomplex)))) (let ((_let_251 (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_231 tptp.tc_Complex_Ocomplex) tptp.v_k) (tptp.c_HOL_Otimes__class_Otimes _let_217 _let_89 tptp.tc_Complex_Ocomplex)))) (let ((_let_252 (= _let_201 (tptp.c_HOL_Otimes__class_Otimes _let_201 _let_24 tptp.tc_Complex_Ocomplex)))) (let ((_let_253 (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_240 tptp.tc_Complex_Ocomplex) tptp.v_k) (tptp.c_HOL_Otimes__class_Otimes _let_89 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_85 tptp.tc_Complex_Ocomplex) tptp.v_k) tptp.tc_Complex_Ocomplex)))) (let ((_let_254 (tptp.c_HOL_Oinverse__class_Oinverse _let_199 tptp.tc_Complex_Ocomplex))) (let ((_let_255 (tptp.c_HOL_Otimes__class_Otimes _let_24 _let_254 tptp.tc_Complex_Ocomplex))) (let ((_let_256 (tptp.c_HOL_Oinverse__class_Odivide _let_24 _let_199 tptp.tc_Complex_Ocomplex))) (let ((_let_257 (= _let_256 _let_255))) (let ((_let_258 (tptp.c_HOL_Otimes__class_Otimes _let_200 _let_254 tptp.tc_Complex_Ocomplex))) (let ((_let_259 (tptp.c_HOL_Oinverse__class_Odivide _let_200 _let_199 tptp.tc_Complex_Ocomplex))) (let ((_let_260 (= _let_259 _let_258))) (let ((_let_261 (tptp.c_HOL_Otimes__class_Otimes _let_24 _let_219 tptp.tc_Complex_Ocomplex))) (let ((_let_262 (= (tptp.c_HOL_Otimes__class_Otimes _let_24 (tptp.c_HOL_Ominus__class_Ominus _let_97 _let_219 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes _let_24 _let_97 tptp.tc_Complex_Ocomplex) _let_261 tptp.tc_Complex_Ocomplex)))) (let ((_let_263 (tptp.c_HOL_Otimes__class_Otimes _let_24 _let_89 tptp.tc_Complex_Ocomplex))) (let ((_let_264 (= (tptp.c_HOL_Otimes__class_Otimes _let_24 (tptp.c_HOL_Ominus__class_Ominus _let_89 _let_219 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ominus__class_Ominus _let_263 _let_261 tptp.tc_Complex_Ocomplex)))) (let ((_let_265 (= _let_226 (tptp.c_HOL_Ouminus__class_Ouminus _let_199 tptp.tc_Complex_Ocomplex)))) (let ((_let_266 (tptp.c_HOL_Ouminus__class_Ouminus _let_201 tptp.tc_Complex_Ocomplex))) (let ((_let_267 (= _let_229 _let_266))) (let ((_let_268 (tptp.c_HOL_Ominus__class_Ominus _let_24 _let_89 tptp.tc_Complex_Ocomplex))) (let ((_let_269 (tptp.c_HOL_Ouminus__class_Ouminus _let_268 tptp.tc_Complex_Ocomplex))) (let ((_let_270 (tptp.c_HOL_Ominus__class_Ominus _let_89 _let_24 tptp.tc_Complex_Ocomplex))) (let ((_let_271 (= _let_270 _let_269))) (let ((_let_272 (= (tptp.c_HOL_Ominus__class_Ominus _let_242 _let_245 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes _let_89 _let_244 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes _let_24 _let_217 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes _let_217 _let_244 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_273 (tptp.c_HOL_Otimes__class_Otimes _let_24 _let_244 tptp.tc_Complex_Ocomplex))) (let ((_let_274 (= (tptp.c_HOL_Ominus__class_Ominus _let_245 _let_93 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus _let_263 _let_273 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes _let_244 _let_89 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_275 (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_101 _let_199 tptp.tc_Complex_Ocomplex) _let_85 tptp.tc_Complex_Ocomplex))) (let ((_let_276 (tptp.c_HOL_Ouminus__class_Ouminus _let_275 tptp.tc_Complex_Ocomplex))) (let ((_let_277 (= (tptp.c_HOL_Ominus__class_Ominus _let_101 _let_85 tptp.tc_Complex_Ocomplex) _let_276))) (let ((_let_278 (tptp.c_HOL_Otimes__class_Otimes _let_229 _let_254 tptp.tc_Complex_Ocomplex))) (let ((_let_279 (= _let_278 (tptp.c_HOL_Oinverse__class_Odivide _let_229 _let_199 tptp.tc_Complex_Ocomplex)))) (let ((_let_280 (= _let_278 (tptp.c_HOL_Ominus__class_Ominus _let_255 _let_258 tptp.tc_Complex_Ocomplex)))) (let ((_let_281 (= _let_268 (tptp.c_HOL_Ouminus__class_Ouminus _let_269 tptp.tc_Complex_Ocomplex)))) (let ((_let_282 (= _let_275 (tptp.c_HOL_Ouminus__class_Ouminus _let_276 tptp.tc_Complex_Ocomplex)))) (let ((_let_283 (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_89 _let_199 tptp.tc_Complex_Ocomplex) _let_85 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_89 _let_85 tptp.tc_Complex_Ocomplex) _let_199 tptp.tc_Complex_Ocomplex)))) (let ((_let_284 (= (tptp.c_HOL_Oinverse__class_Odivide _let_201 _let_226 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Odivide _let_266 _let_227 tptp.tc_Complex_Ocomplex)))) (let ((_let_285 (not _let_203))) (let ((_let_286 (= _let_24 _let_208))) (let ((_let_287 (not _let_210))) (let ((_let_288 (not _let_2))) (let ((_let_289 (not _let_3))) (let ((_let_290 (or _let_289 _let_288 _let_287 _let_286))) (let ((_let_291 (= _let_212 (tptp.c_HOL_Otimes__class_Otimes _let_234 _let_20 tptp.tc_Complex_Ocomplex)))) (let ((_let_292 (= _let_202 (tptp.c_HOL_Otimes__class_Otimes _let_201 _let_254 tptp.tc_Complex_Ocomplex)))) (let ((_let_293 (= _let_165 (tptp.c_HOL_Oinverse__class_Odivide _let_24 _let_20 tptp.tc_Complex_Ocomplex)))) (let ((_let_294 (tptp.hAPP _let_216 tptp.v_n))) (let ((_let_295 (tptp.hAPP _let_246 tptp.v_n))) (let ((_let_296 (= _let_295 (tptp.c_HOL_Oinverse__class_Odivide _let_294 _let_208 tptp.tc_Complex_Ocomplex)))) (let ((_let_297 (tptp.c_HOL_Oinverse__class_Odivide _let_24 _let_208 tptp.tc_Complex_Ocomplex))) (let ((_let_298 (= _let_295 _let_297))) (let ((_let_299 (= _let_24 _let_294))) (let ((_let_300 (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_263 tptp.tc_Complex_Ocomplex) tptp.v_n) (tptp.c_HOL_Otimes__class_Otimes _let_294 _let_208 tptp.tc_Complex_Ocomplex)))) (let ((_let_301 (= _let_297 (tptp.c_HOL_Oinverse__class_Oinverse _let_208 tptp.tc_Complex_Ocomplex)))) (let ((_let_302 (= (tptp.c_HOL_Oinverse__class_Oinverse _let_200 tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_101 tptp.tc_Complex_Ocomplex) tptp.v_n)))) (let ((_let_303 (tptp.c_HOL_Ominus__class_Ominus _let_24 _let_208 tptp.tc_Complex_Ocomplex))) (let ((_let_304 (tptp.c_HOL_Ouminus__class_Ouminus _let_303 tptp.tc_Complex_Ocomplex))) (let ((_let_305 (= _let_209 _let_304))) (let ((_let_306 (tptp.c_HOL_Oinverse__class_Odivide _let_235 _let_208 tptp.tc_Complex_Ocomplex))) (let ((_let_307 (tptp.c_HOL_Otimes__class_Otimes _let_306 _let_219 tptp.tc_Complex_Ocomplex))) (let ((_let_308 (= _let_307 (tptp.c_HOL_Oinverse__class_Odivide _let_236 _let_208 tptp.tc_Complex_Ocomplex)))) (let ((_let_309 (tptp.c_HOL_Oinverse__class_Odivide _let_235 _let_20 tptp.tc_Complex_Ocomplex))) (let ((_let_310 (= (tptp.c_HOL_Otimes__class_Otimes _let_309 _let_219 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Odivide _let_236 _let_20 tptp.tc_Complex_Ocomplex)))) (let ((_let_311 (tptp.c_HOL_Otimes__class_Otimes _let_24 _let_208 tptp.tc_Complex_Ocomplex))) (let ((_let_312 (= (tptp.c_HOL_Ominus__class_Ominus _let_297 _let_245 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus _let_273 _let_311 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes _let_208 _let_244 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_313 (= (tptp.c_HOL_Ominus__class_Ominus _let_245 _let_297 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus _let_311 _let_273 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes _let_244 _let_208 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_314 (= (tptp.c_HOL_Oinverse__class_Oinverse _let_307 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse _let_306 tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oinverse__class_Oinverse _let_219 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_315 (= _let_309 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_309 _let_24 tptp.tc_Complex_Ocomplex) _let_24 tptp.tc_Complex_Ocomplex)))) (let ((_let_316 (= _let_303 (tptp.c_HOL_Ouminus__class_Ouminus _let_304 tptp.tc_Complex_Ocomplex)))) (let ((_let_317 (= _let_20 (tptp.c_HOL_Oinverse__class_Odivide _let_20 _let_199 tptp.tc_Complex_Ocomplex)))) (let ((_let_318 (ASSUME :args (_let_3)))) (let ((_let_319 (ASSUME :args (_let_2)))) (let ((_let_320 (_let_73))) (let ((_let_321 (ASSUME :args _let_320))) (let ((_let_322 (not _let_6))) (let ((_let_323 (or _let_322 _let_213))) (let ((_let_324 (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_325 (EQ_RESOLVE (ASSUME :args (_let_75)) (MACRO_SR_EQ_INTRO :args (_let_75 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_326 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_325 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_OrderedGroup_Ogroup__add T_a) false))))) :args (_let_324))))) (let ((_let_327 (ASSUME :args (_let_6)))) (let ((_let_328 (REORDERING (CNF_OR_POS :args (_let_323)) :args ((or _let_322 _let_213 (not _let_323)))))) (let ((_let_329 (MACRO_RESOLUTION_TRUST _let_328 _let_327 (MACRO_RESOLUTION_TRUST _let_326 _let_325 :args (_let_323 false _let_324)) :args (_let_213 false _let_6 false _let_323)))) (let ((_let_330 (or _let_111 _let_215))) (let ((_let_331 (_let_54))) (let ((_let_332 (ASSUME :args _let_331))) (let ((_let_333 ((tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))) (let ((_let_334 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_330)) :args ((or _let_111 _let_215 (not _let_330)))) _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_332 :args (tptp.tc_Complex_Ocomplex _let_24 _let_23 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_333)) :args _let_331)) _let_332 :args (_let_330 false _let_54)) :args (_let_215 false _let_4 false _let_330)))) (let ((_let_335 (not _let_1))) (let ((_let_336 (not _let_10))) (let ((_let_337 (or _let_336 _let_335 _let_220))) (let ((_let_338 (_let_42))) (let ((_let_339 (ASSUME :args _let_338))) (let ((_let_340 (ASSUME :args (_let_1)))) (let ((_let_341 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_337)) :args ((or _let_336 _let_335 _let_220 (not _let_337)))) (ASSUME :args (_let_10)) _let_340 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_339 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_Ring__and__Field_Osemiring__0 T_a) false))))) :args _let_338))) _let_339 :args (_let_337 false _let_42)) :args (_let_220 false _let_10 false _let_1 false _let_337)))) (let ((_let_342 (or _let_111 _let_127 _let_221))) (let ((_let_343 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not 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_let_248))) (let ((_let_396 (_let_36))) (let ((_let_397 (ASSUME :args _let_396))) (let ((_let_398 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_395)) :args ((or _let_335 _let_248 (not _let_395)))) _let_340 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_397 :args (tptp.tc_Complex_Ocomplex _let_234 QUANTIFIERS_INST_CBQI_PROP)) :args _let_396))) _let_397 :args (_let_395 false _let_36)) :args (_let_248 false _let_1 false _let_395)))) (let ((_let_399 (or _let_335 _let_249))) (let ((_let_400 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_399)) :args ((or _let_335 _let_249 (not _let_399)))) _let_340 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_397 :args _let_151) :args _let_396))) _let_397 :args (_let_399 false _let_36)) :args (_let_249 false _let_1 false _let_399)))) (let ((_let_401 (or _let_105 _let_127 _let_250))) (let ((_let_402 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args 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(MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_204)) :args ((or _let_111 _let_203 _let_103 (not _let_204)))) _let_115 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_920 _let_924 _let_566 _let_568 _let_911 _let_888 _let_619 _let_916 _let_913 _let_628 _let_710 _let_633 _let_586 _let_631 _let_590 _let_610 _let_579 _let_571 _let_658 _let_907 _let_656 _let_729 _let_909 _let_863 _let_191 _let_622 _let_625 _let_896 _let_661 _let_817 _let_104 _let_639 _let_892 _let_861 _let_865 _let_926 _let_606 _let_608 _let_677 _let_467 _let_859 _let_615 _let_666 _let_715 _let_898 _let_874 _let_867) (SCOPE (FALSE_ELIM (TRANS (CONG _let_469 (TRANS _let_751 _let_572 _let_860 (CONG _let_864 _let_862 _let_565 :args _let_595) _let_866 (CONG _let_710 _let_867 _let_565 :args _let_595) (CONG (TRANS _let_711 _let_715) (TRANS _let_868 (TRANS (CONG _let_608 _let_872 _let_565 :args _let_564) (CONG (SYMM _let_943) (SYMM _let_873) _let_565 :args _let_564) _let_875 (CONG (TRANS (CONG _let_743 _let_942 _let_565 :args _let_564) (SYMM _let_946)) (TRANS (CONG (SYMM (TRANS _let_609 _let_467)) _let_606 _let_565 :args _let_574) _let_742 _let_616 _let_741 _let_740) _let_565 :args _let_595) (CONG (TRANS _let_946 (CONG (TRANS (SYMM _let_740) _let_923 _let_898 (SYMM _let_940) (CONG _let_939 _let_938 _let_565 :args _let_574)) (TRANS _let_608 (TRANS _let_609 _let_656 _let_685 _let_945 _let_666 _let_944 (CONG _let_657 (TRANS _let_876 _let_612) _let_565 :args _let_574))) _let_565 :args _let_564)) (TRANS (TRANS _let_893 _let_612) (TRANS _let_611 _let_656 _let_685 _let_945 _let_666 _let_944 (CONG (TRANS _let_657 _let_612) (SYMM _let_941) _let_565 :args _let_574))) _let_565 :args _let_595) _let_908 (CONG (TRANS _let_910 _let_740) (TRANS _let_943 _let_609) _let_565 :args _let_564) (CONG (TRANS _let_893 (SYMM _let_942)) (TRANS _let_892 (SYMM _let_743)) _let_565 :args _let_564) (CONG _let_942 _let_743 _let_565 :args _let_564) _let_912 (CONG (TRANS _let_914 (TRANS (CONG _let_919 _let_608 _let_565 :args _let_564) _let_915)) _let_565 :args _let_692) _let_917 (CONG (CONG _let_902 _let_714 _let_565 :args _let_574) _let_918 _let_565 :args _let_574) _let_921 (CONG (TRANS (CONG (SYMM _let_939) _let_922 _let_565 :args _let_574) _let_940 _let_899 _let_897 _let_740 _let_606 _let_904 _let_903) _let_714 _let_565 :args _let_574) (CONG (TRANS _let_902 _let_893) (CONG _let_872 _let_656 _let_565 :args _let_564) _let_565 :args _let_574) _let_925 (CONG (TRANS (CONG _let_612 _let_870 _let_565 :args _let_574) _let_927 (CONG (CONG (TRANS _let_626 _let_191) _let_565 :args _let_578) _let_618 :args _let_576) _let_869) _let_937 _let_565 :args _let_564))) _let_565 :args _let_595) _let_717 _let_730) :args _let_190) _let_728)) :args (_let_283 _let_262 _let_260 _let_257 _let_281 _let_264 _let_250 _let_282 _let_271 _let_225 _let_230 _let_224 _let_95 _let_239 _let_247 _let_222 _let_94 _let_280 _let_221 _let_272 _let_220 _let_203 _let_243 _let_267 _let_88 _let_233 _let_215 _let_241 _let_213 _let_277 _let_559 _let_98 _let_211 _let_228 _let_284 _let_238 _let_100 _let_86 _let_248 _let_249 _let_279 _let_251 _let_237 _let_252 _let_253 _let_274 _let_265))) (MODUS_PONENS (AND_INTRO _let_924 _let_566 _let_568 _let_920 _let_932 _let_911 _let_888 _let_782 _let_817 _let_619 _let_916 _let_913 _let_628 _let_710 _let_633 _let_586 _let_631 _let_590 _let_610 _let_579 _let_571 _let_658 _let_907 _let_656 _let_931 _let_729 _let_909 _let_863 _let_191 _let_622 _let_625 _let_896 _let_661 _let_639 _let_892 _let_861 _let_865 _let_926 _let_606 _let_608 _let_677 _let_467 _let_859 _let_615 _let_666 _let_715 _let_898 _let_874 _let_867) (SCOPE (TRANS _let_784 (CONG (TRANS (CONG _let_919 _let_565 :args _let_578) (CONG (TRANS _let_902 _let_893 _let_586) _let_565 :args _let_578) (CONG (TRANS _let_587 (TRANS _let_608 (SYMM _let_933) (CONG _let_612 _let_894 _let_565 :args _let_595) (SYMM _let_931)) _let_579) _let_565 :args _let_578) _let_581) _let_930 _let_929 _let_565 :args _let_928) (SYMM _let_730) (CONG _let_715 _let_714 _let_565 :args _let_595) (CONG (TRANS _let_716 _let_710) (TRANS (TRANS (CONG (TRANS (SYMM _let_869) (CONG (CONG (TRANS _let_192 _let_627) _let_565 :args _let_578) _let_618 :args _let_576) (SYMM _let_927) (CONG _let_613 _let_640 _let_565 :args _let_574)) (SYMM _let_886) _let_565 :args _let_564) (SYMM _let_925) (CONG (TRANS _let_894 _let_919) (CONG _let_871 _let_657 _let_565 :args _let_564) _let_565 :args _let_574) (CONG (TRANS _let_641 _let_901 _let_607 _let_637 _let_923 _let_898 (SYMM _let_906) (CONG _let_905 (SYMM _let_922) _let_565 :args _let_574)) _let_714 _let_565 :args _let_574) (SYMM _let_921) (CONG (CONG _let_919 _let_714 _let_565 :args _let_574) _let_918 _let_565 :args _let_574) (SYMM _let_917) (CONG (TRANS (TRANS (SYMM _let_915) (CONG _let_902 _let_609 _let_565 :args _let_564)) (SYMM _let_914)) _let_565 :args _let_692) (SYMM _let_912) (CONG _let_882 _let_638 _let_565 :args _let_564) (CONG (TRANS (SYMM _let_882) _let_894) (TRANS _let_887 _let_893) _let_565 :args _let_564) (CONG (TRANS _let_637 (SYMM _let_910)) _let_707 _let_565 :args _let_564) (SYMM _let_908) (CONG (TRANS (CONG (TRANS (CONG (SYMM _let_905) (SYMM _let_731) _let_565 :args _let_574) _let_906 _let_899 _let_897 _let_895) (TRANS (TRANS (CONG _let_656 (TRANS _let_613 _let_878) _let_565 :args _let_574) _let_885 _let_667 _let_884 _let_883 _let_657 _let_608) _let_609) _let_565 :args _let_564) (SYMM _let_891)) (TRANS (TRANS (CONG (TRANS _let_613 _let_656) (SYMM _let_877) _let_565 :args _let_574) _let_885 _let_667 _let_884 _let_883 _let_657 _let_612) (TRANS _let_613 _let_894)) _let_565 :args _let_595) (CONG (TRANS _let_891 (CONG _let_638 _let_882 _let_565 :args _let_564)) (TRANS _let_637 _let_636 _let_617 _let_614 (CONG (TRANS _let_609 _let_597) _let_607 _let_565 :args _let_574)) _let_565 :args _let_595) (SYMM _let_875) (CONG (TRANS _let_592 _let_608) _let_873 _let_565 :args _let_564) (CONG _let_609 _let_871 _let_565 :args _let_564)) _let_867) _let_565 :args _let_595) (CONG _let_711 _let_868 _let_565 :args _let_595) (SYMM _let_866) (CONG (SYMM _let_864) (SYMM _let_862) _let_565 :args _let_595) (SYMM _let_860) _let_573 _let_570) :args (_let_262 _let_260 _let_257 _let_283 _let_99 _let_281 _let_264 _let_92 _let_277 _let_250 _let_282 _let_271 _let_225 _let_230 _let_224 _let_95 _let_239 _let_247 _let_222 _let_94 _let_280 _let_221 _let_272 _let_220 _let_218 _let_203 _let_243 _let_267 _let_88 _let_233 _let_215 _let_241 _let_213 _let_98 _let_211 _let_228 _let_284 _let_238 _let_100 _let_86 _let_248 _let_249 _let_279 _let_251 _let_237 _let_252 _let_253 _let_274 _let_265)))) :args (_let_559 _let_213 _let_86 _let_215 _let_88 _let_203 _let_92 _let_218 _let_220 _let_221 _let_94 _let_211 _let_224 _let_222 _let_95 _let_225 _let_228 _let_230 _let_233 _let_237 _let_98 _let_238 _let_239 _let_241 _let_99 _let_243 _let_247 _let_248 _let_249 _let_250 _let_100 _let_251 _let_252 _let_253 _let_257 _let_260 _let_262 _let_264 _let_265 _let_267 _let_271 _let_272 _let_274 _let_277 _let_279 _let_280 _let_281 _let_282 _let_283 _let_284)) _let_563 :args ((not (and _let_559 _let_213 _let_86 _let_215 _let_88 _let_203 _let_92 _let_218 _let_220 _let_221 _let_94 _let_211 _let_224 _let_222 _let_95 _let_225 _let_228 _let_230 _let_233 _let_237 _let_98 _let_238 _let_239 _let_241 _let_99 _let_243 _let_247 _let_248 _let_249 _let_250 _let_100 _let_251 _let_252 _let_253 _let_257 _let_260 _let_262 _let_264 _let_265 _let_267 _let_271 _let_272 _let_274 _let_277 _let_279 _let_280 _let_281 _let_282 _let_283 _let_284)) SB_LITERAL))) (CONG _let_560 _let_558 _let_557 _let_556 _let_186 _let_555 (REFL :args (_let_810)) (REFL :args ((not _let_218))) _let_554 _let_553 _let_552 (REFL :args ((not _let_211))) _let_551 _let_550 _let_549 _let_548 (REFL :args ((not _let_228))) _let_547 _let_546 _let_545 _let_544 (REFL :args ((not _let_238))) _let_543 (REFL :args ((not _let_241))) (REFL :args (_let_858)) (REFL :args ((not _let_243))) _let_542 _let_541 _let_461 _let_540 _let_539 _let_538 _let_537 (REFL :args ((not _let_253))) _let_536 _let_535 (REFL :args ((not _let_262))) (REFL :args ((not _let_264))) (REFL :args ((not _let_265))) (REFL :args ((not _let_267))) (REFL :args ((not _let_271))) (REFL :args ((not _let_272))) (REFL :args ((not _let_274))) (REFL :args (_let_809)) (REFL :args ((not _let_279))) _let_534 (REFL :args ((not _let_281))) (REFL :args ((not _let_282))) (REFL :args ((not _let_283))) (REFL :args ((not _let_284))) :args _let_185)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_855)) :args ((or _let_127 _let_111 _let_284 (not _let_855)))) _let_132 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_857 :args (tptp.tc_Complex_Ocomplex _let_201 _let_226 QUANTIFIERS_INST_CBQI_PROP)) :args _let_856))) _let_857 :args (_let_855 false _let_59)) :args (_let_284 false _let_17 false _let_4 false _let_855)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_852)) :args ((or _let_134 _let_283 (not _let_852)))) _let_138 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_854 :args (tptp.tc_Complex_Ocomplex _let_89 _let_199 _let_85 QUANTIFIERS_INST_CBQI_PROP)) :args _let_853)) _let_854 :args (_let_852 false _let_70)) :args (_let_283 false _let_16 false _let_852)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_851)) :args ((or _let_322 _let_282 (not _let_851)))) _let_327 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_484 :args (tptp.tc_Complex_Ocomplex _let_275 QUANTIFIERS_INST_CBQI_PROP)) :args _let_485)) _let_484 :args (_let_851 false _let_483)) :args (_let_282 false _let_6 false _let_851)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_850)) :args ((or _let_322 _let_281 (not _let_850)))) _let_327 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_484 :args (tptp.tc_Complex_Ocomplex _let_268 QUANTIFIERS_INST_CBQI_PROP)) :args _let_485)) _let_484 :args (_let_850 false _let_483)) :args (_let_281 false _let_6 false _let_850)) _let_481 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_849)) :args ((or _let_111 _let_288 _let_279 (not _let_849)))) _let_115 _let_319 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_423 :args (tptp.tc_Complex_Ocomplex _let_229 _let_199 QUANTIFIERS_INST_CBQI_PROP)) :args _let_422))) _let_423 :args (_let_849 false _let_53)) :args (_let_279 false _let_4 false _let_2 false _let_849)) _let_793 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_848)) :args ((or _let_111 _let_444 _let_439 _let_274 (not _let_848)))) _let_115 _let_449 _let_470 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_442 :args (tptp.tc_Complex_Ocomplex _let_24 _let_244 _let_24 _let_89 QUANTIFIERS_INST_E_MATCHING _let_443)) :args _let_441))) _let_442 :args (_let_848 false _let_72)) :args (_let_274 false _let_4 true _let_444 true _let_439 false _let_848)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_844)) :args ((or _let_111 _let_439 _let_843 _let_272 (not _let_844)))) _let_115 _let_470 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_846)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_465 _let_610) (SCOPE (FALSE_ELIM (TRANS (CONG _let_469 _let_611 :args _let_190) _let_466)) :args _let_847)) :args _let_847)) :args (true _let_846)) (CONG _let_462 _let_550 (REFL :args (_let_845)) :args _let_185)) _let_459 _let_352 :args (_let_845 true _let_451 false _let_222)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_442 :args (tptp.tc_Complex_Ocomplex _let_89 _let_217 _let_24 _let_244 QUANTIFIERS_INST_E_MATCHING _let_443)) :args _let_441))) _let_442 :args (_let_844 false _let_72)) :args (_let_272 false _let_4 true _let_439 true _let_843 false _let_844)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_842)) :args ((or _let_361 _let_271 (not _let_842)))) _let_366 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_364 :args (tptp.tc_Complex_Ocomplex _let_24 _let_89 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_365)) :args _let_363))) _let_364 :args (_let_842 false _let_78)) :args (_let_271 false _let_9 false _let_842)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_841)) :args ((or _let_361 _let_267 (not _let_841)))) _let_366 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_364 :args (tptp.tc_Complex_Ocomplex _let_200 _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_365)) :args _let_363))) _let_364 :args (_let_841 false _let_78)) :args (_let_267 false _let_9 false _let_841)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_840)) :args ((or _let_361 _let_265 (not _let_840)))) _let_366 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_364 :args (tptp.tc_Complex_Ocomplex _let_26 _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_365)) :args _let_363))) _let_364 :args (_let_840 false _let_78)) :args (_let_265 false _let_9 false _let_840)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_839)) :args ((or _let_476 _let_264 (not _let_839)))) _let_480 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_837 :args (tptp.tc_Complex_Ocomplex _let_24 _let_89 _let_219 QUANTIFIERS_INST_E_MATCHING _let_838)) :args _let_836)) _let_837 :args (_let_839 false _let_81)) :args (_let_264 false _let_15 false _let_839)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_835)) :args ((or _let_476 _let_262 (not _let_835)))) _let_480 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_837 :args (tptp.tc_Complex_Ocomplex _let_24 _let_97 _let_219 QUANTIFIERS_INST_E_MATCHING _let_838)) :args _let_836)) _let_837 :args (_let_835 false _let_81)) :args (_let_262 false _let_15 false _let_835)) _let_427 _let_425 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_834)) :args ((or _let_412 _let_253 (not _let_834)))) _let_417 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_415 :args (tptp.tc_Complex_Ocomplex _let_23 _let_85 tptp.v_k QUANTIFIERS_INST_E_MATCHING _let_416)) :args _let_414)) _let_415 :args (_let_834 false _let_63)) :args (_let_253 false _let_14 false _let_834)) _let_410 _let_406 _let_152 _let_402 _let_400 _let_398 _let_394 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_833)) :args ((or _let_111 _let_451 _let_243 (not _let_833)))) _let_115 _let_459 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_828 :args (tptp.tc_Complex_Ocomplex _let_23 _let_24 tptp.v_k QUANTIFIERS_INST_E_MATCHING _let_829)) :args _let_827))) _let_828 :args (_let_833 false _let_43)) :args (_let_243 false _let_4 true _let_451 false _let_833)) _let_146 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_832)) :args ((or _let_111 _let_241 (not _let_832)))) _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_332 :args (tptp.tc_Complex_Ocomplex _let_23 _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_333)) :args _let_331)) _let_332 :args (_let_832 false _let_54)) :args (_let_241 false _let_4 false _let_832)) _let_386 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_831)) :args ((or _let_412 _let_238 (not _let_831)))) _let_417 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_415 :args (tptp.tc_Complex_Ocomplex _let_24 _let_87 tptp.v_k QUANTIFIERS_INST_E_MATCHING _let_416)) :args _let_414)) _let_415 :args (_let_831 false _let_63)) :args (_let_238 false _let_14 false _let_831)) _let_143 _let_382 _let_377 _let_367 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_830)) :args ((or _let_361 _let_228 (not _let_830)))) _let_366 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_364 :args (tptp.tc_Complex_Ocomplex _let_24 _let_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_365)) :args _let_363))) _let_364 :args (_let_830 false _let_78)) :args (_let_228 false _let_9 false _let_830)) _let_360 _let_139 _let_356 _let_352 _let_133 _let_345 _let_341 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_826)) :args ((or _let_111 _let_169 _let_218 (not _let_826)))) _let_115 _let_176 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_828 :args (tptp.tc_Complex_Ocomplex _let_24 _let_23 tptp.v_k QUANTIFIERS_INST_E_MATCHING _let_829)) :args _let_827))) _let_828 :args (_let_826 false _let_43)) :args (_let_218 false _let_4 true _let_169 false _let_826)) _let_126 _let_116 _let_334 _let_110 _let_329 _let_104 (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_775)) :args ((or _let_289 _let_774 _let_772 _let_773 (not _let_775)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_825 :args (tptp.tc_Complex_Ocomplex _let_270 _let_209 QUANTIFIERS_INST_CBQI_PROP)) :args _let_824))) _let_825 :args (_let_775 false _let_77)) _let_318 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_822)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_782 _let_779 _let_814 _let_812 _let_823) (SCOPE (TRANS _let_784 _let_781 (CONG _let_820 (SYMM _let_823) _let_565 :args _let_595) _let_815 _let_813) :args (_let_92 _let_753 _let_762 _let_771 _let_773))) :args (_let_92 _let_753 _let_773 _let_771 _let_762))) :args (true _let_822)) :args ((or _let_810 _let_776 _let_770 (not _let_773) _let_808 _let_807))) _let_806 _let_804 _let_126 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_811)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_782 _let_661 _let_821 _let_608 _let_191 _let_817 _let_579 _let_816 _let_696 _let_693 _let_812 _let_779 _let_606 _let_702 _let_639 _let_814) (SCOPE (TRANS _let_661 _let_750 (CONG _let_785 _let_565 :args _let_692) (SYMM (SYMM _let_821)) (CONG _let_820 (TRANS (CONG (SYMM _let_819) _let_565 :args _let_692) (CONG (TRANS _let_819 (TRANS (SYMM (SYMM _let_816)) (CONG _let_696 _let_565 :args _let_692) _let_703)) _let_565 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:args (_let_794 false _let_61)) :args (_let_767 false _let_17 false _let_4 false _let_794)) _let_793 _let_432 _let_152 _let_143 _let_373 _let_133 _let_126 _let_116 _let_110 _let_329 (REORDERING (CNF_OR_POS :args (_let_766)) :args ((or _let_111 _let_210 _let_755 _let_764 _let_765 (not _let_766)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_789 :args (tptp.tc_Complex_Ocomplex _let_209 _let_270 _let_270 _let_209 QUANTIFIERS_INST_CBQI_PROP)) :args _let_788))) _let_789 :args (_let_766 false _let_56)) _let_115 (REORDERING (CNF_OR_POS :args (_let_763)) :args ((or _let_127 _let_111 _let_210 _let_762 (not _let_763)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_787 :args (tptp.tc_Complex_Ocomplex _let_209 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_786))) _let_787 :args (_let_763 false _let_31)) _let_115 _let_132 (RESOLUTION (CNF_AND_NEG :args (_let_777)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_778 _let_779 _let_782 _let_661 _let_693 _let_194) (SCOPE (TRANS _let_780 _let_783 _let_196 (CONG _let_749 _let_565 :args _let_621) (CONG _let_785 _let_565 :args _let_621) (SYMM (SYMM _let_778))) :args (_let_759 _let_753 _let_92 _let_213 _let_291 _let_167))) :args (_let_213 _let_167 _let_92 _let_291 _let_753 _let_759))) :args (true _let_777)) _let_328 _let_327 _let_326 _let_325 _let_181 _let_180 _let_179 _let_125 _let_124 _let_123 _let_122 _let_121 _let_372 _let_319 _let_371 _let_370 (REORDERING (CNF_OR_POS :args (_let_760)) :args ((or _let_127 _let_111 _let_759 (not _let_760)))) _let_132 _let_115 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_385 :args (tptp.tc_Complex_Ocomplex _let_209 _let_270 QUANTIFIERS_INST_E_MATCHING ((tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a)))) :args _let_384)) _let_385 :args ((or _let_776 _let_210 _let_755) false _let_775 false _let_3 true _let_773 false _let_771 true _let_770 false _let_92 true _let_772 false _let_316 false _let_771 true _let_770 false _let_767 false _let_277 false _let_305 false _let_100 false _let_98 false _let_291 false _let_94 false _let_92 false _let_88 false _let_86 false _let_213 false _let_764 false _let_766 false _let_4 false _let_762 false _let_763 false _let_4 false _let_17 false _let_761 false _let_213 false _let_6 false _let_323 false _let_324 false _let_167 false _let_177 false _let_178 false _let_92 false _let_49 false _let_48 false _let_119 false _let_120 false _let_291 false _let_2 false _let_368 false _let_71 false _let_759 false _let_17 false _let_4 false _let_760 false _let_60)) (REORDERING (CNF_OR_POS :args (_let_757)) :args ((or _let_289 _let_288 _let_211 _let_756 (not _let_757)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_321 :args (tptp.tc_Complex_Ocomplex _let_89 _let_24 QUANTIFIERS_INST_CBQI_PROP)) :args _let_320))) _let_321 :args (_let_757 false _let_73)) _let_319 _let_318 (REORDERING (CNF_OR_POS :args (_let_754)) :args ((or _let_111 _let_211 _let_753 (not _let_754)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_206 :args (tptp.tc_Complex_Ocomplex _let_89 tptp.v_n QUANTIFIERS_INST_E_MATCHING _let_207)) :args _let_205))) _let_206 :args (_let_754 false _let_46)) _let_115 :args ((or _let_211 _let_210) true _let_755 false _let_757 false _let_2 false _let_3 false _let_753 false _let_754 false _let_4)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO (MODUS_PONENS (AND_INTRO _let_104 _let_729 _let_712 _let_710 _let_579 _let_583 _let_586 _let_590 _let_705 _let_467 _let_656 _let_608 _let_677 _let_666 _let_661 _let_658 _let_598 _let_603 _let_606 _let_610 _let_615 _let_619 _let_622 _let_625 _let_628 _let_631 _let_633 _let_639 _let_191 _let_702 _let_696 _let_689 _let_693 _let_647 _let_650 _let_654 _let_673 _let_670 _let_593 _let_571 _let_568 _let_566) (SCOPE (FALSE_ELIM (TRANS (CONG _let_469 (TRANS _let_751 _let_572 (CONG (TRANS (TRANS (CONG _let_707 _let_708 _let_565 :args _let_564) _let_594 (CONG (TRANS (TRANS (CONG (SYMM _let_746) (SYMM _let_747) _let_565 :args _let_564) _let_690) (TRANS _let_663 _let_750 (CONG (TRANS _let_748 (TRANS _let_691 _let_698)) _let_565 :args _let_692) _let_701) (TRANS _let_699 _let_703 (CONG _let_747 _let_746 _let_565 :args _let_564))) (TRANS _let_745 _let_604 _let_744 (SYMM _let_737) _let_648 _let_681 (CONG (TRANS _let_651 (TRANS _let_680 _let_654 (CONG (TRANS _let_599 (TRANS _let_656 _let_739 _let_738 _let_668)) _let_596 _let_565 :args _let_595) _let_671)) _let_565 :args _let_621) _let_674 (CONG (TRANS (CONG (TRANS (TRANS (CONG (TRANS _let_678 _let_600) _let_596 _let_565 :args _let_595) _let_655 _let_582) _let_653) _let_565 :args _let_621) _let_652 _let_649 _let_737) _let_735 _let_565 :args _let_574)) _let_565 :args _let_595) _let_706 (CONG _let_585 _let_592 _let_565 :args _let_564)) _let_710) _let_575 _let_565 :args _let_574) (CONG _let_711 _let_575 _let_565 :args _let_574) _let_713 _let_730) :args _let_190) _let_728)) :args (_let_559 _let_203 _let_292 _let_230 _let_94 _let_298 _let_95 _let_247 _let_312 _let_249 _let_220 _let_86 _let_248 _let_237 _let_213 _let_221 _let_299 _let_300 _let_100 _let_222 _let_251 _let_250 _let_233 _let_215 _let_225 _let_239 _let_224 _let_98 _let_88 _let_316 _let_305 _let_210 _let_291 _let_302 _let_301 _let_296 _let_314 _let_308 _let_313 _let_280 _let_257 _let_260))) (MODUS_PONENS (AND_INTRO _let_727 _let_593 _let_721 _let_566 _let_598 _let_670 _let_661 _let_702 _let_705 _let_639 _let_710 _let_628 _let_610 _let_579 _let_647 _let_603 _let_718 _let_656 _let_622 _let_625 _let_673 _let_191 _let_633 _let_586 _let_631 _let_712 _let_619 _let_194 _let_571 _let_693 _let_658 _let_719 _let_590 _let_654 _let_568 _let_689 _let_583 _let_467 _let_726 _let_608 _let_677 _let_606 _let_615 _let_666 _let_715 _let_650 _let_696) (SCOPE (TRANS (SYMM (SYMM _let_727)) (CONG (TRANS (TRANS _let_194 _let_719 _let_723 _let_722 (SYMM (SYMM _let_726)) (CONG (TRANS (CONG (SYMM _let_724) _let_725 _let_565 :args _let_574) (CONG _let_724 _let_656 _let_565 :args _let_574) (SYMM (SYMM _let_721)) _let_720 (SYMM _let_719) _let_195) _let_679 _let_565 :args _let_595) (CONG (TRANS (SYMM _let_700) (SYMM _let_704)) (TRANS _let_678 (TRANS (SYMM (SYMM _let_718)) _let_682 _let_648 _let_681 (SYMM _let_672) _let_674 (SYMM _let_683))) _let_565 :args _let_595) _let_706 (SYMM _let_709)) _let_715) _let_714 _let_565 :args _let_595) _let_717 (SYMM _let_713) (CONG _let_710 _let_575 _let_565 :args _let_574) (CONG (TRANS _let_711 (TRANS _let_709 (SYMM _let_706) (CONG (TRANS _let_704 _let_700 (TRANS _let_691 (CONG _let_688 _let_686 _let_565 :args _let_564))) (TRANS _let_683 (SYMM _let_674) _let_672 _let_652 _let_649 _let_646 _let_645 _let_605 _let_602) _let_565 :args _let_595) (SYMM _let_594) (CONG _let_592 _let_585 _let_565 :args _let_564))) _let_575 _let_565 :args _let_574) _let_573 _let_570) :args (_let_317 _let_313 _let_310 _let_260 _let_299 _let_308 _let_213 _let_316 _let_312 _let_98 _let_230 _let_225 _let_222 _let_94 _let_302 _let_300 _let_286 _let_220 _let_233 _let_215 _let_314 _let_88 _let_224 _let_95 _let_239 _let_292 _let_250 _let_167 _let_280 _let_291 _let_221 _let_293 _let_247 _let_296 _let_257 _let_210 _let_298 _let_249 _let_315 _let_86 _let_248 _let_100 _let_251 _let_237 _let_252 _let_301 _let_305)))) :args (_let_559 _let_213 _let_167 _let_86 _let_215 _let_88 _let_203 _let_220 _let_221 _let_94 _let_224 _let_222 _let_95 _let_225 _let_230 _let_291 _let_233 _let_237 _let_98 _let_239 _let_292 _let_293 _let_296 _let_298 _let_247 _let_248 _let_249 _let_210 _let_286 _let_250 _let_100 _let_251 _let_252 _let_299 _let_300 _let_301 _let_257 _let_260 _let_302 _let_305 _let_312 _let_313 _let_308 _let_310 _let_314 _let_315 _let_280 _let_316 _let_317)) _let_563 :args ((not (and _let_559 _let_213 _let_167 _let_86 _let_215 _let_88 _let_203 _let_220 _let_221 _let_94 _let_224 _let_222 _let_95 _let_225 _let_230 _let_291 _let_233 _let_237 _let_98 _let_239 _let_292 _let_293 _let_296 _let_298 _let_247 _let_248 _let_249 _let_210 _let_286 _let_250 _let_100 _let_251 _let_252 _let_299 _let_300 _let_301 _let_257 _let_260 _let_302 _let_305 _let_312 _let_313 _let_308 _let_310 _let_314 _let_315 _let_280 _let_316 _let_317)) SB_LITERAL))) (CONG _let_560 _let_558 _let_187 _let_557 _let_556 _let_186 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 (REFL :args (_let_522)) _let_546 _let_545 _let_544 _let_543 (REFL :args (_let_517)) (REFL :args (_let_516)) (REFL :args (_let_515)) (REFL :args (_let_514)) _let_542 _let_541 _let_461 (REFL :args (_let_287)) (REFL :args (_let_511)) _let_540 _let_539 _let_538 _let_537 (REFL :args (_let_506)) (REFL :args (_let_505)) (REFL :args (_let_504)) _let_536 _let_535 (REFL :args (_let_501)) (REFL :args (_let_500)) (REFL :args (_let_499)) (REFL :args (_let_498)) (REFL :args (_let_497)) (REFL :args (_let_496)) (REFL :args (_let_495)) (REFL :args (_let_494)) _let_534 (REFL :args (_let_492)) (REFL :args (_let_491)) :args _let_185)) :args ((or _let_84 _let_533 _let_184 _let_532 _let_531 _let_183 _let_285 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_287 _let_512 _let_460 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_488)) :args ((or _let_487 _let_317 (not _let_488)))) (ASSUME :args (_let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_490 :args (tptp.tc_Complex_Ocomplex _let_199 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_489))) _let_490 :args (_let_488 false _let_489)) :args (_let_317 false _let_12 false _let_488)) _let_486 _let_481 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_473)) :args ((or _let_127 _let_111 _let_451 _let_315 (not _let_473)))) _let_132 _let_115 _let_459 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_475 :args (tptp.tc_Complex_Ocomplex _let_309 _let_24 QUANTIFIERS_INST_CBQI_PROP)) :args _let_474))) _let_475 :args (_let_473 false _let_52)) :args (_let_315 false _let_17 false _let_4 true _let_451 false _let_473)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_472)) :args ((or _let_127 _let_111 _let_314 (not _let_472)))) _let_132 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_376 :args (tptp.tc_Complex_Ocomplex _let_306 _let_219 QUANTIFIERS_INST_CBQI_PROP)) :args _let_375)) _let_376 :args (_let_472 false _let_68)) :args (_let_314 false _let_17 false _let_4 false _let_472)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_471)) :args ((or _let_111 _let_439 _let_438 _let_313 (not _let_471)))) _let_115 _let_470 _let_450 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_442 :args (tptp.tc_Complex_Ocomplex _let_24 _let_244 _let_24 _let_208 QUANTIFIERS_INST_E_MATCHING _let_443)) :args _let_441))) _let_442 :args (_let_471 false _let_72)) :args (_let_313 false _let_4 true _let_439 true _let_438 false _let_471)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_440)) :args ((or _let_111 _let_439 _let_438 _let_312 (not _let_440)))) _let_115 _let_470 _let_450 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_442 :args (tptp.tc_Complex_Ocomplex _let_24 _let_208 _let_24 _let_244 QUANTIFIERS_INST_E_MATCHING _let_443)) :args _let_441))) _let_442 :args (_let_440 false _let_72)) :args (_let_312 false _let_4 true _let_439 true _let_438 false _let_440)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_437)) :args ((or _let_127 _let_111 _let_310 (not _let_437)))) _let_132 _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_435 :args 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_let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 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 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(tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_x T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.c_Suc V_q)) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.hAPP _let_1 V_q) T_a))))) _let_82 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_w $$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.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_P $$unsorted) (T_a $$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 $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$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 ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (= V_m V_n))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.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) tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_m V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_n V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_x $$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.c_HOL_Oord__class_Oless V_x (tptp.c_Suc _let_2) tptp.tc_nat)))))) (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)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$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_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat))))) _let_81 (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)))) _let_80 (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)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_n tptp.tc_nat) tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_k))) (or (tptp.c_HOL_Oord__class_Oless (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) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_m))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= _let_1 V_n) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a) (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_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.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a))))) (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.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_i V_k tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_j V_k tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_i tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_j tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (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) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))) (forall ((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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m T_a))))) _let_79 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) _let_78 (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) (tptp.c_Suc V_n) tptp.tc_nat)))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_x) (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_x V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((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.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) _let_77 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x (tptp.c_HOL_Ominus__class_Ominus V_y V_z T_a) T_a) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_z T_a)) (not (tptp.c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_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_21 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.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_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 $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (= V_x V_y))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$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 $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_i) V_k tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_j V_k tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_i V_j tptp.tc_nat)))) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat)) (forall ((V_n $$unsorted)) (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_n) tptp.tc_nat)) (forall ((T_a $$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.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (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) tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_k V_m tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes V_k V_n tptp.tc_nat) tptp.tc_nat)))) (forall ((T_a $$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.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_lessequals _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$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.c_lessequals _let_2 _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (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.c_lessequals _let_2 V_a T_a) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals _let_2 V_a T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_lessequals V_a _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_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 $$unsorted) (V_b $$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_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (= V_a _let_1) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((V_n $$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 (= 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(tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Suc V_m) V_n tptp.tc_nat)))) _let_76 (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.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a))))) (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 $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) _let_75 (forall ((T_a $$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))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$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_74 (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_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) _let_73 (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_x T_a) (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) _let_1) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) _let_1) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.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.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.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_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1)) (= V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_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.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_w $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$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))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$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.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_a T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_a T_a) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a)))))) (forall ((T_a $$unsorted) (V_w $$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.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_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))))) _let_72 (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$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_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_w $$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))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals _let_2 _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) _let_71 (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals _let_2 V_a T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_lessequals V_a _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) _let_70 (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_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (not (tptp.c_lessequals V_x _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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 ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_Suc V_x) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))) _let_69 (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) _let_68 (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 $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat) (not 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(tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (= V_a _let_1) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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 $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_b T_a) V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) _let_67 (forall ((T_a $$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))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a) V_x))) _let_66 (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)))) (not (tptp.c_HOL_Oord__class_Oless _let_21 _let_21 tptp.tc_nat)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= V_n _let_1)))) (forall ((V_nat_H $$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 ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (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_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 ((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.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (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.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_x) (tptp.hAPP _let_1 V_y) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$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.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_n) (tptp.hAPP _let_1 V_N) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_m $$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.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) (tptp.c_Suc V_n)) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) _let_65 (forall ((T_a $$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.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_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.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (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))))) (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))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))))) _let_64 _let_63 _let_62 (forall ((T_a $$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)))) _let_61 _let_60 (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) (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 $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) _let_59 (forall ((T_a $$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_58 (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.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) V_x T_a)))) (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.c_lessequals V_xa (tptp.c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1 V_xa V_x V_f V_g T_a T_b) 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.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_N) (tptp.hAPP _let_1 V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_N tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) (tptp.c_Suc V_n)) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.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.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= _let_2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) _let_2) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) _let_1) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (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.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_Finite__Set_Osetsum V_f (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_Suc V_n) tptp.tc_nat) tptp.tc_nat T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) _let_57 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_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.c_lessequals (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) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) V_n) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) V_n) _let_1 T_a))))) (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))))) _let_56 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_w $$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.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_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.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$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.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_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.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _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))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_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.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((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))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b 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_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.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (tptp.c_HOL_Oord__class_Oless _let_21 _let_55 tptp.tc_nat) (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.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_Suc V_m) tptp.tc_nat)) (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_Suc V_n) tptp.tc_nat)))) (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.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_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.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (= (tptp.c_HOL_Otimes__class_Otimes _let_55 _let_55 tptp.tc_nat) _let_55) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n V_n tptp.tc_nat))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_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.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_lessequals _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$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 ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Otimes__class_Otimes V_n V_m tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Otimes__class_Otimes V_m V_n tptp.tc_nat) tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat))))) _let_54 _let_53 (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.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals _let_2 _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$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.c_lessequals _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_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.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals _let_2 V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_lessequals V_a _let_2 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not 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(tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_lessequals _let_2 _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_lessequals _let_1 _let_2 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_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.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_a $$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.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let 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T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not 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(V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_c $$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))) _let_52 (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_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))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_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.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_d tptp.tc_nat)))) (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.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_m V_n)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) V_n) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (tptp.c_Ring__and__Field_Odvd__class_Odvd _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) V_n) T_a)))) _let_51 _let_50 (forall ((T_a $$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_49 _let_48 (= (tptp.c_Complex_Oexpi _let_20) _let_24) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_lessequals (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (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.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower V_a T_a) _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) V_n) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_1 T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) _let_47 (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$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))))) _let_46 _let_45 _let_44 (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_43 _let_42 _let_41 _let_40 _let_39 _let_38 (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower _let_1 T_a) V_n) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) _let_37 _let_36 _let_35 (forall ((T_a $$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_34 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.c_FFT__Mirabelle_Oroot V_n) tptp.tc_Complex_Ocomplex) V_n) (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (forall ((T_a $$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))))) _let_33 _let_32 (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)))) _let_31 (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)))) _let_30 _let_29 (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) _let_19 (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) _let_18 _let_17 _let_16 _let_15 (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex) _let_14 _let_13 _let_12 (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Complex_Ocomplex) _let_11 (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 (tptp.class_Ring__and__Field_Oring tptp.tc_Complex_Ocomplex) _let_3 (tptp.class_Ring__and__Field_Odvd tptp.tc_Complex_Ocomplex) (tptp.class_Int_Oring__char__0 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 33.73/34.36  )
% 33.73/34.37  % SZS output end Proof for SWV618-1
% 33.73/34.37  % cvc5---1.0.5 exiting
% 33.73/34.37  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------