%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV693-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 21:52:58 EDT 2023

% Result   : Unsatisfiable 1.72s 1.92s
% Output   : Proof 1.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.28  % Problem    : SWV693-1 : TPTP v8.1.2. Released v4.1.0.
% 0.29/0.29  % Command    : do_cvc5 %s %d
% 0.30/0.50  % Computer : n011.cluster.edu
% 0.30/0.50  % Model    : x86_64 x86_64
% 0.30/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.30/0.50  % Memory   : 8042.1875MB
% 0.30/0.50  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.30/0.50  % CPULimit   : 300
% 0.30/0.50  % WCLimit    : 300
% 0.30/0.50  % DateTime   : Tue Aug 29 10:44:11 EDT 2023
% 0.30/0.50  % CPUTime    : 
% 0.55/0.80  %----Proving TF0_NAR, FOF, or CNF
% 0.55/0.80  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ZqU1BUU3PU/cvc5---1.0.5_15518.p...
% 0.65/1.09  ------- get file name : TPTP file name is SWV693-1
% 0.65/1.09  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15518.smt2...
% 0.65/1.09  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.72/1.92  % SZS status Unsatisfiable for SWV693-1
% 1.72/1.92  % SZS output start Proof for SWV693-1
% 1.72/1.97  (
% 1.72/1.97  (let ((_let_1 (tptp.class_Orderings_Olinorder tptp.tc_nat))) (let ((_let_2 (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (let ((_let_3 (tptp.c_Orderings_Obot__class_Obot _let_2))) (let ((_let_4 (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert tptp.v_i _let_3 tptp.tc_nat) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan tptp.v_i tptp.v_n tptp.tc_nat) _let_2))) (let ((_let_5 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_6 (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_5 tptp.v_n tptp.tc_nat))) (let ((_let_7 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_8 (tptp.c_FFT__Mirabelle_Oroot tptp.v_n))) (let ((_let_9 (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex))) (let ((_let_10 (tptp.c_COMBB tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_nat))) (let ((_let_11 (tptp.hAPP (tptp.hAPP _let_10 (tptp.hAPP _let_9 _let_8)) (tptp.hAPP (tptp.c_COMBC _let_7 tptp.tc_nat tptp.tc_nat tptp.tc_nat) tptp.v_i)))) (let ((_let_12 (tptp.tc_fun tptp.tc_nat tptp.tc_Complex_Ocomplex))) (let ((_let_13 (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex _let_12 tptp.tc_nat) _let_9))) (let ((_let_14 (tptp.c_Finite__Set_Osetsum tptp.tc_nat tptp.tc_Complex_Ocomplex))) (let ((_let_15 (tptp.hAPP (tptp.c_COMBB _let_12 (tptp.tc_fun _let_2 tptp.tc_Complex_Ocomplex) tptp.tc_nat) _let_14))) (let ((_let_16 (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex))) (let ((_let_17 (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex _let_16 tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes tptp.tc_Complex_Ocomplex)))) (let ((_let_18 (tptp.hAPP _let_14 (tptp.c_COMBS (tptp.hAPP _let_17 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP _let_15 (tptp.hAPP _let_13 _let_11)) tptp.tc_nat _let_2 tptp.tc_Complex_Ocomplex) _let_6)) tptp.v_a tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex)))) (let ((_let_19 (tptp.c_SetInterval_Oord__class_OatLeastLessThan tptp.v_i tptp.v_n tptp.tc_nat))) (let ((_let_20 (tptp.hAPP _let_18 _let_19))) (let ((_let_21 (= _let_20 (tptp.hAPP _let_18 _let_4)))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless tptp.v_i tptp.tc_nat) tptp.v_n)))) (let ((_let_24 (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_l (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan V_l V_u T_a) _let_1) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_l T_a) V_u)))))))) (let ((_let_25 (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (let ((_let_26 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_27 (tptp.hAPP _let_26 _let_5))) (let ((_let_28 (tptp.c_HOL_Oord__class_Oless _let_5 tptp.tc_nat))) (let ((_let_29 (tptp.hAPP tptp.c_Suc _let_5))) (let ((_let_30 (tptp.hAPP _let_27 _let_29))) (let ((_let_31 (tptp.hAPP (tptp.hAPP _let_26 _let_29) _let_5))) (let ((_let_32 (= _let_19 _let_4))) (let ((_let_33 (not _let_23))) (let ((_let_34 (not _let_1))) (let ((_let_35 (or _let_34 _let_32 _let_33))) (let ((_let_36 (_let_24))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (_let_32))) (let ((_let_39 (ASSUME :args _let_38))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_39 (SCOPE (CONG (REFL :args (_let_18)) (SYMM (SYMM _let_39)) :args (APPLY_UF tptp.hAPP)) :args _let_38)) :args _let_38)) :args ((or _let_21 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_33 _let_34 _let_32 (not _let_35)))) (ASSUME :args (_let_23)) (ASSUME :args (_let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.tc_nat tptp.v_i tptp.v_n QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_SetInterval_Oord__class_OgreaterThanLessThan V_l V_u T_a)))) :args _let_36))) _let_37 :args (_let_35 false _let_24)) :args (_let_32 false _let_23 false _let_1 false _let_35)) (ASSUME :args (_let_22)) :args (false false _let_32 true _let_21)) :args ((forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_i) tptp.tc_nat) (tptp.hAPP _let_1 V_j))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.hAPP _let_1 V_a) (tptp.hAPP _let_1 V_b))) (= V_a V_b)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_n))) (let ((_let_2 (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_2 (tptp.c_SetInterval_Oord__class_OatMost _let_1 tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP _let_2 (tptp.c_SetInterval_Oord__class_OatMost V_n tptp.tc_nat))) (tptp.hAPP V_f _let_1))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_m V_n)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_x)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat))) (tptp.hAPP V_f V_n))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_HOL_Oone__class_Oone T_a))) (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) V_b))) (forall ((V_n $$unsorted)) (not (= (tptp.hAPP tptp.c_Suc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.hAPP tptp.c_Suc V_n)))) (forall ((V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_r))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x))) (or (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_c)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_d)))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_D $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Lim_OisCont V_f V_x T_a T_a) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (= V_a _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_lessequals V_a T_a))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_2 _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_3 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_D $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Odifferentiable V_f V_x T_a) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Odifferentiable V_f V_x T_a) (not (tptp.c_Deriv_Oderiv V_f V_x V_xa T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Series_Osuminf V_X T_a)) (tptp.c_Series_Osuminf V_Y T_a)) (tptp.c_Series_Osuminf (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) V_Y tptp.tc_nat T_a T_a) T_a)) (not (tptp.c_Series_Osummable V_Y T_a)) (not (tptp.c_Series_Osummable V_X T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_n)))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_x)))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_i) tptp.tc_nat) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_j tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) V_j))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_k)) (tptp.hAPP tptp.c_Suc V_j))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_L $$unsorted) (V_M $$unsorted) (V_f $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_b)) (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= V_L V_M) (not (tptp.c_Lim_OLIM V_f V_a V_M T_a T_b)) (not (tptp.c_Lim_OLIM V_f V_a V_L T_a T_b)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (= V_m V_n))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_X $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (= V_a V_b) (not (tptp.c_SEQ_OLIMSEQ V_X V_b T_a)) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a)))) (forall ((T_a $$unsorted) (V_D $$unsorted) (V_E $$unsorted) (V_f $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= V_D V_E) (not (tptp.c_Deriv_Oderiv V_f V_x V_E T_a)) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a)))) (forall ((V_P $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P V_n) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m)) (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y tptp.tc_nat) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_y)) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (= (tptp.c_HOL_Oord__class_Oless tptp.v_n tptp.tc_nat) (tptp.c_lessequals (tptp.hAPP tptp.c_Suc tptp.v_n) tptp.tc_nat)) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) _let_2)) (= _let_2 _let_1))))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_2) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x) T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_j)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_j))))))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_i)) V_k) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_j))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m))) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) (tptp.hAPP _let_1 V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))) (= V_m (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_i)) V_u)) V_n)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) V_i))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_i) V_j)) V_u)) V_m) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_y) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))) (= V_x _let_1))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (= _let_2 _let_1))))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 _let_2)) (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) T_a) V_b)))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_3 (tptp.c_lessequals _let_2 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP V_f V_m)) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.hAPP tptp.c_Suc V_m) V_n tptp.tc_nat)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) (tptp.hAPP tptp.c_Suc _let_1))) (= V_m _let_1) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_m))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_n)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_x) V_z) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_w T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_x))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) T_a) (tptp.hAPP _let_1 V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_x) T_a) (tptp.hAPP _let_1 V_y)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_x) T_a) (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j)))))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_x)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_m)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_m))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_n))) (let ((_let_2 (tptp.c_lessequals V_m tptp.tc_nat))) (or (= V_m _let_1) (tptp.hBOOL (tptp.hAPP _let_2 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_2 _let_1) _let_1)) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (let ((_let_2 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP _let_3 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_3 _let_2) _let_2)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_y)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_x))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_m V_n)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x))) (or (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_1 V_y) (tptp.hAPP _let_1 V_z))) (= V_y V_z)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))) (= V_b V_c)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.hAPP tptp.c_Suc V_n))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.hAPP tptp.c_Suc V_m) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_n _let_2) (= V_n _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (not (= _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_m _let_1) (= V_m _let_2))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_n) T_a) (tptp.hAPP _let_1 V_N))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_N)))))) (= _let_29 _let_30) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a)) V_c) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_b V_c T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c) T_a))))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) V_i))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_i) V_j)) V_u)) V_m))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Ometric__space T_b)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_b T_a) V_f) (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x)) (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP V_f V_x) T_a T_b) (not (tptp.c_Lim_OisCont V_f V_x T_a T_b)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Ometric__space T_b)) (tptp.c_Lim_OisCont V_f V_x T_a T_b) (not (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_b T_a) V_f) (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x)) (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.hAPP V_f V_x) T_a T_b)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_z T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y) T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) T_a) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= 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))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x) T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)) V_n) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_j) tptp.tc_nat) V_k))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_j))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) V_m))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_b T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_b T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) tptp.tc_nat) V_j)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_k)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_j))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) tptp.tc_nat) V_j))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_j))))) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_m))))) (forall ((V_i $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_i))))) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_x))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_i)) V_u)) V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_i)) V_u)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_i) V_j)) V_u)) V_m) tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) V_i))))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_i) V_j)) V_u)) V_m) tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) V_i))))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_SEQ_OCauchy V_X T_a) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_x)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_2 V_a) T_a) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_2 V_a) T_a) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))))))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) V_m) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_j)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_j)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_x) V_z) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_w T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x))))))) (= _let_31 _let_29) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) V_n)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_g $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Ometric__space T_b)) (not (tptp.class_RealVector_Ometric__space T_c)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_b T_c) V_g) V_f) V_a (tptp.hAPP V_g V_l) T_c T_b) (not (tptp.c_Lim_OLIM V_f V_a V_l T_c T_a)) (not (tptp.c_Lim_OisCont V_g V_l T_a T_b)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (let ((_let_3 (tptp.hAPP _let_1 V_z))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2))))))) (forall ((V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (let ((_let_3 (tptp.hAPP _let_1 V_d))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2))))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1)))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) tptp.c_Suc) V_l T_a) (not (tptp.c_SEQ_OLIMSEQ V_f V_l T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_SEQ_OLIMSEQ V_f V_l T_a) (not (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) tptp.c_Suc) V_l T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse 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.hAPP _let_1 (tptp.hAPP _let_1 V_a)) V_a)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_Series_Osuminf (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_f) tptp.tc_nat T_a T_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Series_Osuminf V_f T_a)) V_c)) (not (tptp.c_Series_Osummable V_f T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC _let_1 T_a T_a T_a) V_y) V_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_y) T_a T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) _let_1))))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (T_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Finite__Set_Osetprod V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b T_a) (tptp.c_HOL_Oone__class_Oone 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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_z T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_b))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_c)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z)))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_m))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_n)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_z))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_c)) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.hAPP _let_1 V_c))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (tptp.hBOOL (tptp.hAPP _let_1 V_m)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_y) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_z)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_k) tptp.tc_nat) V_n))))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_k) tptp.tc_nat) V_n))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_i tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_i $$unsorted) (V_m $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_i tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_j))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_x)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__meet T_a)) (= (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_b V_c T_a)) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP _let_1 V_b) (tptp.hAPP _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_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__meet T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_a V_b T_a)) V_c) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (= V_a _let_1) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_2 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP _let_3 _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_2 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_3 V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP _let_3 _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (let ((_let_3 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_2 _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_3)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_3 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_3 V_u))) (= (tptp.hAPP _let_2 V_z) V_u)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_m)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n))))))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Suc V_n)) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_b) T_a) (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_b) T_a) (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n) tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_m)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_n)))))) (forall ((V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_x))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_x))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_i) V_u)) V_m)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_u)) V_n)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)) V_u)) V_m)) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) V_i)))))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_i) V_u)) V_m)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_u)) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_i)) V_u)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osummable V_f T_a) (not (tptp.c_Series_Osums V_f V_l T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osummable V_f T_a) (not (tptp.c_Series_Osums V_f V_x T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)) V_n) (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m))) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP tptp.c_Suc (tptp.hAPP _let_1 V_n))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_N) T_a) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_N)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_N) T_a) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_N)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c) T_a) V_b))) (tptp.hBOOL (tptp.hAPP _let_1 V_c)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b))) (tptp.hBOOL (tptp.hAPP _let_2 _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_2 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP _let_3 V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (let ((_let_3 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_3)) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_3))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_c))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_a))))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_l) (tptp.hAPP (tptp.hAPP _let_1 V_k) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_k tptp.tc_nat) V_l))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_m)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless 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_let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_b) T_a) (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Lim_OisCont (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Oinverse__class_Odivide T_a) T_a T_a T_a) V_y) V_a 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.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP 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(tptp.c_HOL_Oord__class_Oless _let_2 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP 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(tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b)))))))) (forall ((V_k $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_k))) (= (tptp.c_SetInterval_Oord__class_OatMost _let_1 tptp.tc_nat) (tptp.c_Set_Oinsert _let_1 (tptp.c_SetInterval_Oord__class_OatMost V_k tptp.tc_nat) tptp.tc_nat)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_i)) V_u)) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n)))))) (tptp.hBOOL (tptp.hAPP _let_28 _let_29)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP tptp.c_Suc _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_m _let_1) (= V_n _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (or (not (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n))) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_k) tptp.tc_nat) V_i)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k)))))) (forall ((V_j $$unsorted) (V_i $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_k) tptp.tc_nat) V_i))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_i) V_j)) V_u)) V_m) tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) V_i))))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_i) V_j)) V_u)) V_m) tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) V_i))))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted) (V_u $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_i)) V_u)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_m $$unsorted) (V_j $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_u)) V_m) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_u)) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_i)) V_u)) V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_2 V_d)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_2 V_c)))) (= V_c V_d) (= V_a V_b))))))) (forall ((V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_w))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_y)) (tptp.hAPP _let_2 V_z)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_2 V_y)))) (= V_y V_z) (= V_w V_x))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat))) (or (= V_n V_m) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat))) (or (= V_m V_n) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)))) (tptp.hBOOL (tptp.hAPP _let_1 V_m))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat))) (or (= V_m V_n) (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_b))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_x) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_b T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of V_v T_a)))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x) T_a) _let_1)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (= V_x _let_2) (= V_x _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) (tptp.hAPP tptp.c_Suc _let_2)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Oring__char__0 T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_Int_Onumber__class_Onumber__of V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (not (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_x)))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_n)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_i $$unsorted) (V_u $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_i) V_u)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_u)) V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_i) V_j)) V_u)) V_k))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_m)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) T_a) _let_1)))))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c tptp.tc_nat) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a tptp.tc_nat) V_b)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_m))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 tptp.tc_nat) V_n)) (= _let_1 V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) V_m))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x) T_a) _let_1)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m)) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a))))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_2)) (= V_m _let_1) (= V_m _let_2))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP tptp.c_Suc _let_1))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_2)) (= V_n _let_2) (= V_n _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_k)))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (tptp.c_Lim_OLIM _let_1 V_a (tptp.hAPP _let_1 V_a) T_a T_a) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_n))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 tptp.tc_nat) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)))))) (forall ((V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_m)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) V_j)))))) (forall ((V_k $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_i) tptp.tc_nat) (tptp.hAPP _let_1 V_j))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) V_j)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_k)))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_a T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_ya) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ya)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_ya))))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_n)))))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc V_x) tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted) (V_x $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun tptp.tc_nat T_a) T_a) _let_1) V_f) T_a tptp.tc_nat T_a) (tptp.hAPP tptp.c_Suc V_n)) V_x (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (tptp.hAPP (tptp.hAPP _let_2 V_D) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP V_f V_x)) V_n))) T_a) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_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.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_a)) V_a) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) _let_1) _let_1) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) _let_1) _let_1)))) (forall ((T_a $$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.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) _let_1) _let_1)))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_29) _let_29) _let_29) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) V_m) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Oone__class_Oone T_a))) V_m)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_m) (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) (tptp.c_HOL_Oone__class_Oone T_a))) V_m)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 V_i) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k)) V_j)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_a) V_b)) _let_1) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x))))))) (= _let_29 _let_31) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_n)))) (forall ((V_x $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) V_i))) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) _let_1))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) _let_1) V_i) V_k)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((V_k $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k) V_x)))) (forall ((V_m $$unsorted) (V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_x)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_k tptp.tc_nat) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) V_j)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_y))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_x)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Series_Osuminf V_X T_a)) V_y) (tptp.c_Series_Osuminf (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) tptp.tc_nat T_a T_a) V_y) T_a)) (not (tptp.c_Series_Osummable V_X T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_x) V_z) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_w T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_w))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Suc V_n)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OLIMSEQ V_f (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_Series_Osummable V_f T_a)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n)) V_n) V_m) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n)) V_m) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j))) (= V_j (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_i)) V_i)))) (forall ((T_a $$unsorted) (V_s $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= V_s (tptp.c_Series_Osuminf V_f T_a)) (not (tptp.c_Series_Osums V_f V_s T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Series_Osuminf V_f T_a) V_x) (not (tptp.c_Series_Osums V_f V_x T_a)))) (forall ((V_j $$unsorted) (V_k $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_k)) V_i) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_j) V_i)) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_j))))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_j) V_k)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_j)) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_k tptp.tc_nat) V_j))))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a)))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (= V_m V_n)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_2 _let_1)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_2) _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_m tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat) V_n))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_n) V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_y))))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) V_n)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_k tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_k tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a))) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) _let_1) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.c_HOL_Oone__class_Oone T_a)) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) T_a) (tptp.hAPP _let_1 V_n)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_N $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_n) T_a) (tptp.hAPP _let_1 V_N))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_N)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_x) T_a) (tptp.hAPP _let_1 V_y)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_x) T_a) (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x tptp.tc_nat) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_b)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c))) (let ((_let_3 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b)))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals (tptp.c_Int_Onumber__class_Onumber__of V_w T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_Int_Onumber__class_Onumber__of V_w T_a) T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_i) tptp.tc_nat) V_i)))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_j) tptp.tc_nat) V_i)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) tptp.tc_nat) V_j))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_i) V_k) tptp.tc_nat) V_j)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_k)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP _let_3 _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osums V_f (tptp.c_Series_Osuminf V_f T_a) T_a) (not (tptp.c_Series_Osummable V_f T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.c_Series_Osummable V_f T_a)) (tptp.c_Series_Osums V_f (tptp.c_Series_Osuminf V_f T_a) T_a))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olower__semilattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_x)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_i) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_j) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_i tptp.tc_nat) V_j)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_m) tptp.tc_nat) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.hAPP _let_2 V_a) (tptp.hAPP _let_2 V_b))) (= V_a V_b) (= V_b _let_1) (= V_a _let_1))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) V_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_1) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) _let_1) V_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.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) _let_1) V_y) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Ometric__space T_b)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_b T_a) V_f) (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a T_b) (not (tptp.c_Lim_OLIM V_f V_a _let_1 T_a T_b))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP V_f V_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Ometric__space T_b)) (tptp.c_Lim_OLIM V_f V_a _let_1 T_a T_b) (not (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_b T_a) V_f) (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_L $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_b)) (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_b T_a) V_f) (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a) V_L T_a T_b) (not (tptp.c_Lim_OLIM V_f V_a V_L T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_L $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_b)) (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Lim_OLIM V_f V_a V_L T_a T_b) (not (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_b T_a) V_f) (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a)) (tptp.c_HOL_Ozero__class_Ozero T_a) V_L T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_L $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_b))) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_b T_a) _let_1) V_f) V_a (tptp.hAPP _let_1 V_L) T_a T_b) (= V_L (tptp.c_HOL_Ozero__class_Ozero T_b)) (not (tptp.c_Lim_OLIM V_f V_a V_L T_a T_b))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Oreal__normed__div__algebra T_b)) (tptp.c_Lim_OisCont (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse T_b)) V_f) V_a T_a T_b) (= (tptp.hAPP V_f V_a) (tptp.c_HOL_Ozero__class_Ozero T_b)) (not (tptp.c_Lim_OisCont V_f V_a T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Odifferentiable (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse T_a)) V_f) V_x T_a) (= (tptp.hAPP V_f V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Deriv_Odifferentiable V_f V_x T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_net $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_b))) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_b)) (tptp.c_Limits_Otendsto (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_b T_a) _let_1) V_f) (tptp.hAPP _let_1 V_a) V_net T_a T_b) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_b)) (not (tptp.c_Limits_Otendsto V_f V_a V_net T_a T_b))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) _let_1)) (= V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_2 V_a) T_a) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_2 V_a) T_a) (tptp.hAPP _let_2 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_2)) _let_2) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_4 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_4 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_4 V_w) V_z)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_2 V_w) V_y))) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z))) (= V_z _let_1) (= V_y _let_1))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)) V_c) _let_1) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1)) _let_1) V_b) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1)) _let_1)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)) V_c)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b))) (tptp.hBOOL (tptp.hAPP _let_1 V_c))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)) V_c) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_y) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_y) V_x) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_z) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y))) V_y)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y))) V_y)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_b))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_5 (tptp.hAPP _let_2 V_a))) (let ((_let_6 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_5) _let_3) (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP (tptp.hAPP _let_6 _let_5) (tptp.hAPP (tptp.hAPP _let_4 V_a) V_b))) _let_3)) (= V_b _let_1) (= V_a _let_1))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_b))) (let ((_let_4 (tptp.hAPP _let_2 V_a))) (let ((_let_5 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_6 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_5 _let_4) _let_3) (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP (tptp.hAPP _let_5 V_a) V_b)) _let_4)) _let_3)) (= V_b _let_1) (= V_a _let_1))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)) V_c))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_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.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a)) V_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.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a)) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_z T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y) T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_x) V_y) T_a) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_z) V_y)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_y))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c) T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1)) _let_1)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$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.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1)) _let_1) V_a) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y)) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w 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.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) _let_1)) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_y))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_y _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_x _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)))) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)))) (= V_x _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (let ((_let_2 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_g $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.hAPP V_g V_l))) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Ometric__space T_b)) (not (tptp.class_RealVector_Ometric__space T_c)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_b T_c) V_g) V_f) V_a _let_1 T_c T_b) (not (tptp.c_Lim_OLIM V_f V_a V_l T_c T_a)) (not (tptp.c_Lim_OLIM V_g V_l _let_1 T_a T_b))))) (forall ((T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_f $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Ometric__space T_c)) (not (tptp.class_RealVector_Ometric__space T_b)) (tptp.c_Lim_OisCont (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_c T_a) V_g) V_f) V_a T_a T_c) (not (tptp.c_Lim_OisCont V_g (tptp.hAPP V_f V_a) T_b T_c)) (not (tptp.c_Lim_OisCont V_f V_a T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Odifferentiable (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a T_a) V_f) V_g) V_x T_a) (not (tptp.c_Deriv_Odifferentiable V_g V_x T_a)) (not (tptp.c_Deriv_Odifferentiable V_f (tptp.hAPP V_g V_x) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (let ((_let_3 (tptp.hAPP _let_1 V_w))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_y)) (tptp.hAPP _let_2 V_z)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_z)) (tptp.hAPP _let_2 V_y)))) (= V_y V_z) (= V_w V_x))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_b))) (let ((_let_3 (tptp.hAPP _let_1 V_a))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_c)) (tptp.hAPP _let_2 V_d)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP _let_3 V_d)) (tptp.hAPP _let_2 V_c)))) (= V_c V_d) (= V_a V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_m)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_m)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_m)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_c))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_x)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_x)))) (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x tptp.tc_nat) V_x))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_i tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP _let_1 V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_j tptp.tc_nat) V_k))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_j)))))) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_b))) (let ((_let_2 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_c)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_z T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_z T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_z T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_z T_a))) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_x)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_x) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_x)))))) (= _let_30 _let_29) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) _let_1))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c) T_a) _let_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_2) V_c) T_a) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_c)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatMost V_x T_a) (tptp.c_SetInterval_Oord__class_OatMost V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Ometric__space T_b)) (tptp.c_Lim_OisCont V_f V_a T_a T_b) (not (tptp.c_Lim_OLIM V_f V_a (tptp.hAPP V_f V_a) T_a T_b)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Ometric__space T_b)) (tptp.c_Lim_OLIM V_f V_a (tptp.hAPP V_f V_a) T_a T_b) (not (tptp.c_Lim_OisCont V_f V_a T_a T_b)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1) T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (let ((_let_3 (tptp.c_lessequals V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.hBOOL (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) _let_1))) (not (tptp.hBOOL (tptp.hAPP _let_3 (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_2))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_2 T_a) V_b)))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= V_n V_m) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_m)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_f $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (T_b $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x)))))) (forall ((V_A $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A (tptp.hAPP V_f V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Ovimage V_f V_A T_a T_b) V_x))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osums V_f (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_l) (tptp.hAPP V_f (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) T_a) (not (tptp.c_Series_Osums (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) tptp.c_Suc) V_l T_a)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n)) V_m) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_m)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) V_Y tptp.tc_nat T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_SEQ_OLIMSEQ V_Y V_b T_a)) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n)) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_s $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (= (tptp.hAPP V_f (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.c_Series_Osums V_f V_s T_a) (not (tptp.c_Series_Osums (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) tptp.c_Suc) V_s T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_n $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) V_p)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_n) V_p))) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_p tptp.tc_nat) V_n))))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Series_Osuminf V_X T_a)) V_y) (tptp.c_Series_Osuminf (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) tptp.tc_nat T_a T_a) V_y) T_a)) (not (tptp.c_Series_Osummable V_X T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Series_Osuminf V_f T_a)) V_c) (tptp.c_Series_Osuminf (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_f) tptp.tc_nat T_a T_a) V_c) T_a)) (not (tptp.c_Series_Osummable V_f T_a))))) (forall ((V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat tptp.tc_Complex_Ocomplex) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex)) (tptp.c_FFT__Mirabelle_Oroot V_n))) V_k))) (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_n tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_k tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 tptp.tc_nat) V_k))))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Series_Osuminf V_X T_a)) (tptp.c_Series_Osuminf V_Y T_a)) (tptp.c_Series_Osuminf (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) V_Y tptp.tc_nat T_a T_a) T_a)) (not (tptp.c_Series_Osummable V_Y T_a)) (not (tptp.c_Series_Osummable V_X T_a))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_L $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OLIMSEQ V_X V_L T_a) (not (tptp.c_SEQ_OZseq (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus T_a)) V_X) tptp.tc_nat T_a T_a) V_L) T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_L $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OZseq (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus T_a)) V_X) tptp.tc_nat T_a T_a) V_L) T_a) (not (tptp.c_SEQ_OLIMSEQ V_X V_L T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) V_m))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan V_l V_u T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m T_a) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_l T_a) V_m))))) (forall ((V_d $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_d))) (or (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_FFT__Mirabelle_Oroot (tptp.hAPP _let_2 V_n))) (tptp.hAPP _let_2 V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_FFT__Mirabelle_Oroot V_n)) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_d))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP V_f V_m)) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan V_m V_n tptp.tc_nat))) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_a)) (tptp.hAPP _let_2 V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_c) V_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_c)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_c) V_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_c)) V_c)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_c)) (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_d)))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) _let_1)) (= V_x _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_x) V_x)) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_y)) _let_1)) (= V_y _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_y)) (tptp.hAPP _let_1 V_z))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_a_H)) V_b) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_ya) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ya)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_ya))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_b_H)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_b_H))))))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_xa))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_2 V_z) V_w)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_w))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Lim_OLIM _let_1 V_a (tptp.hAPP _let_1 V_a) T_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Lim_OisCont (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_a T_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_x) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_HOL_Oone__class_Oone T_a)) V_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (let ((_let_3 (tptp.hAPP _let_1 V_z))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_c))) (let ((_let_3 (tptp.hAPP _let_1 V_d))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_2) _let_3) (tptp.hAPP (tptp.hAPP _let_4 _let_3) _let_2)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_e)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_e)) V_c)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) V_e)) V_c)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z)) V_y)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c) V_x V_c T_a))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) _let_1) V_X) (tptp.hAPP _let_1 V_a) T_a) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c) T_a) V_d))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c) T_a) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_4 (tptp.hAPP _let_3 V_a))) (or (not (tptp.class_RealVector_Oreal__field T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_4 V_b)) (tptp.hAPP (tptp.hAPP _let_3 V_c) V_d))) V_h) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_d)) V_h))) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) V_h)) V_d))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c) T_a) V_d))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c) T_a) V_d)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_n))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.hAPP tptp.c_Suc V_n))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_3 V_a) _let_2) (tptp.hAPP (tptp.hAPP _let_3 V_b) _let_2))) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_4 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_4 V_i) V_j))) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_4 V_k) V_i))) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_j)) (tptp.hAPP _let_2 V_k))) V_i)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) T_a) _let_1)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_net $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_b))) (or (not (tptp.class_RealVector_Oreal__normed__field T_b)) (tptp.c_Limits_Otendsto (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_g) T_a T_b T_b) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_y) V_net T_a T_b) (not (tptp.c_Limits_Otendsto V_g V_a V_net T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_b))) (or (not (tptp.class_RealVector_Oreal__normed__field T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_g) T_a T_b T_b) V_y) V_a (tptp.hAPP (tptp.hAPP _let_1 V_l) V_y) T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a V_l T_a T_b))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_c $$unsorted) (V_x $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) _let_1) V_f) T_a T_a T_a) V_c) V_x (tptp.hAPP (tptp.hAPP _let_1 V_D) V_c) T_a) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_y $$unsorted) (V_net $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_b)) (tptp.c_Limits_OZfun (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Oinverse__class_Odivide T_b)) V_g) T_a T_b T_b) V_y) V_net T_a T_b) (not (tptp.c_Limits_OZfun V_g V_net T_a T_b)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y_H T_a) V_x_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y_H T_a) V_x_H)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x_H T_a) V_y_H)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x_H T_a) V_y_H)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_ya) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ya)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_ya))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_b) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c)) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_c) V_d))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a) V_b)) V_b) V_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_f $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_Series_Osuminf (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) _let_1) V_f) T_a) (tptp.hAPP _let_1 (tptp.c_Series_Osuminf V_f T_a))) (not (tptp.c_Series_Osummable V_f T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_X $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.c_Series_Osuminf V_X T_a)) (tptp.c_Series_Osuminf (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) _let_1) V_X) T_a)) (not (tptp.c_Series_Osummable V_X T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Odifferentiable (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus T_a)) V_f) V_g T_a T_a T_a) V_x T_a) (not (tptp.c_Deriv_Odifferentiable V_g V_x T_a)) (not (tptp.c_Deriv_Odifferentiable V_f V_x T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted) (V_L $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_b))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_f) V_g T_a T_b T_b) V_a (tptp.hAPP (tptp.hAPP _let_1 V_L) V_M) T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a V_M T_a T_b)) (not (tptp.c_Lim_OLIM V_f V_a V_L T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_net $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (tptp.c_Limits_OZfun (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Oplus__class_Oplus T_b)) V_f) V_g T_a T_b T_b) V_net T_a T_b) (not (tptp.c_Limits_OZfun V_g V_net T_a T_b)) (not (tptp.c_Limits_OZfun V_f V_net T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_D $$unsorted) (V_E $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) _let_1) V_f) V_g T_a T_a T_a) V_x (tptp.hAPP (tptp.hAPP _let_1 V_D) V_E) T_a) (not (tptp.c_Deriv_Oderiv V_g V_x V_E T_a)) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (tptp.c_Lim_OisCont (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Oplus__class_Oplus T_b)) V_f) V_g T_a T_b T_b) V_a T_a T_b) (not (tptp.c_Lim_OisCont V_g V_a T_a T_b)) (not (tptp.c_Lim_OisCont V_f V_a T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_net $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_b))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (tptp.c_Limits_Otendsto (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_f) V_g T_a T_b T_b) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_net T_a T_b) (not (tptp.c_Limits_Otendsto V_g V_b V_net T_a T_b)) (not (tptp.c_Limits_Otendsto V_f V_a V_net T_a T_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_5 tptp.tc_nat) _let_5)) (not (tptp.hBOOL (tptp.hAPP _let_28 _let_5))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 tptp.tc_nat) V_n)) (= V_n _let_1)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.hAPP tptp.c_Suc V_nat_H) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted)) (not (= (tptp.hAPP tptp.c_Suc V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) _let_1) V_n) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) _let_1) _let_1))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_m V_n) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (or (not (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n)))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k))) (= V_k (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (= V_m V_n)))) (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_m $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (= (tptp.hAPP _let_1 V_m) (tptp.hAPP _let_1 V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_2 V_m) _let_1) (tptp.hAPP (tptp.hAPP _let_2 V_n) _let_1))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= V_n _let_1) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) _let_1)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_m _let_1)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) _let_1)) (= V_n _let_1)))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (or (not (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) V_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n) V_m)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_nat_H)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_m)))) (= (tptp.hAPP _let_27 _let_5) _let_5) (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))) (forall ((V_x $$unsorted)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_m)) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_n) V_n)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Obot T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_m)) (tptp.hAPP _let_3 V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_HOL_Oone__class_Oone T_a)) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n) V_m))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.c_HOL_Oinverse__class_Oinverse T_a) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP _let_2 V_m)) (tptp.hAPP _let_2 V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((V_f $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf _let_2 V_B _let_1) _let_2)))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_m) V_n)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m)) V_n)))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) V_n)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_a)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_lessequals _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 V_b)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_d))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_c))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_c T_a) V_d))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b)))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) _let_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_2 T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_b))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_b) V_a) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) _let_1))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals _let_1 T_a) V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_b)) (tptp.hAPP _let_2 V_a))) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)) V_c))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_b (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_c)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) V_b) V_c)) V_c) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) _let_1))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) _let_2) _let_2) _let_1))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_1 V_a) T_a) (tptp.hAPP _let_1 V_b))))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_b T_a) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_c)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_c T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_3 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_3 V_w) V_z))) (= V_z _let_2) (= V_y _let_2) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_y))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_3 V_x) V_z) (tptp.hAPP (tptp.hAPP _let_3 V_w) V_y))) (= V_z _let_2) (= V_y _let_2) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_w) V_z))))))) (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.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_c)) V_c) _let_1)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_Da $$unsorted) (V_Db $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a T_a) V_f) V_g) V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_Da) V_Db) T_a) (not (tptp.c_Deriv_Oderiv V_g V_x V_Db T_a)) (not (tptp.c_Deriv_Oderiv V_f (tptp.hAPP V_g V_x) V_Da T_a)))) (forall ((T_a $$unsorted) (V_g $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_E $$unsorted) (V_D $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a T_a) V_g) V_f) V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_E) V_D) T_a) (not (tptp.c_Deriv_Oderiv V_g (tptp.hAPP V_f V_x) V_E T_a)) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (V_net $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (tptp.c_Limits_OZfun (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_b T_a) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) V_x)) V_g) V_net T_a T_b) (not (tptp.c_Limits_OZfun V_g V_net T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_a $$unsorted) (V_f $$unsorted) (V_net $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (tptp.c_Limits_OZfun (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_b T_a) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) V_a)) V_f) V_net T_a T_b) (not (tptp.c_Limits_OZfun V_f V_net T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (V_a $$unsorted) (V_net $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) V_x))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (tptp.c_Limits_Otendsto (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_b T_a) _let_1) V_g) (tptp.hAPP _let_1 V_a) V_net T_a T_b) (not (tptp.c_Limits_Otendsto V_g V_a V_net T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (V_a $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) V_x))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_b T_a) _let_1) V_g) V_a (tptp.hAPP _let_1 V_l) T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a V_l T_a T_b))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a T_a) _let_1) V_f) V_x (tptp.hAPP _let_1 V_D) T_a) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_b))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_4 (tptp.hAPP _let_3 V_a))) (let ((_let_5 (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_a)))) (let ((_let_6 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_3 V_x) V_y)) (tptp.hAPP _let_4 V_b)) (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP _let_5 _let_2)) (tptp.hAPP _let_5 V_b))) (tptp.hAPP _let_4 _let_2))))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d)))))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of V_v T_a)))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_c)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_a) V_b)) _let_1) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_b) _let_1)))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b)) V_e)) V_c) V_d))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_e)) V_c) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_e)) V_d))) (= V_c (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_b) V_a)) V_e)) V_d)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat)) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_x T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) T_a) _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n) T_a) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_b)))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.hAPP tptp.c_Suc V_n)) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_a)) V_n)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Lim_OisCont (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Otimes__class_Otimes T_a) T_a T_a T_a) V_y) V_a T_a T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC _let_1 T_a T_a T_a) V_y) V_a (tptp.hAPP (tptp.hAPP _let_1 V_a) V_y) T_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_X $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OCauchy (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x)) V_X) T_a) (not (tptp.c_SEQ_OCauchy V_X T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_X $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) _let_1) V_X) (tptp.hAPP _let_1 V_a) T_a) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_X $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OZseq (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x)) V_X) T_a) (not (tptp.c_SEQ_OZseq V_X T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_X $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OZseq (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a)) V_X) T_a) (not (tptp.c_SEQ_OZseq V_X T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Series_Osummable (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c)) V_f) T_a) (not (tptp.c_Series_Osummable V_f T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_X $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Series_Osummable (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x)) V_X) T_a) (not (tptp.c_Series_Osummable V_X T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_X $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Series_Osums (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) _let_1) V_X) (tptp.hAPP _let_1 V_a) T_a) (not (tptp.c_Series_Osums V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_f $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_c))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Series_Osums (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_nat) _let_1) V_f) (tptp.hAPP _let_1 V_a) T_a) (not (tptp.c_Series_Osums V_f V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_q)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_n)) V_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_p)) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_p) V_q)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) (tptp.hAPP _let_1 V_q)) (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.hAPP _let_1 V_q)) V_x) (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_q)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) (tptp.c_Orderings_Obot__class_Obot T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) V_a))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n) V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n) V_m)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))) (forall ((V_P $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_P (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a tptp.tc_nat) V_b))) (not (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_a) V_b)))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n) tptp.tc_nat) V_m)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted) (V_x $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun tptp.tc_nat T_a) T_a) _let_1) V_f) T_a tptp.tc_nat T_a) V_n) V_x (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a)) (tptp.hAPP (tptp.hAPP _let_2 V_D) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP V_f V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n) (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) T_a) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a V_A T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a (tptp.c_Complete__Lattice_OSup__class_OSup V_A T_a) T_a)))) (forall ((T_a $$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.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_a V_b T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) V_b)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.c_Series_Osummable V_f T_a)) (= (tptp.c_Series_Osuminf (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_k)) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.c_Series_Osuminf V_f T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a) (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_l V_u T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m T_a) V_u))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_l T_a) V_m))))) (= (tptp.c_GCD_Ogcd__class_OGCD _let_3 tptp.tc_nat) _let_5) (forall ((T_a $$unsorted) (V_k $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan V_k V_l T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_l T_a) V_k))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_p)) V_q) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_p) V_q))))))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_m))))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n) (tptp.hAPP tptp.c_Suc V_i)) tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (= (tptp.hAPP tptp.c_Suc (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n) (tptp.hAPP tptp.c_Suc _let_1))) V_n) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 tptp.tc_nat) V_n)))))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osums (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) V_Y tptp.tc_nat T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (not (tptp.c_Series_Osums V_Y V_b T_a)) (not (tptp.c_Series_Osums V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osummable (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus T_a)) V_X) V_Y tptp.tc_nat T_a T_a) T_a) (not (tptp.c_Series_Osummable V_Y T_a)) (not (tptp.c_Series_Osummable V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) V_Y tptp.tc_nat T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (not (tptp.c_SEQ_OLIMSEQ V_Y V_b T_a)) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OZseq (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Oplus__class_Oplus T_a)) V_X) V_Y tptp.tc_nat T_a T_a) T_a) (not (tptp.c_SEQ_OZseq V_Y T_a)) (not (tptp.c_SEQ_OZseq V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Series_Osummable (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Oinverse__class_Odivide T_a)) V_X) tptp.tc_nat T_a T_a) V_y) T_a) (not (tptp.c_Series_Osummable V_X T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Series_Osummable (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Oinverse__class_Odivide T_a)) V_f) tptp.tc_nat T_a T_a) V_c) T_a) (not (tptp.c_Series_Osummable V_f T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) tptp.tc_nat T_a T_a) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_y) T_a) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_SEQ_OZseq (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Oinverse__class_Odivide T_a)) V_X) tptp.tc_nat T_a T_a) V_y) T_a) (not (tptp.c_SEQ_OZseq V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_SEQ_OCauchy (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Oinverse__class_Odivide T_a)) V_X) tptp.tc_nat T_a T_a) V_y) T_a) (not (tptp.c_SEQ_OCauchy V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Series_Osums (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) tptp.tc_nat T_a T_a) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_y) T_a) (not (tptp.c_Series_Osums V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Series_Osums (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_f) tptp.tc_nat T_a T_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (not (tptp.c_Series_Osums V_f V_a T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_f) tptp.tc_nat T_a T_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (not (tptp.c_SEQ_OLIMSEQ V_f V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_y) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_y))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_z))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_z))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_z T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_x))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_x T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_y T_a) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_z))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_x T_a) V_z)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_z))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_x T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_b T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_a T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a) T_a) V_x))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_z T_a) T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) V_x T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_y V_x T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_z V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Odistrib__lattice T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_y T_a) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__join T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)) V_c) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__join T_a)) (= (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_b V_c T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_b V_c T_a)) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP _let_1 V_b) (tptp.hAPP _let_1 V_c) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)) V_c) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c) T_a))))) (forall ((V_j $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_j) V_n) tptp.tc_nat) V_k)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_j tptp.tc_nat) V_k))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)) (tptp.hAPP tptp.c_Suc V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oord__class_Oless V_m tptp.tc_nat))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_l))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP _let_2 V_n) tptp.tc_nat) (tptp.hAPP _let_2 V_m))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_l))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))))))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_b) V_d)) V_b)))) (tptp.hBOOL (tptp.hAPP V_P V_d)))) (forall ((V_P $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP V_P (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_b) V_x)) V_b)))) (tptp.hBOOL (tptp.hAPP V_P V_x)))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_k))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_m)) (tptp.hAPP _let_2 V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP tptp.c_Suc V_m)) V_n)) (tptp.hAPP tptp.c_Suc V_k)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_m) V_n)) V_k)))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n))) (or (= (tptp.hAPP _let_1 (tptp.hAPP _let_1 V_i)) V_i) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_n)))))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_k tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k)))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_k tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_2 V_m) V_k) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))))))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP _let_1 V_m) V_l) tptp.tc_nat) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_l))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_l))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP _let_1 V_n) tptp.tc_nat) (tptp.hAPP _let_1 V_m))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_i))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_j)) V_k) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_k)))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_k tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m))) (= V_m V_n))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_n) tptp.tc_nat) V_m))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k)) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k)))))) (forall ((V_k $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) V_k))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_m)) (tptp.hAPP _let_1 V_n)))))) (forall ((V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_lessequals V_k tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_3 (tptp.hAPP _let_2 V_m))) (or (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_k)) (tptp.hAPP (tptp.hAPP _let_2 V_n) V_k)) (tptp.hAPP _let_3 V_n)) (not (tptp.hBOOL (tptp.hAPP _let_1 V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_m)))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_n) V_m)) V_n) V_m)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_m) V_n)) V_n) V_m)) (forall ((V_f $$unsorted) (V_A $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_b tptp.tc_bool)) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f V_A T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_C _let_1) _let_1)))) (forall ((V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) V_A _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_A _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Olower__semilattice__class_Oinf V_A V_B _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_B V_C _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf V_C V_A _let_1) _let_1) (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_C V_A _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_l $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_X) (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_l)) V_x T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_l))) (not (tptp.c_SEQ_OLIMSEQ V_X V_x T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat))) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_n V_p tptp.tc_nat))) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_p tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_p))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osummable (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_k)) T_a) (not (tptp.c_Series_Osummable V_f T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_k)) V_a T_a) (not (tptp.c_SEQ_OLIMSEQ V_f V_a T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_SEQ_OLIMSEQ V_f V_a T_a) (not (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_k)) V_a T_a)))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OatMost V_l T_a) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan V_l V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat) (tptp.c_Set_Oinsert V_n (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat) tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n))))) (forall ((V_n $$unsorted)) (not (= (tptp.c_FFT__Mirabelle_Oroot V_n) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_2 (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Lim_OLIM (tptp.c_COMBS (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a)) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_f) T_a T_a T_a) (tptp.hAPP V_f V_x))) (tptp.hAPP (tptp.c_COMBC _let_1 T_a T_a T_a) V_x) T_a T_a T_a) V_x V_D T_a T_a) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_x $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_2 (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv V_f V_x V_D T_a) (not (tptp.c_Lim_OLIM (tptp.c_COMBS (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_HOL_Oinverse__class_Odivide T_a)) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_f) T_a T_a T_a) (tptp.hAPP V_f V_x))) (tptp.hAPP (tptp.c_COMBC _let_1 T_a T_a T_a) V_x) T_a T_a T_a) V_x V_D T_a T_a)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) V_j) V_k))) (or (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_i _let_1 tptp.tc_nat) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_i V_j tptp.tc_nat) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_j _let_1 tptp.tc_nat) (tptp.tc_fun tptp.tc_nat tptp.tc_bool))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_i tptp.tc_nat) V_j)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Series_Osuminf V_f T_a) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))) (tptp.c_Series_Osuminf (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_k)) T_a))) (not (tptp.c_Series_Osummable V_f T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_RealVector_Oreal__normed__field T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Oinverse__class_Odivide T_b)) V_g) T_a T_b T_b) V_y) V_a _let_1 T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a _let_1 T_a T_b))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Odifferentiable (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide T_a)) V_f) V_g T_a T_a T_a) V_x T_a) (= (tptp.hAPP V_g V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Deriv_Odifferentiable V_g V_x T_a)) (not (tptp.c_Deriv_Odifferentiable V_f V_x T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Oplus__class_Oplus T_b)) V_f) V_g T_a T_b T_b) V_a _let_1 T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a _let_1 T_a T_b)) (not (tptp.c_Lim_OLIM V_f V_a _let_1 T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_net $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_b))) (or (not (tptp.class_RealVector_Oreal__normed__field T_b)) (tptp.c_Limits_Otendsto (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_f) V_g T_a T_b T_b) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_net T_a T_b) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_b)) (not (tptp.c_Limits_Otendsto V_g V_b V_net T_a T_b)) (not (tptp.c_Limits_Otendsto V_f V_a V_net T_a T_b))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) T_a) _let_1)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted) (V_a $$unsorted) (V_L $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_b)) (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_b T_a) V_f) (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Oplus__class_Oplus T_a) T_a T_a T_a) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_k) V_L T_a T_b) (not (tptp.c_Lim_OLIM V_f V_a V_L T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_net $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (tptp.c_Limits_OZfun (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Ominus__class_Ominus T_b)) V_f) T_a T_b T_b) V_a) V_net T_a T_b) (not (tptp.c_Limits_Otendsto V_f V_a V_net T_a T_b)))) (forall ((T_b $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_net $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (tptp.c_Limits_Otendsto V_f V_a V_net T_a T_b) (not (tptp.c_Limits_OZfun (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Ominus__class_Ominus T_b)) V_f) T_a T_b T_b) V_a) V_net T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_Da $$unsorted) (V_Db $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) _let_1) V_f) V_g T_a T_a T_a) V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_1 V_Da) (tptp.hAPP V_g V_x))) (tptp.hAPP (tptp.hAPP _let_1 V_Db) (tptp.hAPP V_f V_x))) T_a) (not (tptp.c_Deriv_Oderiv V_g V_x V_Db T_a)) (not (tptp.c_Deriv_Oderiv V_f V_x V_Da T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_E $$unsorted) (V_D $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) _let_1) V_f) V_g T_a T_a T_a) V_x (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP V_f V_x)) V_E)) (tptp.hAPP (tptp.hAPP _let_1 V_D) (tptp.hAPP V_g V_x))) T_a) (not (tptp.c_Deriv_Oderiv V_g V_x V_E T_a)) (not (tptp.c_Deriv_Oderiv V_f V_x V_D 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_HOL_Oord__class_Oless _let_1 T_a))) (let ((_let_3 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= _let_3 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) _let_3)))) (tptp.hBOOL (tptp.hAPP _let_2 _let_1))))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) _let_1) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) _let_1) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_a) V_n) (tptp.hAPP (tptp.hAPP _let_2 V_b) V_n))) (= V_a V_b) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_b))) (not (tptp.hBOOL (tptp.hAPP _let_1 V_a))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_X $$unsorted) (V_S $$unsorted) (V_L $$unsorted)) (let ((_let_1 (tptp.c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1 V_L V_S V_X T_a T_b))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_a T_b))) (let ((_let_3 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_a T_b) (tptp.tc_fun _let_3 T_b) tptp.tc_nat) _let_2) (tptp.c_COMBC V_X T_a tptp.tc_nat T_b)) tptp.tc_nat _let_3 T_b) V_S) (tptp.hAPP (tptp.hAPP _let_2 V_L) V_S) T_b) (not (tptp.c_SEQ_OLIMSEQ (tptp.hAPP V_X _let_1) (tptp.hAPP V_L _let_1) T_b))))))) (= (tptp.c_FFT__Mirabelle_Oroot _let_5) _let_25) _let_23 (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_d $$unsorted) (V_e $$unsorted)) (let ((_let_1 (tptp.hAPP V_g V_x))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) _let_3) V_f) V_g T_a T_a T_a) V_x (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_d) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_e) (tptp.hAPP V_f V_x)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) (tptp.hAPP tptp.c_Suc (tptp.hAPP tptp.c_Suc (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) T_a) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Deriv_Oderiv V_g V_x V_e T_a)) (not (tptp.c_Deriv_Oderiv V_f V_x V_d T_a))))))) (forall ((V_a $$unsorted)) (= (tptp.c_GCD_Ogcd__class_OLCM (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool)) tptp.tc_nat) tptp.tc_nat) V_a)) (forall ((V_a $$unsorted)) (= (tptp.c_GCD_Ogcd__class_OGCD (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool)) tptp.tc_nat) tptp.tc_nat) V_a)) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_D $$unsorted) (V_E $$unsorted)) (let ((_let_1 (tptp.hAPP V_g V_x))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) _let_3) V_f) V_g T_a T_a T_a) V_x (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP (tptp.hAPP _let_2 V_D) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP V_f V_x)) V_E))) (tptp.hAPP (tptp.hAPP _let_2 _let_1) _let_1)) T_a) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_Deriv_Oderiv V_g V_x V_E T_a)) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a))))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_FFT__Mirabelle_Oroot V_n)) V_n) (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (forall ((V_l $$unsorted) (V_u $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.hAPP tptp.c_Suc V_l) V_u tptp.tc_nat) (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan V_l V_u tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_3 (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) _let_3) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_n)) _let_1)) (tptp.hAPP (tptp.hAPP _let_2 V_x) _let_1))) (= V_x _let_1)))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_f))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP _let_3 (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 (tptp.hAPP (tptp.hAPP _let_4 V_n) V_k) tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) (tptp.hAPP (tptp.c_COMBC _let_4 tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_k))) (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_n tptp.tc_nat))) (tptp.hAPP _let_3 (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_k tptp.tc_nat)))))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_x $$unsorted) (V_g $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_b T_a) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) V_x)) V_g) V_a _let_1 T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a _let_1 T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_f $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_b T_a) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_b) V_c)) V_f) V_a _let_1 T_a T_b) (not (tptp.c_Lim_OLIM V_f V_a _let_1 T_a T_b))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_4 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_4 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_4 V_w) V_z)) (tptp.hAPP (tptp.hAPP _let_4 (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_z)) (tptp.hAPP (tptp.hAPP _let_2 V_w) V_y))) (tptp.hAPP (tptp.hAPP _let_2 V_y) V_z))) (= V_z _let_1) (= V_y _let_1))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_b))) (let ((_let_4 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_5 (tptp.hAPP _let_2 V_a))) (let ((_let_6 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.hAPP (tptp.hAPP _let_4 _let_5) _let_3) (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP (tptp.hAPP _let_6 _let_5) (tptp.hAPP (tptp.hAPP _let_4 V_b) V_a))) _let_3)) (= V_b _let_1) (= V_a _let_1))))))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_g) T_a T_b T_b) V_y) V_a (tptp.hAPP (tptp.hAPP _let_1 V_l) V_y) T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a V_l T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_net $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (tptp.c_Limits_Otendsto (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_g) T_a T_b T_b) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_y) V_net T_a T_b) (not (tptp.c_Limits_Otendsto V_g V_a V_net T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_y $$unsorted) (V_net $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (tptp.c_Limits_OZfun (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Otimes__class_Otimes T_b)) V_g) T_a T_b T_b) V_y) V_net T_a T_b) (not (tptp.c_Limits_OZfun V_g V_net T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_net $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (tptp.c_Limits_OZfun (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Otimes__class_Otimes T_b)) V_f) T_a T_b T_b) V_a) V_net T_a T_b) (not (tptp.c_Limits_OZfun V_f V_net T_a T_b)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (tptp.c_Lim_OisCont (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Otimes__class_Otimes T_b)) V_f) V_g T_a T_b T_b) V_a T_a T_b) (not (tptp.c_Lim_OisCont V_g V_a T_a T_b)) (not (tptp.c_Lim_OisCont V_f V_a T_a T_b)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Finite__Set_Osetprod (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_1) V_f) V_g T_b T_a T_a) V_A T_b T_a) (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_Finite__Set_Osetprod V_f V_A T_b T_a)) (tptp.c_Finite__Set_Osetprod V_g V_A T_b T_a)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_net $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (tptp.c_Limits_OZfun (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Otimes__class_Otimes T_b)) V_f) V_g T_a T_b T_b) V_net T_a T_b) (not (tptp.c_Limits_OZfun V_g V_net T_a T_b)) (not (tptp.c_Limits_OZfun V_f V_net T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Odifferentiable (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes T_a)) V_f) V_g T_a T_a T_a) V_x T_a) (not (tptp.c_Deriv_Odifferentiable V_g V_x T_a)) (not (tptp.c_Deriv_Odifferentiable V_f V_x T_a)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_net $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (tptp.c_Limits_Otendsto (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_f) V_g T_a T_b T_b) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_net T_a T_b) (not (tptp.c_Limits_Otendsto V_g V_b V_net T_a T_b)) (not (tptp.c_Limits_Otendsto V_f V_a V_net T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted) (V_L $$unsorted) (V_M $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_f) V_g T_a T_b T_b) V_a (tptp.hAPP (tptp.hAPP _let_1 V_L) V_M) T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a V_M T_a T_b)) (not (tptp.c_Lim_OLIM V_f V_a V_L T_a T_b))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oord__class_Oless _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (not (tptp.hBOOL (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n)))) (tptp.hBOOL (tptp.hAPP _let_2 _let_1)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) _let_1) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_2) _let_1) _let_2) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_2) _let_1) _let_2) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_net $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_b))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (tptp.c_Limits_Otendsto (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_f) V_g T_a T_b T_b) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) V_net T_a T_b) (not (tptp.c_Limits_Otendsto V_g V_b V_net T_a T_b)) (not (tptp.c_Limits_Otendsto V_f V_a V_net T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_l $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_b))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) _let_1) V_f) V_g T_a T_b T_b) V_x (tptp.hAPP (tptp.hAPP _let_1 V_l) V_m) T_a T_b) (not (tptp.c_Lim_OLIM V_g V_x V_m T_a T_b)) (not (tptp.c_Lim_OLIM V_f V_x V_l T_a T_b))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted) (V_D $$unsorted) (V_E $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Oderiv (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) _let_1) V_f) V_g T_a T_a T_a) V_x (tptp.hAPP (tptp.hAPP _let_1 V_D) V_E) T_a) (not (tptp.c_Deriv_Oderiv V_g V_x V_E T_a)) (not (tptp.c_Deriv_Oderiv V_f V_x V_D T_a))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (tptp.c_Lim_OisCont (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Ominus__class_Ominus T_b)) V_f) V_g T_a T_b T_b) V_a T_a T_b) (not (tptp.c_Lim_OisCont V_g V_a T_a T_b)) (not (tptp.c_Lim_OisCont V_f V_a T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_net $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (tptp.c_Limits_OZfun (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Ominus__class_Ominus T_b)) V_f) V_g T_a T_b T_b) V_net T_a T_b) (not (tptp.c_Limits_OZfun V_g V_net T_a T_b)) (not (tptp.c_Limits_OZfun V_f V_net T_a T_b)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Odifferentiable (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus T_a)) V_f) V_g T_a T_a T_a) V_x T_a) (not (tptp.c_Deriv_Odifferentiable V_g V_x T_a)) (not (tptp.c_Deriv_Odifferentiable V_f V_x T_a)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_g) V_A)) V_y) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_1) V_g) T_b T_a T_a) V_y)) V_A)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oinverse__class_Odivide T_a))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_f) V_A)) V_r) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_1) V_f) T_b T_a T_a) V_r)) V_A)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Osetsum T_b T_a))) (let ((_let_2 (tptp.c_HOL_Oplus__class_Oplus T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_2) V_f) V_g T_b T_a T_a)) V_A) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_f) V_A)) (tptp.hAPP (tptp.hAPP _let_1 V_g) V_A))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (T_c $$unsorted) (V_g $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_c tptp.tc_bool))) (let ((_let_2 (tptp.tc_fun T_c T_a))) (let ((_let_3 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_4 (tptp.tc_fun T_a T_a))) (let ((_let_5 (tptp.c_Finite__Set_Osetsum T_c T_a))) (let ((_let_6 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_6 V_f) V_A)) (tptp.hAPP (tptp.hAPP _let_5 V_g) V_B)) (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_2 (tptp.tc_fun _let_1 T_a) T_b) _let_5) (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB _let_4 (tptp.tc_fun _let_2 _let_2) T_b) (tptp.c_COMBB T_a T_a T_c)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a _let_4 T_b) _let_3) V_f)) T_b _let_2 _let_2) V_g)) T_b _let_1 T_a) V_B)) V_A)))))))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OZseq (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes T_a)) V_X) V_Y tptp.tc_nat T_a T_a) T_a) (not (tptp.c_SEQ_OZseq V_Y T_a)) (not (tptp.c_SEQ_OZseq V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) V_Y tptp.tc_nat T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (not (tptp.c_SEQ_OLIMSEQ V_Y V_b T_a)) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OZseq (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes T_a)) V_X) tptp.tc_nat T_a T_a) V_y) T_a) (not (tptp.c_SEQ_OZseq V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OZseq (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes T_a)) V_X) tptp.tc_nat T_a T_a) V_a) T_a) (not (tptp.c_SEQ_OZseq V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) tptp.tc_nat T_a T_a) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_y) T_a) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_SEQ_OCauchy (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes T_a)) V_X) tptp.tc_nat T_a T_a) V_y) T_a) (not (tptp.c_SEQ_OCauchy V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Series_Osummable (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes T_a)) V_X) tptp.tc_nat T_a T_a) V_y) T_a) (not (tptp.c_Series_Osummable V_X T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Series_Osummable (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes T_a)) V_f) tptp.tc_nat T_a T_a) V_c) T_a) (not (tptp.c_Series_Osummable V_f T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Series_Osums (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) tptp.tc_nat T_a T_a) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_y) T_a) (not (tptp.c_Series_Osums V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_Series_Osums (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_f) tptp.tc_nat T_a T_a) V_c) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_c) T_a) (not (tptp.c_Series_Osums V_f V_a T_a))))) (forall ((V_n $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex))) (or (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat tptp.tc_Complex_Ocomplex) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_2 (tptp.c_FFT__Mirabelle_Oroot V_n)) V_k))) (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_n tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_k tptp.tc_nat) V_n))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless _let_1 tptp.tc_nat) V_k))))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osums (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) V_Y tptp.tc_nat T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (not (tptp.c_Series_Osums V_Y V_b T_a)) (not (tptp.c_Series_Osums V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OZseq (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus T_a)) V_X) V_Y tptp.tc_nat T_a T_a) T_a) (not (tptp.c_SEQ_OZseq V_Y T_a)) (not (tptp.c_SEQ_OZseq V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osummable (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus T_a)) V_X) V_Y tptp.tc_nat T_a T_a) T_a) (not (tptp.c_Series_Osummable V_Y T_a)) (not (tptp.c_Series_Osummable V_X T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_Y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_X) V_Y tptp.tc_nat T_a T_a) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (not (tptp.c_SEQ_OLIMSEQ V_Y V_b T_a)) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_1) V_f) tptp.tc_nat T_a T_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) T_a) (not (tptp.c_SEQ_OLIMSEQ V_f V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_a)) (= (tptp.c_Complete__Lattice_OSup__class_OSup (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) T_a) T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_a V_b T_a)))) (forall ((V_f $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a V_B T_b) T_a T_b) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Ovimage V_f (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool)) T_b) T_a T_b) (tptp.c_Set_Ovimage V_f V_B T_a T_b) (tptp.tc_fun T_a tptp.tc_bool)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_p $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_p tptp.tc_nat))) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat))) (tptp.hAPP _let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_n V_p tptp.tc_nat))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_n tptp.tc_nat) V_p))) (not (tptp.hBOOL (tptp.hAPP (tptp.c_lessequals V_m tptp.tc_nat) V_n)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_Power_Opower T_b)) (tptp.c_Lim_OisCont (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun tptp.tc_nat T_b) T_a) (tptp.c_Power_Opower__class_Opower T_b)) V_f) T_a tptp.tc_nat T_b) V_n) V_a T_a T_b) (not (tptp.c_Lim_OisCont V_f V_a T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (V_l $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_Power_Opower T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun tptp.tc_nat T_b) T_a) _let_1) V_f) T_a tptp.tc_nat T_b) V_n) V_a (tptp.hAPP (tptp.hAPP _let_1 V_l) V_n) T_a T_b) (not (tptp.c_Lim_OLIM V_f V_a V_l T_a T_b))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_Deriv_Odifferentiable (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun tptp.tc_nat T_a) T_a) (tptp.c_Power_Opower__class_Opower T_a)) V_f) T_a tptp.tc_nat T_a) V_n) V_x T_a) (not (tptp.c_Deriv_Odifferentiable V_f V_x T_a)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted) (V_s $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_Series_Osums (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) (tptp.hAPP (tptp.c_COMBC (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat) tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_s) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_k tptp.tc_nat))) T_a) (not (tptp.c_Series_Osums V_f V_s T_a)))) (forall ((T_a $$unsorted) (V_X $$unsorted) (V_m $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (not (tptp.class_Power_Opower T_a)) (tptp.c_SEQ_OLIMSEQ (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun tptp.tc_nat T_a) tptp.tc_nat) _let_1) V_X) tptp.tc_nat tptp.tc_nat T_a) V_m) (tptp.hAPP (tptp.hAPP _let_1 V_a) V_m) T_a) (not (tptp.c_SEQ_OLIMSEQ V_X V_a T_a))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_f) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.hAPP tptp.c_Suc V_m) (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) tptp.c_Suc)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat)))))) (forall ((T_a $$unsorted) (V_l $$unsorted) (V_m $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (or (not (tptp.class_Orderings_Oorder T_a)) (= (tptp.c_Lattices_Olower__semilattice__class_Oinf (tptp.c_SetInterval_Oord__class_OgreaterThanLessThan V_l V_m T_a) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_u T_a) _let_1) (tptp.c_Orderings_Obot__class_Obot _let_1))))) (forall ((V_k $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_k) tptp.v_i) tptp.tc_nat) tptp.v_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless V_k tptp.tc_nat) tptp.v_n))))) (forall ((V_k $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_HOL_Oord__class_Oless (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) tptp.v_i) V_k) tptp.tc_nat) tptp.v_n))) (= (tptp.c_SetInterval_Oord__class_OatMost _let_5 tptp.tc_nat) (tptp.c_Set_Oinsert _let_5 _let_3 tptp.tc_nat)) (forall ((V_m $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.hAPP tptp.c_Suc V_m) tptp.tc_nat) (tptp.c_Set_Oinsert V_m (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool)) tptp.tc_nat))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_g $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Otimes__class_Otimes T_b)) V_g) T_a T_b T_b) V_y) V_a _let_1 T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a _let_1 T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Otimes__class_Otimes T_b)) V_f) T_a T_b T_b) V_c) V_a _let_1 T_a T_b) (not (tptp.c_Lim_OLIM V_f V_a _let_1 T_a T_b))))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_a $$unsorted) (V_l $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM V_f V_a V_l T_a T_b) (not (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Ominus__class_Ominus T_b)) V_f) T_a T_b T_b) V_l) V_a (tptp.c_HOL_Ozero__class_Ozero T_b) T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_l $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Ominus__class_Ominus T_b)) V_f) T_a T_b T_b) V_l) V_a (tptp.c_HOL_Ozero__class_Ozero T_b) T_a T_b) (not (tptp.c_Lim_OLIM V_f V_a V_l T_a T_b)))) (forall ((T_b $$unsorted) (T_a $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_b))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_b)) (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_Lim_OLIM (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b (tptp.tc_fun T_b T_b) T_a) (tptp.c_HOL_Otimes__class_Otimes T_b)) V_f) V_g T_a T_b T_b) V_a _let_1 T_a T_b) (not (tptp.c_Lim_OLIM V_g V_a _let_1 T_a T_b)) (not (tptp.c_Lim_OLIM V_f V_a _let_1 T_a T_b))))) (forall ((V_n $$unsorted) (V_a $$unsorted)) (= (tptp.c_FFT__Mirabelle_OIDFT V_n V_a tptp.v_i) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat tptp.tc_Complex_Ocomplex) (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex) tptp.tc_nat) (tptp.c_HOL_Oinverse__class_Odivide tptp.tc_Complex_Ocomplex)) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_nat) (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_FFT__Mirabelle_Oroot V_n))) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) tptp.v_i)) tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_L $$unsorted) (V_g $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OLIMSEQ V_f V_L T_a) (not (tptp.c_SEQ_OLIMSEQ (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus T_a)) V_f) V_g tptp.tc_nat T_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_SEQ_OLIMSEQ V_g V_L T_a)))) (forall ((T_a $$unsorted) (V_g $$unsorted) (V_L $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_SEQ_OLIMSEQ V_g V_L T_a) (not (tptp.c_SEQ_OLIMSEQ (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Ominus__class_Ominus T_a)) V_f) V_g tptp.tc_nat T_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_SEQ_OLIMSEQ V_f V_L T_a)))) (= (tptp.hAPP (tptp.hAPP _let_14 (tptp.c_COMBS (tptp.hAPP _let_17 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP _let_15 (tptp.hAPP _let_13 (tptp.c_COMBS (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_bool (tptp.tc_fun tptp.tc_Complex_Ocomplex _let_16) tptp.tc_nat) (tptp.c_HOL_OIf tptp.tc_Complex_Ocomplex)) (tptp.c_lessequals tptp.v_i tptp.tc_nat)) _let_11 tptp.tc_nat tptp.tc_Complex_Ocomplex _let_16) (tptp.hAPP (tptp.hAPP _let_10 (tptp.hAPP _let_9 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oinverse__class_Odivide tptp.tc_Complex_Ocomplex) _let_25) _let_8))) (tptp.hAPP _let_7 tptp.v_i)) tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex))) tptp.tc_nat _let_2 tptp.tc_Complex_Ocomplex) _let_6)) tptp.v_a tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex)) _let_6) _let_20) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) V_f))) (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.hAPP _let_2 (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.hAPP tptp.c_Suc _let_1) V_k tptp.tc_nat)) (tptp.hAPP _let_2 (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_k tptp.tc_nat))))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_m $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 V_f) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.hAPP (tptp.hAPP _let_1 V_m) V_k) (tptp.hAPP (tptp.hAPP _let_1 V_n) V_k) tptp.tc_nat)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) (tptp.hAPP (tptp.c_COMBC _let_1 tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_k))) (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m V_n tptp.tc_nat))))))) _let_24 (forall ((T_a $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_Series_Osuminf (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes T_a)) V_f) (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) tptp.tc_nat T_a T_a) T_a) (tptp.hAPP V_f (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_k $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_f))) (let ((_let_4 (tptp.c_HOL_Oplus__class_Oplus tptp.tc_nat))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) V_f) (tptp.hAPP (tptp.c_COMBC _let_4 tptp.tc_nat tptp.tc_nat tptp.tc_nat) V_k))) (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_n tptp.tc_nat)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) (tptp.hAPP _let_3 (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 (tptp.hAPP (tptp.hAPP _let_4 V_n) V_k) tptp.tc_nat))) (tptp.hAPP _let_3 (tptp.c_SetInterval_Oord__class_OatLeastLessThan _let_1 V_k tptp.tc_nat)))))))))) (forall ((V_n $$unsorted) (V_a $$unsorted)) (= (tptp.c_FFT__Mirabelle_ODFT V_n V_a tptp.v_i) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat tptp.tc_Complex_Ocomplex) (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes tptp.tc_Complex_Ocomplex)) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_nat) (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_FFT__Mirabelle_Oroot V_n))) (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes tptp.tc_nat) tptp.v_i))) V_a tptp.tc_nat tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_f $$unsorted) (V_n $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (let ((_let_3 (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_3 V_f) _let_1)) (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a)) V_r)) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_2) V_f) tptp.tc_nat T_a T_a) V_r)) _let_1))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_n))) (let ((_let_2 (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) _let_1 tptp.tc_nat))) (let ((_let_3 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_4 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_5 (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) (tptp.hAPP _let_4 V_y)))) (let ((_let_6 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_7 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_6) (tptp.hAPP _let_4 V_x)))) (let ((_let_8 (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_COMBS _let_7 (tptp.hAPP _let_5 (tptp.hAPP _let_3 _let_1)) tptp.tc_nat T_a T_a)) _let_2) (tptp.hAPP (tptp.hAPP _let_6 V_y) (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_COMBS _let_7 (tptp.hAPP _let_5 (tptp.hAPP _let_3 V_n)) tptp.tc_nat T_a T_a)) _let_2))))))))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) (tptp.hAPP tptp.c_Suc V_n) tptp.tc_nat))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_y))) (let ((_let_4 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n))) (let ((_let_5 (tptp.hAPP _let_2 V_x))) (let ((_let_6 (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat))) (let ((_let_7 (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) (tptp.c_HOL_Otimes__class_Otimes T_a)))) (let ((_let_8 (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a))) (or (not (tptp.class_Power_Opower T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_COMBS (tptp.hAPP _let_7 _let_5) (tptp.hAPP (tptp.hAPP _let_6 _let_3) _let_4) tptp.tc_nat T_a T_a)) _let_1) (tptp.hAPP (tptp.hAPP _let_8 (tptp.c_COMBS (tptp.hAPP _let_7 (tptp.hAPP (tptp.hAPP _let_6 _let_5) _let_4)) _let_3 tptp.tc_nat T_a T_a)) _let_1)))))))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.c_Suc V_n))) (let ((_let_2 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_3 (tptp.hAPP _let_2 V_y))) (let ((_let_4 (tptp.hAPP _let_2 V_x))) (let ((_let_5 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_6 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_6 (tptp.hAPP _let_4 _let_1)) (tptp.hAPP _let_3 _let_1)) (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP (tptp.hAPP _let_6 V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a) (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat) _let_5) _let_4) (tptp.hAPP (tptp.hAPP (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat) _let_3) (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_n)) tptp.tc_nat T_a T_a)) (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) _let_1 tptp.tc_nat)))))))))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_h $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_SetInterval_Oord__class_OatLeastLessThan (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_m tptp.tc_nat))) (let ((_let_2 (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m))) (let ((_let_3 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_4 (tptp.hAPP _let_3 V_z))) (let ((_let_5 (tptp.c_COMBB tptp.tc_nat T_a tptp.tc_nat))) (let ((_let_6 (tptp.hAPP (tptp.hAPP _let_5 (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Oplus__class_Oplus T_a) V_z) V_h))) _let_2))) (let ((_let_7 (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_nat))) (let ((_let_8 (tptp.hAPP _let_7 (tptp.c_HOL_Ominus__class_Ominus T_a)))) (let ((_let_9 (tptp.hAPP _let_7 (tptp.c_HOL_Otimes__class_Otimes T_a)))) (let ((_let_10 (tptp.c_Finite__Set_Osetsum tptp.tc_nat T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_10 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP _let_8 (tptp.c_COMBS (tptp.hAPP _let_9 _let_6) _let_4 tptp.tc_nat T_a T_a)) tptp.tc_nat T_a T_a) (tptp.hAPP _let_4 V_m))) _let_1) (tptp.hAPP (tptp.hAPP _let_10 (tptp.c_COMBS (tptp.hAPP _let_9 _let_4) (tptp.c_COMBS (tptp.hAPP _let_8 _let_6) (tptp.hAPP (tptp.hAPP _let_5 _let_4) _let_2) tptp.tc_nat T_a T_a) tptp.tc_nat T_a T_a)) _let_1)))))))))))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_b) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_A $$unsorted)) (not (= (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)) (tptp.c_Set_Oinsert V_a V_A T_a)))) (forall ((V_m $$unsorted)) (= (tptp.c_SetInterval_Oord__class_OatLeastLessThan V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun tptp.tc_nat tptp.tc_bool)))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_x V_A T_a) V_x))) (forall ((T_a $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (V_f $$unsorted) (V_B $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.tc_fun T_b tptp.tc_bool))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (let ((_let_3 (tptp.c_Finite__Set_Osetsum T_c T_a))) (let ((_let_4 (tptp.tc_fun T_c tptp.tc_bool))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_c T_a) (tptp.tc_fun _let_4 T_a) T_b) _let_3) V_f) T_b _let_4 T_a) V_B)) V_A) (tptp.hAPP (tptp.hAPP _let_3 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun T_b T_a) (tptp.tc_fun _let_1 T_a) T_c) _let_2) (tptp.c_COMBC V_f T_b T_c T_a)) T_c _let_1 T_a) V_A)) V_B)))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_x) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_b) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_y) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) _let_1) V_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_2 _let_1) V_a) (tptp.hAPP (tptp.hAPP _let_2 V_a) _let_1)))))) (forall ((V_A $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_A V_x)) (= V_y V_x) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x))))) (forall ((V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Set_Oinsert V_x V_A T_a))) (= (tptp.c_Set_Oinsert V_x _let_1 T_a) _let_1))) (forall ((V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a V_B T_a) V_C _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) T_a)))) (forall ((V_A $$unsorted) (V_a $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Set_Oinsert V_a V_B T_a) _let_1) (tptp.c_Set_Oinsert V_a (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) T_a)))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.c_Finite__Set_Osetsum T_b T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.c_COMBS (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_2) V_f) V_g T_b T_a T_a)) V_A) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_f) V_A)) (tptp.hAPP (tptp.hAPP _let_1 V_g) V_A))))))) (forall ((V_xa $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (= (tptp.c_Set_Oinsert V_xa (tptp.c_Set_Oinsert V_x _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_xa _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_r))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_f) V_A)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a T_b) _let_1) V_f)) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_A $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_g) V_A)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a T_a T_b) _let_1) V_g)) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_x))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_y) V_z)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_y)) V_z)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ry)))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_rx))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) V_rx) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) V_ly)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_b)) V_c) (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_b) V_c))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup _let_2 _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_n)) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_n))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_q)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_q))))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted) (V_A $$unsorted) (V_r $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_f) V_A)) V_r) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_1) V_f) T_b T_a T_a) V_r)) V_A)))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_g $$unsorted) (V_A $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_Finite__Set_Osetsum T_b T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_g) V_A)) V_y) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.c_COMBC (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) T_b) _let_1) V_g) T_b T_a T_a) V_y)) V_A)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x) V_x) V_x))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring__0 T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) _let_1) V_n) _let_1) (= V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_x))) (let ((_let_2 (tptp.hAPP _let_1 V_y))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.hAPP _let_1 _let_2) _let_2))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_a V_c)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_a V_d) (= V_b V_d)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a (tptp.c_Set_Oinsert V_b _let_1 T_a) T_a) (tptp.c_Set_Oinsert V_c (tptp.c_Set_Oinsert V_d _let_1 T_a) T_a))) (= V_b V_c) (= V_b V_d)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (or (not (= (tptp.hAPP (tptp.hAPP _let_2 V_n) V_m) _let_1)) (not (= (tptp.hAPP (tptp.hAPP _let_2 V_m) V_n) _let_1)) (= V_m V_n))))) (forall ((T_a $$unsorted) (T_b $$unsorted) (V_f $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Finite__Set_Osetsum T_b T_a) V_f) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_b tptp.tc_bool))) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$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_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_1 V_lx) V_ly)))) (let ((_let_3 (tptp.hAPP _let_1 V_rx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP _let_2 (tptp.hAPP _let_3 V_ry)) (tptp.hAPP _let_3 (tptp.hAPP _let_2 V_ry)))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry))) (let ((_let_3 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_3 V_ly)) _let_2) (tptp.hAPP _let_3 (tptp.hAPP (tptp.hAPP _let_1 V_ly) _let_2)))))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.hAPP _let_1 V_lx))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_ly)) (tptp.hAPP (tptp.hAPP _let_1 V_rx) V_ry)) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_rx)) (tptp.hAPP (tptp.hAPP _let_1 V_ly) V_ry))))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Orderings_Obot__class_Obot T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Orderings_Obot__class_Obot _let_1) V_B _let_1) V_B))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Orderings_Obot__class_Obot _let_1) _let_1) V_A))) (forall ((V_B $$unsorted) (V_x $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (or (tptp.hBOOL (tptp.hAPP V_B V_x)) (tptp.hBOOL (tptp.hAPP V_A V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_B V_x))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B (tptp.tc_fun T_a tptp.tc_bool)) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a) V_b) _let_1)) (= V_a _let_1) (= V_b _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_x) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) V_m) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) V_m)) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (not (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_x))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b) (tptp.hAPP (tptp.hAPP _let_1 V_b) V_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_x T_a) V_x))) (forall ((V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_A (tptp.tc_fun T_a tptp.tc_bool)) V_A)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (= (tptp.c_Set_Oinsert V_x (tptp.c_Set_Oinsert V_y V_A T_a) T_a) (tptp.c_Set_Oinsert V_y (tptp.c_Set_Oinsert V_x V_A T_a) T_a))) (forall ((T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_P) V_Q) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBS V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x) (tptp.hAPP (tptp.hAPP _let_1 V_x_H) V_y_H))) (= V_x_H V_y_H)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP _let_1 V_xa) V_y) (tptp.hAPP (tptp.hAPP _let_1 V_x) V_x))) (= V_xa V_y)))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat) _let_1) V_n) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted) (V_C $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) V_C _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (V_C $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_C _let_1) _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_C _let_1) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) V_z T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_z T_a) T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot (tptp.tc_fun T_a tptp.tc_bool)))) (or (not (= (tptp.c_Set_Oinsert V_a _let_1 T_a) (tptp.c_Set_Oinsert V_b _let_1 T_a))) (= V_a V_b)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_a) V_b) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_HOL_Ominus__class_Ominus T_a) V_x) V_y) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_xa))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_x)) (tptp.hAPP _let_1 V_y))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (let ((_let_1 (tptp.hAPP (tptp.c_HOL_Otimes__class_Otimes T_a) V_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_b) V_b_H)) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP _let_1 V_b)) (tptp.hAPP _let_1 V_b_H))))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_a) V_a_H)) V_b) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_a) V_b)) (tptp.hAPP (tptp.hAPP _let_1 V_a_H) V_b))))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP (tptp.hAPP _let_2 V_x) V_y)) V_ya) (tptp.hAPP (tptp.hAPP _let_2 (tptp.hAPP (tptp.hAPP _let_1 V_x) V_ya)) (tptp.hAPP (tptp.hAPP _let_1 V_y) V_ya))))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.tc_nat))) (let ((_let_2 (tptp.hAPP _let_1 V_i))) (= (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_j)) V_k) (tptp.hAPP (tptp.hAPP _let_1 (tptp.hAPP _let_2 V_k)) V_j))))) (forall ((V_y $$unsorted) (V_A $$unsorted) (T_a $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Set_Oinsert V_y V_A T_a) V_x)) (not (tptp.hBOOL (tptp.hAPP V_A V_x))))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_B _let_1)))) (forall ((T_a $$unsorted) (V_A $$unsorted) (V_B $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Obot__class_Obot T_a))) (or (not (tptp.class_Lattices_Obounded__lattice T_a)) (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B T_a) _let_1)) (= V_A _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_A _let_2))))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Orderings_Obot__class_Obot _let_1))) (or (not (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) _let_2)) (= V_B _let_2))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_B V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup V_y V_x T_a)))) (forall ((V_a $$unsorted) (V_A $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (= (tptp.c_Set_Oinsert V_a V_A T_a) (tptp.c_Lattices_Oupper__semilattice__class_Osup (tptp.c_Set_Oinsert V_a (tptp.c_Orderings_Obot__class_Obot _let_1) T_a) V_A _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Oupper__semilattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) (forall ((V_A $$unsorted) (V_B $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_fun T_a tptp.tc_bool))) (let ((_let_2 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A V_B _let_1))) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_A _let_2 _let_1) _let_2)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x V_y T_a))) (or (not (tptp.class_Lattices_Olattice T_a)) (= (tptp.c_Lattices_Oupper__semilattice__class_Osup V_x _let_1 T_a) _let_1)))) _let_23 _let_22 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Complete__Lattice_Ocomplete__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Complete__Lattice_Ocomplete__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Oupper__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olower__semilattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Odistrib__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Odistrib__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Obounded__lattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Obounded__lattice T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)) (not (tptp.class_Orderings_Opreorder T_1)))) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (or (tptp.class_Lattices_Olattice (tptp.tc_fun T_2 T_1)) (not (tptp.class_Lattices_Olattice T_1)))) (forall ((T_2 $$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)))) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Lattices_Oupper__semilattice tptp.tc_nat) (tptp.class_Lattices_Olower__semilattice tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_Lattices_Odistrib__lattice tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) _let_1 (tptp.class_Lattices_Olattice 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_Complete__Lattice_Ocomplete__lattice tptp.tc_bool) (tptp.class_Lattices_Oupper__semilattice tptp.tc_bool) (tptp.class_Lattices_Olower__semilattice tptp.tc_bool) (tptp.class_Lattices_Odistrib__lattice tptp.tc_bool) (tptp.class_Lattices_Obounded__lattice tptp.tc_bool) (tptp.class_Orderings_Opreorder tptp.tc_bool) (tptp.class_Lattices_Olattice tptp.tc_bool) (tptp.class_Orderings_Oorder tptp.tc_bool) (tptp.class_Orderings_Obot tptp.tc_bool) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add__meet tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add__join tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__ring__strict tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocancel__semigroup__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_Ring__and__Field_Ocomm__semiring__0 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__ring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_Int_Oint) (tptp.class_Lattices_Oupper__semilattice tptp.tc_Int_Oint) (tptp.class_Lattices_Olower__semilattice tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Int_Oint) (tptp.class_Lattices_Odistrib__lattice tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oidom tptp.tc_Int_Oint) (tptp.class_Nat_Osemiring__char__0 tptp.tc_Int_Oint) (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint) (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint) (tptp.class_Lattices_Olattice tptp.tc_Int_Oint) (tptp.class_Orderings_Oorder tptp.tc_Int_Oint) (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint) (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint) (tptp.class_Power_Opower tptp.tc_Int_Oint) (tptp.class_Int_Onumber tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odivision__ring tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Ometric__space tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__field tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ofield tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oidom tptp.tc_Complex_Ocomplex) (tptp.class_Nat_Osemiring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex) (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber tptp.tc_Complex_Ocomplex) (forall ((V_P $$unsorted) (V_Q $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.c_COMBS V_P V_Q T_b T_c T_a) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) (tptp.hAPP V_Q V_R)))) (forall ((V_P $$unsorted) (T_b $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBC V_P T_b T_c T_a) V_Q) V_R) (tptp.hAPP (tptp.hAPP V_P V_R) V_Q))) (forall ((T_b $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (V_P $$unsorted) (V_Q $$unsorted) (V_R $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c) V_P) V_Q) V_R) (tptp.hAPP V_P (tptp.hAPP V_Q V_R)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (tptp.c_fequal V_x V_x T_a)) (forall ((V_X $$unsorted) (V_Y $$unsorted) (T_a $$unsorted)) (or (= V_X V_Y) (not (tptp.c_fequal V_X V_Y T_a))))))))))))))))))))))))))))))))))))))))))))))
% 1.72/1.97  )
% 1.72/1.98  % SZS output end Proof for SWV693-1
% 1.72/1.98  % cvc5---1.0.5 exiting
% 1.72/1.99  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------