TSTP Solution File: SWV573-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV573-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 21:52:33 EDT 2023
% Result : Unsatisfiable 1.08s 1.33s
% Output : Proof 1.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.25 % Problem : SWV573-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.26 % Command : do_cvc5 %s %d
% 0.26/0.47 % Computer : n004.cluster.edu
% 0.26/0.47 % Model : x86_64 x86_64
% 0.26/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.47 % Memory : 8042.1875MB
% 0.26/0.47 % OS : Linux 3.10.0-693.el7.x86_64
% 0.26/0.47 % CPULimit : 300
% 0.26/0.47 % WCLimit : 300
% 0.26/0.47 % DateTime : Tue Aug 29 10:33:07 EDT 2023
% 0.26/0.47 % CPUTime :
% 0.47/0.73 %----Proving TF0_NAR, FOF, or CNF
% 0.47/0.73 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.B2HuW6llch/cvc5---1.0.5_18848.p...
% 0.57/0.87 ------- get file name : TPTP file name is SWV573-1
% 0.57/0.88 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18848.smt2...
% 0.57/0.88 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.08/1.33 % SZS status Unsatisfiable for SWV573-1
% 1.08/1.33 % SZS output start Proof for SWV573-1
% 1.08/1.36 (
% 1.08/1.36 (let ((_let_1 (tptp.class_RealVector_Oreal__algebra__1 tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_3 (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.v_n tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.c_Complex_Ocomplex_OComplex _let_3 _let_2))) (let ((_let_5 (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.v_n tptp.tc_Complex_Ocomplex))) (let ((_let_6 (= _let_5 _let_4))) (let ((_let_7 (not _let_6))) (let ((_let_8 (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n tptp.tc_RealDef_Oreal) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a)))))) (let ((_let_9 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_10 (tptp.c_Complex_Ocomplex_OComplex _let_2 _let_2))) (let ((_let_11 (forall ((V_x $$unsorted)) (= (tptp.c_Complex_Ocomplex_OComplex V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealVector_Oof__real V_x tptp.tc_Complex_Ocomplex))))) (let ((_let_12 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_13 (tptp.c_Complex_Ocomplex_OComplex _let_12 _let_2))) (let ((_let_14 (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (let ((_let_15 (tptp.c_Complex_Ocomplex_OComplex _let_2 _let_12))) (let ((_let_16 (tptp.c_RealVector_Oof__real _let_3 tptp.tc_Complex_Ocomplex))) (let ((_let_17 (= _let_4 _let_16))) (let ((_let_18 (= _let_5 _let_16))) (let ((_let_19 (ASSUME :args (_let_7)))) (let ((_let_20 (_let_11))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (not _let_1))) (let ((_let_23 (or _let_22 _let_18))) (let ((_let_24 (_let_8))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (and _let_7 _let_17))) (let ((_let_27 (_let_7 _let_17))) (let ((_let_28 (ASSUME :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_26)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_19 _let_28) (SCOPE (FALSE_ELIM (TRANS (CONG (REFL :args (_let_5)) (SYMM _let_28) :args (=)) (FALSE_INTRO _let_19))) :args _let_27)) :args _let_27)) :args (true _let_26)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) (REFL :args ((not _let_17))) (REFL :args ((not _let_18))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_18 (not _let_23)))) (ASSUME :args (_let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.tc_Complex_Ocomplex tptp.v_n QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a)))) :args _let_24))) _let_25 :args (_let_23 false _let_8)) :args (_let_18 false _let_1 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Complex_Ocomplex_OComplex V_x _let_2)))) :args _let_20)) _let_21 :args (_let_17 false _let_11)) _let_19 :args (false false _let_18 false _let_17 true _let_6)) :args ((forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= V_a (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x_H V_y_H T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals _let_2 _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_RealVector_Oof__real V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b))) (= (tptp.c_Complex_ORe _let_14) _let_12) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Osgn__div__norm T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) tptp.tc_RealDef_Oreal) V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_a V_b) (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (= V_a (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_r V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_r V_d T_a) T_a))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 (tptp.c_Log_Opowr V_x V_a) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (= V_a _let_1) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_h $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) V_h T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_h T_a) T_a) _let_2 T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Osgn__class_Osgn V_x T_a) T_a) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_RealVector_Oreal__div__algebra T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Oinverse__class_Oinverse V_x tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_RealVector_Oof__real V_x T_a) T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 (tptp.c_NthRoot_Osqrt V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals _let_1 V_y tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((V_x $$unsorted)) (tptp.c_lessequals (tptp.c_Transcendental_Ocos V_x) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal) (= V_x V_y) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_r V_s tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) V_s tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) V_r tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real V_r T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Oone__class_Oone T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals _let_2 V_a T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_lessequals V_a _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ly T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly V_rx T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ry T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a)))) (forall ((V_z1 $$unsorted) (V_z2 $$unsorted) (V_z3 $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_z1 V_z2 tptp.tc_RealDef_Oreal) V_z3 tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_z1 (tptp.c_HOL_Otimes__class_Otimes V_z2 V_z3 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_xa V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_b_H T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_ya T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_a_H T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (not (tptp.c_lessequals V_x _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((V_x $$unsorted)) (tptp.c_lessequals (tptp.c_Transcendental_Osin V_x) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a))) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_m T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_m T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (= V_z _let_1) (= V_y _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (forall ((V_x $$unsorted)) (or (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_x tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Osgn__class_Osgn V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((V_z $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_RealVector_Oof__real V_z tptp.tc_Complex_Ocomplex)) V_z)) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_b T_a)))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= (tptp.c_NthRoot_Oroot V_n V_x) _let_1) (tptp.c_HOL_Oord__class_Oless V_x _let_1 tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal)))) (= (tptp.c_Complex_ORe tptp.c_Complex_Oii) _let_2) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_OrderedGroup_Olordered__ab__group__add__class_Opprt V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) tptp.tc_RealDef_Oreal) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_lessequals V_a _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals _let_2 V_a T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_2 V_a T_a) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1 T_a)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1 T_a) V_a) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_2 _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_lessequals _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Osgn__class_Osgn V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_z V_w T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_w T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Ominus__class_Ominus V_b V_b_H T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (= V_z V_w) (not (tptp.c_lessequals V_w V_z tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_z V_w tptp.tc_RealDef_Oreal)))) (forall ((V_w $$unsorted)) (not (= tptp.c_Complex_Oii (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_Complex_Ocomplex)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_NthRoot_Osqrt V_x) _let_1)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_v $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_Complex_Ocomplex)) (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_2)) (= _let_2 _let_1))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 _let_2)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= V_a _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1 T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Ocos V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_y V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes _let_1 V_ry T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_ly V_ry T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_lessequals (tptp.c_RealVector_Odist__class_Odist V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a) V_a) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__div__algebra T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Oinverse__class_Oinverse V_a tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_RealVector_Oreal__div__algebra T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Oinverse__class_Oinverse V_a tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_x T_a) V_y T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (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_Osgn__if T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= (tptp.c_HOL_Osgn__class_Osgn V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_2 _let_1 T_a) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x _let_1 tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals V_x _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_3 T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_k $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_k T_a) (tptp.c_HOL_Otimes__class_Otimes V_k (tptp.c_HOL_Osgn__class_Osgn V_k T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((V_x $$unsorted)) (not (= (tptp.c_Transcendental_Ocos (tptp.c_Transcendental_Oarctan V_x)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a) V_y T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a) V_y T_a)) (= V_y (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) _let_2 T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Osgn__class_Osgn V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Osgn__class_Osgn V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_lessequals (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_x V_b) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_a V_b tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a))) (= V_y V_z))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a))) (= V_b V_c))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocancel__semigroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a))) (= V_b V_c))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Log_Opowr V_x V_a) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Ocos V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) tptp.tc_RealDef_Oreal)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1)))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (= (tptp.c_Transcendental_Ocos _let_2) _let_12) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_NthRoot_Osqrt V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (= (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_RealVector_Odist__class_Odist V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_a T_a) V_b T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) V_y T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_b T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) V_y T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_y T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (= V_a _let_1) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_a T_a) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_a T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Oexp V_x T_a) (tptp.c_Transcendental_Oexp V_y T_a) T_a) (tptp.c_Transcendental_Oexp (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted) (V_u $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_u T_a))) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) V_u))) (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_Osgn__if T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a) (= V_x _let_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_NthRoot_Osqrt V_x) _let_1)) (not (tptp.c_lessequals _let_1 V_x tptp.tc_RealDef_Oreal)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_OrderedGroup_Olordered__ab__group__add__class_Opprt V_a T_a) V_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_OrderedGroup_Olordered__ab__group__add__class_Opprt V_a T_a) V_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))) (= _let_2 _let_1))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_2 _let_1)) (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_1 _let_2)) (= _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Osgn__class_Osgn V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Osgn__class_Osgn V_a T_a) T_a))))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_y V_a) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals _let_1 V_a tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oabs__if T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_z (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Otimes__class_Otimes V_z V_y T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_NthRoot_Osqrt V_x) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.c_HOL_Oabs__class_Oabs V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) T_a))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transcendental_Oarctan V_x) (tptp.c_Transcendental_Oarctan V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Ominus__class_Ominus V_b V_c T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Odist__class_Odist V_x V_x T_a) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_Log_Opowr (tptp.c_Log_Opowr V_x V_a) V_b) (tptp.c_Log_Opowr (tptp.c_Log_Opowr V_x V_b) V_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (not (= (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_RealVector_Oof__real V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Olordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_lessequals V_c _let_1 T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_Transcendental_Oexp (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Transcendental_Oexp V_x T_a) (tptp.c_Transcendental_Oexp V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_x T_a) V_x))) (forall ((V_z $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal) V_z)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a) V_a))) (forall ((V_y $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_Transcendental_Oarctan V_y)) V_y)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_x T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_2 T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_c T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_x V_d T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_2 T_a) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (let ((_let_2 (tptp.c_HOL_Oabs__class_Oabs V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_a T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)))))) (= (tptp.c_Complex_Ocnj _let_9) _let_9) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless V_x _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) T_a) T_a) T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.c_lessequals _let_1 _let_1 T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a)))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_z V_w tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_w V_z tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_Transcendental_Oexp (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) V_y T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_x V_b) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_x V_b) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_x V_b) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_x V_b) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (tptp.c_lessequals (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_x V_b) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_a V_b tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_a V_b tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_x V_b) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_x $$unsorted)) (or (not (= (tptp.c_Transcendental_Ocos V_x) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Transcendental_Osin V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_h $$unsorted)) (or (not (tptp.class_RealVector_Oreal__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_d T_a) T_a) V_h T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) V_h T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) V_h T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) _let_1 T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= (tptp.c_Log_Opowr (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_RealDef_Oreal) V_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_y V_a) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (or (= (tptp.c_Log_Opowr V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (not (= (tptp.c_Log_Opowr V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= (tptp.c_Transcendental_Ocos (tptp.c_Complex_Oarg (tptp.c_Complex_Ocomplex_OComplex _let_1 V_y))) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= (tptp.c_Transcendental_Ocos (tptp.c_Complex_Oarg (tptp.c_Complex_Ocomplex_OComplex _let_1 V_y))) _let_1) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oarctan V_x) (tptp.c_Transcendental_Oarctan V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_RealVector_Oof__real V_r T_a) T_a) (tptp.c_RealVector_Oof__real (tptp.c_HOL_Osgn__class_Osgn V_r tptp.tc_RealDef_Oreal) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_RealDef_Oreal) T_a) (tptp.c_Int_Onumber__class_Onumber__of V_w T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a))) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a))) (= V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((V_z $$unsorted)) (= (tptp.c_Complex_Ocnj (tptp.c_Complex_Ocnj V_z)) V_z)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_OrderedGroup_Olordered__ab__group__add__class_Opprt V_a T_a) _let_1) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_OrderedGroup_Olordered__ab__group__add__class_Opprt V_a T_a) _let_1)) (tptp.c_lessequals V_a _let_1 T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_b T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_RealVector_OscaleR__class_OscaleR V_b V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_b (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_ra $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_ra (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_RealVector_OscaleR__class_OscaleR V_ra V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)))))) (not (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.c_HOL_Otimes__class_Otimes _let_2 _let_2 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (= tptp.c_Complex_Oii _let_14)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_x1 $$unsorted) (V_u $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_x tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Oinverse V_x1 tptp.tc_RealDef_Oreal) V_u tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_x1 V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_x V_u tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x1 tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_u $$unsorted) (V_x1 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_y (tptp.c_HOL_Oinverse__class_Oinverse V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_u (tptp.c_HOL_Oinverse__class_Oinverse V_x1 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_x1 V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_x V_u tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x1 tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_b T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ouminus__class_Ouminus V_a_H T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((V_x $$unsorted)) (= (tptp.c_Log_Opowr V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_v $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Int_Onumber__class_Onumber__of V_v tptp.tc_Complex_Ocomplex)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oplus__class_Oplus V_a V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Oof__real V_r T_a) V_x T_a)))) (= (tptp.c_Complex_ORe _let_9) _let_2) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a))) (forall ((V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_Complex_Ocomplex))) (= (tptp.c_Complex_Ocnj _let_1) _let_1))) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Transcendental_Opi _let_2 tptp.tc_RealDef_Oreal)) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 (tptp.c_Transcendental_Osin V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (= (tptp.c_Transcendental_Osin tptp.c_Transcendental_Opi) _let_2) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_x T_a) (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_z V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_z V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_z V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_z V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_z tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_z tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (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_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus V_y V_b T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes _let_2 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes _let_2 V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_RealVector_OscaleR__class_OscaleR V_b V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Otimes__class_Otimes V_a V_b tptp.tc_RealDef_Oreal) V_x T_a)))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_e T_a) V_c T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_a V_b) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_Complex_Ocomplex))) (= V_a (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_y _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= V_x _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) _let_1 T_a))))) (= (tptp.c_Complex_OIm tptp.c_Complex_Oii) _let_12) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_xa V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ominus__class_Ominus V_b V_b_H T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_a_H T_a) V_b T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_ya T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ominus__class_Ominus V_c V_d T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals V_x _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x _let_1 tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a) (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a))))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Log_Opowr V_x V_a) (tptp.c_Log_Opowr V_y V_a) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Log_Opowr V_y V_a) (tptp.c_Log_Opowr V_x V_a) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_r T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) T_a) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_y T_a) T_a) T_a) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_b_H T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_m V_m T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) V_m T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= V_b (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1 T_a)) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1 T_a) V_b) (= _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_d T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a))) (= V_c V_d) (= V_a V_b))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_w V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a))) (= V_y V_z) (= V_w V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (= (tptp.c_Complex_OIm _let_9) _let_2) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals _let_1 V_y tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 (tptp.c_NthRoot_Osqrt V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_2 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (= V_z _let_1) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= V_b (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a) V_b) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((V_x $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_Log_Opowr (tptp.c_Log_Opowr V_x V_a) V_b) (tptp.c_Log_Opowr V_x (tptp.c_HOL_Otimes__class_Otimes V_a V_b tptp.tc_RealDef_Oreal)))) (= (tptp.c_Complex_Ocnj _let_14) _let_14) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) V_m T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_m T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_m T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_r tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_r tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_r (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless V_x _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_y T_a) V_x T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_x T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Transcendental_Osin V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_x V_y) tptp.c_Complex_Oii)) (= V_y (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted)) (or (not (tptp.class_Divides_Oring__div T_a)) (not (= (tptp.c_Divides_Odiv__class_Omod V_b V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_b_H V_c T_a))) (not (= (tptp.c_Divides_Odiv__class_Omod V_a V_c T_a) (tptp.c_Divides_Odiv__class_Omod V_a_H V_c T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Ominus__class_Ominus V_a_H V_b_H T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) V_b))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Complex_OIm V_x) (tptp.c_Complex_OIm V_y))) (not (= (tptp.c_Complex_ORe V_x) (tptp.c_Complex_ORe V_y))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__div__algebra T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Oinverse__class_Oinverse V_x tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_RealVector_Oof__real V_x T_a) T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_x $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Ocnj V_x)) (tptp.c_Complex_ORe V_x))) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_2 T_a) _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Log_Opowr V_x V_y) tptp.tc_RealDef_Oreal)) (forall ((V_z $$unsorted)) (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Complex_ORe V_z) (tptp.c_Complex_OIm V_z)) V_z)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (not (= (tptp.c_Complex_Ocnj V_z) _let_1)) (= V_z _let_1)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_lessequals _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Complex_Ocnj V_x) (tptp.c_Complex_Ocnj V_y))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= _let_2 _let_1)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y)) (= V_x (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_z $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_RealVector_Oof__real V_z tptp.tc_Complex_Ocomplex)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_Transcendental_Oexp (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Oexp V_x T_a) (tptp.c_Transcendental_Oexp V_y T_a) T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) V_y T_a)))) (= (tptp.c_HOL_Otimes__class_Otimes _let_12 _let_12 tptp.tc_RealDef_Oreal) _let_12) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (= V_x V_y) (not (tptp.c_lessequals (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_z V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_z V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_z tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_z tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) V_b T_a) (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oplus__class_Oplus V_a V_r T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_r T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_m V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_n T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_m T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (not (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_b V_x T_a))) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a _let_1 T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= 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(tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted)) (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)) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) V_a) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (not (= (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a) (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (= V_a V_b) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Osgn__class_Osgn V_r tptp.tc_RealDef_Oreal) (tptp.c_HOL_Osgn__class_Osgn V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1)) (= V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a)) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a))))) (= (tptp.c_NthRoot_Osqrt _let_12) _let_12) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Oinverse__class_Oinverse V_y T_a) T_a)))) (not (= tptp.c_Complex_Oii _let_9)) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_RealVector_Oof__real V_x tptp.tc_Complex_Ocomplex))) (= (tptp.c_Complex_Ocnj _let_1) _let_1))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (= (tptp.c_Transcendental_Otan tptp.c_Transcendental_Opi) _let_2) (forall ((T_a $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Int_Onumber T_a)) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_1 T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oabs__if T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_2 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals _let_2 _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 V_c T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals _let_2 V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_lessequals V_a _let_2 T_a)) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) T_a))))) (tptp.c_lessequals _let_2 tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_c V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_j V_k tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_i V_j tptp.tc_RealDef_Oreal)))) (forall ((V_w $$unsorted)) (tptp.c_lessequals V_w V_w tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_d $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Oinverse V_x T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_1 T_a) (not (tptp.c_lessequals _let_2 _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_2 T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) T_a)))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) _let_2 T_a) (not (tptp.c_lessequals _let_1 _let_2 T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes _let_2 V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_Transcendental_Oexp (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_Transcendental_Oexp V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b _let_2 T_a)) (not (tptp.c_lessequals _let_2 V_b T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Oinverse__class_Oinverse V_b T_a))) (let ((_let_3 (tptp.c_HOL_Oinverse__class_Oinverse V_a T_a))) (or (not (tptp.class_Ring__and__Field_Odivision__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus _let_3 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes _let_3 (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a) _let_2 T_a)) (= V_b _let_1) (= V_a _let_1)))))) (forall ((V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Log_Opowr _let_1 V_a) _let_1))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Odiv V_a V_b T_a) V_b T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_c (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oplus__class_Oplus V_a V_r T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= V_x _let_1) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (tptp.c_HOL_Oord__class_Oless _let_2 tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a))) (= V_z _let_1) (= V_y _let_1) (= (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.c_HOL_Osgn__class_Osgn V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Osgn__class_Osgn V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Odist__norm T_a)) (= (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_c (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Divides_Odiv__class_Omod V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1)))) (forall ((V_x $$unsorted)) (or (= (tptp.c_HOL_Osgn__class_Osgn V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))) (= (tptp.c_Complex_OIm _let_14) _let_2) (forall ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.c_HOL_Oinverse__class_Oinverse V_x tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Oinverse__class_Oinverse (tptp.c_NthRoot_Osqrt V_x) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_w V_z tptp.tc_RealDef_Oreal) (tptp.c_lessequals V_z V_w tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_a _let_1) (= V_b _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Odiv _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$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.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x V_a T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_OrderedGroup_Olordered__ab__group__add__class_Opprt _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Divides_Osemiring__div T_a)) (= (tptp.c_Divides_Odiv__class_Omod _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_b _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_x T_a) _let_1)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_SEQ_Obanach T_a)) (not (tptp.class_RealVector_Oreal__normed__field T_a)) (not (= (tptp.c_Transcendental_Oexp V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= V_x (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) V_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) tptp.tc_RealDef_Oreal) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) T_a) T_a))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (not (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_y T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR _let_1 V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR _let_1 V_y T_a))))) (= (tptp.c_HOL_Osgn__class_Osgn _let_2 tptp.tc_RealDef_Oreal) _let_2) (forall ((V_x $$unsorted) (V_a $$unsorted)) (not (= (tptp.c_Log_Opowr V_x V_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_c tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_b V_c tptp.tc_RealDef_Oreal))) (= V_c (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_a V_b))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_c V_a tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_c V_b tptp.tc_RealDef_Oreal))) (= V_c (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_a V_b))) (= (tptp.c_Transcendental_Otan _let_2) _let_2) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_NthRoot_Osqrt V_x) _let_1)) (= V_x _let_1)))) (not (= tptp.c_Transcendental_Opi _let_2)) (not (= _let_2 _let_12)) (= (tptp.c_NthRoot_Osqrt _let_2) _let_2) (= (tptp.c_Transcendental_Osin _let_2) _let_2) (= (tptp.c_HOL_Oinverse__class_Oinverse _let_2 tptp.tc_RealDef_Oreal) _let_2) (= (tptp.c_Transcendental_Oarctan _let_2) _let_2) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_NthRoot_Oroot V_n _let_1) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (= (tptp.c_RealVector_Odist__class_Odist V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (= (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (= _let_13 _let_14) (= tptp.c_Complex_Oii _let_15) (= _let_15 tptp.c_Complex_Oii) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= (tptp.c_Transcendental_Ocos (tptp.c_Complex_Oarg (tptp.c_Complex_Ocomplex_OComplex _let_1 V_y))) _let_1) (= V_y _let_1)))) (forall ((V_w $$unsorted)) (= (tptp.c_Complex_Ocomplex_OComplex (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_Complex_Ocomplex))) (= _let_14 _let_13) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Complex_Ocomplex_OComplex V_x V_y)) V_x)) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Complex_Ocomplex_OComplex V_x V_y)) V_y)) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xa $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_x V_y) (tptp.c_RealVector_Oof__real V_xa tptp.tc_Complex_Ocomplex))) (= V_x V_xa))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n tptp.tc_Complex_Ocomplex))) (= (tptp.c_Complex_Ocnj _let_1) _let_1))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (not (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) _let_1)) (= V_x _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (not (= (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (= (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x 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_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_Fact_Ofact__class_Ofact V_n tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) T_a))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_a V_b) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_a V_b) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= V_b (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (= _let_9 _let_10) _let_11 (= _let_10 _let_9) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_x V_y) tptp.c_Complex_Oii)) (= V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_xa $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_x V_y) (tptp.c_RealVector_Oof__real V_xa tptp.tc_Complex_Ocomplex))) (= V_y (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_a V_b) (tptp.c_HOL_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (= V_b (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Oof__real V_r tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Ocomplex_OComplex V_r (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_w $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_a V_b) (tptp.c_Int_Onumber__class_Onumber__of V_w tptp.tc_Complex_Ocomplex))) (= V_b (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) _let_8 (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n tptp.tc_RealDef_Oreal)))) (forall ((V_n $$unsorted)) (= (tptp.c_Complex_OIm (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n tptp.tc_Complex_Ocomplex)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (forall ((V_n $$unsorted)) (= (tptp.c_Complex_ORe (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n tptp.tc_Complex_Ocomplex)) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n tptp.tc_RealDef_Oreal))) (forall ((V_real1 $$unsorted) (V_real2 $$unsorted) (V_real1_H $$unsorted) (V_real2_H $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_real1 V_real2) (tptp.c_Complex_Ocomplex_OComplex V_real1_H V_real2_H))) (= V_real1 V_real1_H))) (forall ((V_real1 $$unsorted) (V_real2 $$unsorted) (V_real1_H $$unsorted) (V_real2_H $$unsorted)) (or (not (= (tptp.c_Complex_Ocomplex_OComplex V_real1 V_real2) (tptp.c_Complex_Ocomplex_OComplex V_real1_H V_real2_H))) (= V_real2 V_real2_H))) (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))) _let_7 (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_nat) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring tptp.tc_nat) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_nat) (tptp.class_Divides_Osemiring__div tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Int_Onumber tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add__abs tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add__abs tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__ring__strict tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__ring__abs tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__ring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Olordered__ring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osemiring tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Osgn__if tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oabs__if tptp.tc_Int_Oint) (tptp.class_Divides_Osemiring__div tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oidom tptp.tc_Int_Oint) (tptp.class_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_Divides_Oring__div tptp.tc_Int_Oint) (tptp.class_Orderings_Oorder tptp.tc_Int_Oint) (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint) (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint) (tptp.class_Int_Onumber tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__group__add__abs tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Olordered__ab__group__add__abs tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__ring__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__ring__abs tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__vector 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(tptp.class_RealVector_Oreal__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Osemiring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Osgn__div__norm tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__algebra tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Ometric__space tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__vector tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Osgn__if tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oabs__if tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__field tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ofield tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Odist__norm tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oidom tptp.tc_RealDef_Oreal) (tptp.class_Nat_Osemiring__char__0 tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal) (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal) (tptp.class_SEQ_Obanach tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber tptp.tc_RealDef_Oreal) (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_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_RealVector_Oreal__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_Complex_Ocomplex) _let_1 (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Osgn__div__norm tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__algebra tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Ometric__space tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__add tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__vector tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ogroup__add 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_RealVector_Odist__norm 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_SEQ_Obanach tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber tptp.tc_Complex_Ocomplex))))))))))))))))))))))))))))))))
% 1.08/1.36 )
% 1.08/1.37 % SZS output end Proof for SWV573-1
% 1.08/1.37 % cvc5---1.0.5 exiting
% 1.08/1.37 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------