%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ALG368-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n018.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 : Wed Aug 30 16:09:24 EDT 2023

% Result   : Unsatisfiable 1.61s 1.85s
% Output   : Proof 1.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.21  % Problem    : ALG368-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.21  % Command    : do_cvc5 %s %d
% 0.22/0.42  % Computer : n018.cluster.edu
% 0.22/0.42  % Model    : x86_64 x86_64
% 0.22/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.42  % Memory   : 8042.1875MB
% 0.22/0.42  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.22/0.42  % CPULimit   : 300
% 0.22/0.42  % WCLimit    : 300
% 0.22/0.42  % DateTime   : Mon Aug 28 04:58:46 EDT 2023
% 0.22/0.42  % CPUTime    : 
% 0.27/0.64  %----Proving TF0_NAR, FOF, or CNF
% 0.27/0.65  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Br5gekaPQR/cvc5---1.0.5_24753.p...
% 0.59/0.80  ------- get file name : TPTP file name is ALG368-1
% 0.59/0.80  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_24753.smt2...
% 0.59/0.81  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.61/1.85  % SZS status Unsatisfiable for ALG368-1
% 1.61/1.85  % SZS output start Proof for ALG368-1
% 1.61/1.87  (
% 1.61/1.87  (let ((_let_1 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex))) (let ((_let_2 (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_Complex_Ocomplex))) (let ((_let_3 (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_RealDef_Oreal))) (let ((_let_5 (forall ((V_xa $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (or (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Polynomial_Opoly _let_1 (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.v_x V_xa) tptp.v_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_Polynomial_Opoly _let_1 (tptp.c_HOL_Ominus__class_Ominus tptp.v_z tptp.v_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) tptp.v_e tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_xa tptp.tc_RealDef_Oreal))))))) (let ((_let_6 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_7 (tptp.c_HOL_Oord__class_Oless _let_6 tptp.v_e tptp.tc_RealDef_Oreal))) (let ((_let_8 (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))))) (let ((_let_9 (forall ((T_a $$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)))))) (let ((_let_10 (tptp.c_HOL_Otimes__class_Otimes _let_6 _let_6 tptp.tc_RealDef_Oreal))) (let ((_let_11 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))))) (let ((_let_12 (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))))) (let ((_let_13 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_14 (= (tptp.c_Transcendental_Oln _let_13) _let_6))) (let ((_let_15 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) (tptp.c_RealVector_Onorm__class_Onorm V_b T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))))) (let ((_let_16 (tptp.c_HOL_Oplus__class_Oplus _let_10 _let_10 tptp.tc_RealDef_Oreal))) (let ((_let_17 (= _let_16 _let_6))) (let ((_let_18 (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)))))) (let ((_let_19 (= _let_6 _let_16))) (let ((_let_20 (= _let_6 _let_10))) (let ((_let_21 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_22 (tptp.c_HOL_Osgn__class_Osgn _let_21 tptp.tc_Complex_Ocomplex))) (let ((_let_23 (= _let_21 _let_22))) (let ((_let_24 (= _let_6 (tptp.c_RealVector_Onorm__class_Onorm _let_22 tptp.tc_Complex_Ocomplex)))) (let ((_let_25 (tptp.c_HOL_Ominus__class_Ominus tptp.v_z tptp.v_z tptp.tc_Complex_Ocomplex))) (let ((_let_26 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (let ((_let_27 (tptp.c_Polynomial_Opoly _let_26 _let_25 tptp.tc_Complex_Ocomplex))) (let ((_let_28 (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.v_x tptp.v_e) tptp.v_z tptp.tc_Complex_Ocomplex))) (let ((_let_29 (tptp.c_Polynomial_Opoly _let_26 _let_28 tptp.tc_Complex_Ocomplex))) (let ((_let_30 (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus _let_29 _let_27 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex))) (let ((_let_31 (tptp.c_lessequals _let_30 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Onorm__class_Onorm _let_29 tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm _let_27 tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (let ((_let_32 (tptp.c_lessequals _let_30 _let_6 tptp.tc_RealDef_Oreal))) (let ((_let_33 (= _let_27 _let_21))) (let ((_let_34 (= _let_21 _let_29))) (let ((_let_35 (SYMM (ASSUME :args (_let_17))))) (let ((_let_36 (not _let_19))) (let ((_let_37 (not _let_4))) (let ((_let_38 (or _let_37 _let_36 _let_20))) (let ((_let_39 (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 (= _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a))) (= V_a _let_1)))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (not _let_1))) (let ((_let_42 (or _let_41 _let_23))) (let ((_let_43 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= _let_1 (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a))))))) (let ((_let_44 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_45 (ASSUME :args (_let_1)))) (let ((_let_46 (or _let_41 _let_24))) (let ((_let_47 (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Osgn__class_Osgn (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) T_a)))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or _let_41 _let_31))) (let ((_let_50 (_let_15))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (not _let_32))) (let ((_let_53 (not _let_7))) (let ((_let_54 (tptp.c_HOL_Oord__class_Oless _let_30 tptp.v_e tptp.tc_RealDef_Oreal))) (let ((_let_55 (not _let_3))) (let ((_let_56 (or _let_55 _let_54 _let_53 _let_52))) (let ((_let_57 (_let_12))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 (not _let_54))) (let ((_let_60 (or _let_59 _let_53))) (let ((_let_61 (_let_5))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (ASSUME :args (_let_7)))) (let ((_let_64 (not _let_2))) (let ((_let_65 (or _let_64 _let_33))) (let ((_let_66 (_let_8))) (let ((_let_67 (ASSUME :args _let_66))) (let ((_let_68 ((tptp.c_Polynomial_Opoly (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_x T_a)))) (let ((_let_69 (ASSUME :args (_let_2)))) (let ((_let_70 (or _let_64 _let_34))) (let ((_let_71 (not _let_34))) (let ((_let_72 (not _let_33))) (let ((_let_73 (not _let_31))) (let ((_let_74 (not _let_24))) (let ((_let_75 (not _let_23))) (let ((_let_76 (not _let_20))) (let ((_let_77 (ASSUME :args (_let_31)))) (let ((_let_78 (REFL :args (tptp.tc_RealDef_Oreal)))) (let ((_let_79 (APPLY_UF tptp.c_RealVector_Onorm__class_Onorm))) (let ((_let_80 (REFL :args (tptp.tc_Complex_Ocomplex)))) (let ((_let_81 (ASSUME :args (_let_33)))) (let ((_let_82 (SYMM _let_81))) (let ((_let_83 (ASSUME :args (_let_23)))) (let ((_let_84 (SYMM _let_83))) (let ((_let_85 (ASSUME :args (_let_24)))) (let ((_let_86 (SYMM (SYMM _let_85)))) (let ((_let_87 (ASSUME :args (_let_20)))) (let ((_let_88 (SYMM _let_87))) (let ((_let_89 (ASSUME :args (_let_34)))) (let ((_let_90 (CONG (SYMM _let_35) (REFL :args (_let_6)) _let_78 :args (APPLY_UF tptp.c_HOL_Otimes__class_Otimes)))) (let ((_let_91 (ASSUME :args (_let_52)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_89 _let_77 _let_85 _let_81 _let_83 _let_87 _let_91 _let_35) :args (_let_19 _let_20 _let_23 _let_24 _let_31 _let_52 _let_33 _let_34)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_91)) (CONG (REFL :args (_let_30)) (TRANS _let_35 (CONG (TRANS (SYMM _let_90) (TRANS _let_90 _let_88) (TRANS _let_86 (CONG (TRANS _let_84 _let_82 (TRANS _let_81 (SYMM (SYMM _let_89)))) _let_80 :args _let_79))) (TRANS _let_88 _let_86 (CONG (TRANS _let_84 _let_82) _let_80 :args _let_79)) _let_78 :args (APPLY_UF tptp.c_HOL_Oplus__class_Oplus))) _let_78 :args (APPLY_UF tptp.c_lessequals)) (TRUE_INTRO _let_77))) :args (_let_34 _let_31 _let_24 _let_33 _let_23 _let_20 _let_52 _let_19)) :args ((not (and _let_19 _let_20 _let_23 _let_24 _let_31 _let_52 _let_33 _let_34)) SB_LITERAL))) (CONG (REFL :args (_let_36)) (REFL :args (_let_76)) (REFL :args (_let_75)) (REFL :args (_let_74)) (REFL :args (_let_73)) (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_32))) (REFL :args (_let_72)) (REFL :args (_let_71)) :args (or))) :args ((or _let_36 _let_76 _let_75 _let_74 _let_32 _let_73 _let_72 _let_71))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_64 _let_34 (not _let_70)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.tc_Complex_Ocomplex _let_28 QUANTIFIERS_INST_E_MATCHING _let_68)) :args _let_66))) _let_67 :args (_let_70 false _let_8)) :args (_let_34 false _let_2 false _let_70)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_64 _let_33 (not _let_65)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (tptp.tc_Complex_Ocomplex _let_25 QUANTIFIERS_INST_E_MATCHING _let_68)) :args _let_66)) _let_67 :args (_let_65 false _let_8)) :args (_let_33 false _let_2 false _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_53 _let_55 _let_54 _let_52 (not _let_56)))) _let_63 (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_53 _let_59 (not _let_60)))) _let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (tptp.v_e QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.c_HOL_Oord__class_Oless _let_6 V_xa tptp.tc_RealDef_Oreal) false))))) :args _let_61)) _let_62 :args (_let_60 false _let_5)) :args (_let_59 false _let_7 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.tc_RealDef_Oreal _let_30 tptp.v_e _let_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) true)) (not (= (tptp.c_HOL_Oord__class_Oless V_y V_z T_a) false))))) :args _let_57)) _let_58 :args (_let_56 false _let_12)) :args (_let_52 false _let_7 false _let_3 true _let_54 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_41 _let_31 (not _let_49)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.tc_Complex_Ocomplex _let_29 _let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)))) :args _let_50)) _let_51 :args (_let_49 false _let_15)) :args (_let_31 false _let_1 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_41 _let_24 (not _let_46)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_RealVector_Oreal__normed__vector T_a) false))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_24 false _let_1 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_23 (not _let_42)))) _let_45 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_RealVector_Oreal__normed__vector T_a) false))))) :args (_let_43))) _let_44 :args (_let_42 false _let_43)) :args (_let_23 false _let_1 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_36 _let_37 _let_20 (not _let_38)))) _let_35 (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.tc_RealDef_Oreal _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a)))) :args (_let_39)))) _let_40 :args (_let_38 false _let_39)) :args (_let_20 false _let_19 false _let_4 false _let_38)) _let_35 :args (false false _let_34 false _let_33 true _let_32 false _let_31 false _let_24 false _let_23 false _let_20 false _let_19)) :args ((forall ((V_z1 $$unsorted) (V_z2 $$unsorted) (V_w $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_z1 V_z2 tptp.tc_RealDef_Oreal) V_w tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_z1 V_w tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_z2 V_w tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$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_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 $$unsorted) (V_b $$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_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_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_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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_n T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_q T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Power_Opower__class_Opower V_x V_q T_a) (tptp.c_Power_Opower__class_Opower V_y V_q T_a) 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_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Complex_Ocnj (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_Complex_Ocomplex)) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_Complex_Ocnj V_x) (tptp.c_Complex_Ocnj V_y) tptp.tc_Complex_Ocomplex))) (forall ((V_x $$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 ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) _let_1 tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_x _let_1 tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ominus__class_Ominus V_x _let_1 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$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_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_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 ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_z V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus V_z V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ominus__class_Ominus V_a V_b tptp.tc_RealDef_Oreal) V_x T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_b V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_xa $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) V_xa T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_OscaleR__class_OscaleR V_x V_xa T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_y V_xa T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ominus__class_Ominus V_a V_a_H tptp.tc_RealDef_Oreal) V_b T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealDef_Oreal V_n tptp.tc_nat) V_x tptp.tc_RealDef_Oreal) _let_1 tptp.tc_RealDef_Oreal) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oplus__class_Oplus V_x _let_1 tptp.tc_RealDef_Oreal) V_n tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n 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 (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 $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Power_Opower__class_Opower V_x V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) V_n tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Osin V_x) (tptp.c_Transcendental_Ocos V_y) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Osin V_y) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((V_x $$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 $$unsorted) (V_b $$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 ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Osin V_x))) (let ((_let_2 (tptp.c_Transcendental_Ocos V_x))) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes _let_2 _let_2 tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (forall ((T_a $$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 ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) V_n T_a))))) (forall ((T_a $$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) (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_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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((V_x $$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 ((V_x $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Transcendental_Ocos V_x) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_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 $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Oone__class_Oone T_a) V_p T_a) V_p))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$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)) (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 $$unsorted) (V_x $$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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus V_y V_b T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_x V_a tptp.tc_RealDef_Oreal))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_OscaleR__class_OscaleR V_x V_y T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_OscaleR__class_OscaleR _let_2 _let_1 T_a) (tptp.c_RealVector_OscaleR__class_OscaleR _let_2 V_b T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a _let_1 T_a) T_a)))))) (forall ((T_a $$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 ((V_x $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Transcendental_Osin V_x) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (= (tptp.c_Transcendental_Ocos _let_6) _let_13) (forall ((T_a $$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_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_Power_Opower__class_Opower _let_1 V_n T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) (tptp.c_RealVector_Onorm__class_Onorm V_b T_a) tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) tptp.tc_RealDef_Oreal))) (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_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 $$unsorted)) (or (not (= (tptp.c_Transcendental_Ocos V_x) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Transcendental_Osin V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Ocos V_y) (tptp.c_Transcendental_Osin V_x) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Osin V_y) (tptp.c_Transcendental_Ocos V_x) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted) (V_h $$unsorted)) (or (not (tptp.class_RealVector_Oreal__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_d T_a) T_a) V_h T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) V_h T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) V_h T_a) V_d T_a) T_a)))) (forall ((V_x $$unsorted)) (or (not (= (tptp.c_Transcendental_Osin V_x) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Transcendental_Ocos V_x) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_z $$unsorted)) (= (tptp.c_Complex_Ocnj (tptp.c_Complex_Ocnj V_z)) V_z)) (forall ((V_x $$unsorted) (V_k $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.c_Power_Opower__class_Opower V_x V_k tptp.tc_RealDef_Oreal)) (tptp.c_Power_Opower__class_Opower (tptp.c_NthRoot_Osqrt V_x) V_k tptp.tc_RealDef_Oreal))) (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 $$unsorted) (V_a $$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 $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (or (not (tptp.class_OrderedGroup_Omonoid__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a))))) (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) (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 $$unsorted) (V_x $$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_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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_m (tptp.c_HOL_Otimes__class_Otimes V_a V_m T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oone__class_Oone T_a) T_a) V_m T_a)))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_HOL_Oplus__class_Oplus V_x tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Otan V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_m T_a) (tptp.c_Power_Opower__class_Opower V_a V_n T_a))) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone T_a) V_a T_a)) (= V_m V_n))) (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))) (= (tptp.c_NthRoot_Osqrt _let_13) _let_13) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)) (= V_b (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Ocos V_y) (tptp.c_Transcendental_Ocos V_x) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Osin V_y) (tptp.c_Transcendental_Osin V_x) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Ocos V_y) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Osin V_x) (tptp.c_Transcendental_Osin V_y) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$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_n $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Power_Opower__class_Opower V_x V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) V_n tptp.tc_RealDef_Oreal)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm V_w tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oplus__class_Oplus V_w V_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm V_z tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Osin V_x) (tptp.c_Transcendental_Ocos V_y) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Osin V_y) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (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_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) T_a) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (forall ((V_x $$unsorted) (V_n $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealDef_Oreal V_n tptp.tc_nat) tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Otan V_x))) (forall ((V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transcendental_Oln (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)) V_x tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_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 $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_x V_n T_a) _let_1 T_a))))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_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_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$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 $$unsorted) (V_c $$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_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_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$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 ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Ocos V_y) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_Transcendental_Osin V_x) (tptp.c_Transcendental_Osin V_y) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (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 $$unsorted) (V_x $$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 ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_e T_a) V_c T_a)))) (forall ((T_a $$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 ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_Polynomial_Opos__poly (tptp.c_Polynomial_OpCons V_a V_p T_a) T_a) (not (tptp.c_Polynomial_Opos__poly V_p T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_n 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 $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Oplus__class_Oplus V_a V_b tptp.tc_RealDef_Oreal) V_x T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_b V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_y T_a) T_a)))) (forall ((T_a $$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_x $$unsorted) (V_y $$unsorted) (V_xa $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) V_xa T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_OscaleR__class_OscaleR V_x V_xa T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_y V_xa T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Oplus__class_Oplus V_a V_a_H tptp.tc_RealDef_Oreal) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a_H V_b T_a) T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oplus__class_Oplus V_b V_a tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm V_b tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm V_a tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) V_y T_a)))) (= (tptp.c_HOL_Otimes__class_Otimes _let_13 _let_13 tptp.tc_RealDef_Oreal) _let_13) (forall ((T_a $$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_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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (not (tptp.class_Power_Opower T_a)) (not (= (tptp.c_Power_Opower__class_Opower V_a V_n T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ozero__neq__one T_a)) (not (= (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))))) _let_18 (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a _let_1 T_a) _let_1)))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide _let_1 V_a T_a) _let_1)))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$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) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Oone__class_Oone T_a) V_b T_a) _let_1 T_a))))) (forall ((T_a $$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_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 $$unsorted) (V_a $$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_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 $$unsorted) (V_c $$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 $$unsorted) (V_c $$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 $$unsorted) (V_a $$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 $$unsorted) (V_a $$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_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 $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_a V_c T_a) (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_ya T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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) (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) (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_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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR _let_1 V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR _let_1 V_y T_a))))) (= (tptp.c_Transcendental_Otan _let_6) _let_6) (not (= _let_6 _let_13)) (= (tptp.c_Transcendental_Osin _let_6) _let_6) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus 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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.c_Polynomial_Opos__poly (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) T_a)))) (forall ((V_z $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Complex_Ocnj V_z) tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm V_z tptp.tc_Complex_Ocomplex))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_Complex_Ocnj (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_Complex_Ocomplex)) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Complex_Ocnj V_x) (tptp.c_Complex_Ocnj V_y) tptp.tc_Complex_Ocomplex))) (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_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$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 ((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_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_lessequals V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y T_a)) (not (tptp.c_lessequals V_x _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_y _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_a $$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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_x V_z T_a) (tptp.c_HOL_Oinverse__class_Odivide V_y V_w T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_w V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_w T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_lessequals _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 V_a T_a) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_c V_a T_a) (tptp.c_HOL_Oinverse__class_Odivide V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted)) (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$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 $$unsorted) (V_x $$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 $$unsorted) (V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_x _let_1) (tptp.c_lessequals V_x _let_1 T_a) (not (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_x V_n T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_Power_Opower__class_Opower V_a V_n T_a) (tptp.c_Power_Opower__class_Opower V_b V_n T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$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_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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted)) (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 $$unsorted) (V_b $$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 $$unsorted) (V_b $$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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (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 $$unsorted) (V_x $$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) (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 $$unsorted) (V_a $$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) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals _let_1 (tptp.c_Power_Opower__class_Opower V_a V_n T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$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 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)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oone__class_Oone T_a) T_a))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$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 $$unsorted) (V_b $$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 $$unsorted) (V_c $$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 ((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 $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) V_a) (= V_c (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_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 $$unsorted) (V_c $$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_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 $$unsorted) (V_x $$unsorted) (V_r $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_r V_c T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Otimes__class_Otimes V_r V_d T_a) T_a))) (= V_c V_d) (= V_r (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$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_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_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)) (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)) (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 $$unsorted) (V_x $$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 $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (= (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Otimes__class_Otimes _let_1 V_c T_a) V_c T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$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 $$unsorted) (V_c $$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 $$unsorted) (V_m $$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_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) (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_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) (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 $$unsorted) (V_e $$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_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_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)) (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) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a))) (forall ((T_a $$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_vskULp $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 V_vskULp T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) _let_1)) (= V_x _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) _let_1)) (= V_y _let_1)))) _let_17 (= (tptp.c_Transcendental_Osin tptp.c_Transcendental_Opi) _let_6) (= (tptp.c_Transcendental_Otan tptp.c_Transcendental_Opi) _let_6) (forall ((T_a $$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 ((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 ((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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 (tptp.c_NthRoot_Osqrt V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_y $$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 ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal))))) (forall ((V_x $$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_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 ((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)) (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 $$unsorted) (V_p $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= V_p (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Polynomial_Opos__poly V_p T_a) (not (tptp.c_Polynomial_Opos__poly (tptp.c_Polynomial_OpCons V_a V_p T_a) T_a)))) _let_14 (forall ((V_x $$unsorted)) (or (not (= (tptp.c_Transcendental_Oexp 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)))) (= (tptp.c_Transcendental_Oexp _let_6 tptp.tc_RealDef_Oreal) _let_13) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_lessequals (tptp.c_RealVector_Odist__class_Odist V_x V_z T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_RealVector_Odist__class_Odist V_y V_z T_a) 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_RealVector_Ometric__space T_a)) (tptp.c_lessequals (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Odist__class_Odist V_x V_z T_a) (tptp.c_RealVector_Odist__class_Odist V_y V_z T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_lessequals (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Odist__class_Odist V_a V_x T_a) (tptp.c_RealVector_Odist__class_Odist V_a V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((V_y $$unsorted) (V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y V_b tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1 V_a V_b V_x) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_x V_b tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_a V_x tptp.tc_RealDef_Oreal)))) (forall ((V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_a V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1 V_a V_b V_x) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_x V_b tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_a V_x tptp.tc_RealDef_Oreal)))) (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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_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_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) (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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) V_x T_a) (not (tptp.c_lessequals V_y (tptp.c_HOL_Oone__class_Oone T_a) T_a)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_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 ((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))))) (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 $$unsorted) (V_b $$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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_w $$unsorted) (V_z $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ofield T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oinverse__class_Odivide V_x V_y T_a) (tptp.c_HOL_Oinverse__class_Odivide V_w V_z T_a) T_a) (tptp.c_HOL_Oinverse__class_Odivide (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a)) (= V_z _let_1) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_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_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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_e T_a) V_c T_a) V_d T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_e $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_e T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_b V_e T_a) V_d T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) V_e T_a) V_d T_a) T_a)))) (forall ((T_a $$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_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_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Power_Opower__class_Opower (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_n T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a))) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_a T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osgn__if T_a)) (= (tptp.c_HOL_Osgn__class_Osgn V_x T_a) (tptp.c_HOL_Oone__class_Oone T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oplus__class_Oplus V_a V_r T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a)))) (forall ((T_a $$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_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 $$unsorted) (V_a $$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_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.c_Polynomial_Opos__poly V_p T_a) (not (tptp.c_Polynomial_Opos__poly (tptp.c_Polynomial_OpCons V_a V_p T_a) T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (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_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (= V_y _let_1)))) (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_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) (tptp.c_RealVector_Onorm__class_Onorm V_b T_a) tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) tptp.tc_RealDef_Oreal))) _let_15 (forall ((T_a $$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 $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Ocos V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_y V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal)))) (forall ((V_x $$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 ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Transcendental_Osin V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (tptp.c_lessequals V_x (tptp.c_NthRoot_Osqrt (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) tptp.tc_RealDef_Oreal)) (forall ((V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (tptp.c_lessequals V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (or (not (tptp.c_HOL_Oord__class_Oless _let_6 _let_13 tptp.tc_RealDef_Oreal)) _let_14) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_Transcendental_Oln V_x) _let_1)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal)) (= V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oln V_x) _let_1 tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oln V_x) _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x) 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_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Transcendental_Oln V_x) tptp.tc_RealDef_Oreal))))) (forall ((V_x $$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_Transcendental_Oln V_x) 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 _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Transcendental_Oln V_x) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_OpCons V_a V_p T_a) V_x T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_Polynomial_Opoly V_p V_x T_a) T_a) T_a)))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (= (tptp.c_Transcendental_Oexp (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealDef_Oreal V_n tptp.tc_nat) V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_Power_Opower__class_Opower (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) V_n tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_Omonom V_a V_n T_a) V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Power_Opower__class_Opower V_x V_n 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_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 $$unsorted) (V_b $$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 $$unsorted) (V_a $$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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__field T_a)) (not (tptp.class_Ring__and__Field_Odivision__by__zero T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b T_a))))) (forall ((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 $$unsorted) (V_b $$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 $$unsorted) (V_b $$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 $$unsorted) (V_a $$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 $$unsorted) (V_z $$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 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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 $$unsorted) (V_c $$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 ((V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y (tptp.c_Transcendental_Otan (tptp.c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1 V_y)) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_K $$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_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_vskULp $$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_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) (tptp.c_RealVector_Onorm__class_Onorm V_b T_a) tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 V_vskULp T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_K $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_K $$unsorted) (V_y $$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_K V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_K $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_K V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_vskULj $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra 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(tptp.c_NthRoot_Osqrt (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) tptp.tc_RealDef_Oreal)) (forall ((V_n $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealDef_Oreal V_n tptp.tc_nat) tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (forall ((V_n $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealDef_Oreal V_n tptp.tc_nat) tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (forall ((V_n $$unsorted)) (= (tptp.c_Transcendental_Osin (tptp.c_HOL_Otimes__class_Otimes tptp.c_Transcendental_Opi (tptp.c_RealDef_Oreal V_n tptp.tc_nat) tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) 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(V_x $$unsorted) (V_a $$unsorted)) (or (tptp.c_lessequals V_y V_b tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_Deriv_Osko__Deriv__Xlemma__interval__1__1 V_a V_b V_x) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_x V_b tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_a V_x tptp.tc_RealDef_Oreal)))) (forall ((V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (tptp.c_lessequals V_a V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_Deriv_Osko__Deriv__Xlemma__interval__1__1 V_a V_b V_x) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_x V_b tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_a V_x tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealDef_Oreal (tptp.c_Transcendental_Osko__Transcendental__Xreals__Archimedean4__1__1 V_x V_y) tptp.tc_nat) V_y tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals _let_1 V_x tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_K $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oinverse__class_Odivide V_K V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_K $$unsorted) (V_vskULt $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 V_vskULt V_r T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (or (= (tptp.c_Transcendental_Oln (tptp.c_Power_Opower__class_Opower V_x V_n tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealDef_Oreal V_n tptp.tc_nat) (tptp.c_Transcendental_Oln V_x) 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 ((V_K $$unsorted)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Complex_Ocnj V_K) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K tptp.tc_Complex_Ocomplex) tptp.c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (= (tptp.c_RealVector_Odist__class_Odist tptp.v_x tptp.v_y tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus tptp.v_x tptp.v_y tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)) (forall ((V_x $$unsorted)) (= (tptp.c_Polynomial_Opoly tptp.v_q____ V_x tptp.tc_Complex_Ocomplex) (tptp.c_Polynomial_Opoly tptp.v_p (tptp.c_HOL_Oplus__class_Oplus tptp.v_z V_x tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) _let_12 (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 $$unsorted) (V_z $$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 $$unsorted) (V_b $$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 ((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 $$unsorted) (V_a $$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_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__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 $$unsorted) (V_a $$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_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 $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$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 $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$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 $$unsorted) (V_x $$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 $$unsorted) (V_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (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) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_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)) (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)) (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 $$unsorted) (V_y $$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 $$unsorted) (V_b $$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 $$unsorted) (V_a $$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 $$unsorted) (V_x $$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 $$unsorted) (V_x $$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 $$unsorted) (V_a $$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 $$unsorted) (V_a $$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 $$unsorted) (V_b $$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_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) _let_11 (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Osgn__if T_a)) (= (tptp.c_HOL_Osgn__class_Osgn _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom 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_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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a (tptp.c_Polynomial_Osmult V_b V_p T_a) T_a) (tptp.c_Polynomial_Osmult (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_p T_a)))) (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 $$unsorted) (V_p $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_Polynomial_Osmult V_a V_p T_a) V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Polynomial_Opoly V_p V_x T_a) T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals V_x _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_NthRoot_Osqrt V_x) (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal))) (forall ((V_n $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal V_n tptp.tc_nat) tptp.tc_RealDef_Oreal)) (forall ((V_x $$unsorted)) (not (tptp.c_lessequals (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_Polynomial_Omonom V_a V_m T_a) V_n T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_m V_n))) (forall ((T_a $$unsorted) (V_K $$unsorted) (V_y $$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_K V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_Polynomial_Osmult V_a V_p T_a) V_n T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_Polynomial_Ocoeff V_p V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((V_z $$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_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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (let ((_let_2 (tptp.c_HOL_Oabs__class_Oabs V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))))) (forall ((V_x $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) T_a))) (forall ((V_x $$unsorted) (V_r $$unsorted)) (or (tptp.c_lessequals V_x V_r tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) V_r tptp.tc_RealDef_Oreal)))) (forall ((T_a $$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_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_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)) (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 ((V_n $$unsorted) (V_m $$unsorted)) (or (not (= (tptp.c_RealDef_Oreal V_n tptp.tc_nat) (tptp.c_RealDef_Oreal V_m tptp.tc_nat))) (= V_n V_m))) (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 $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_ly V_ry T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes _let_1 V_ry T_a) T_a))))) (forall ((T_a $$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 $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (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_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_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_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 $$unsorted) (V_b $$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_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 $$unsorted) (V_x $$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_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 $$unsorted) (V_a $$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_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$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_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_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y_H V_x_H T_a) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_y_H V_x_H T_a)))) (forall ((T_a $$unsorted) (V_xa $$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 ((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))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_NthRoot_Osqrt V_x) _let_1)) (= V_x _let_1)))) (not (= tptp.c_Transcendental_Opi _let_6)) (= (tptp.c_NthRoot_Osqrt _let_6) _let_6) (forall ((V_n $$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 $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (= (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_x V_y))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals (tptp.c_Transcendental_Oln V_x) (tptp.c_Transcendental_Oln V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_Transcendental_Oln V_x) (tptp.c_Transcendental_Oln V_y) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y (tptp.c_RealDef_Oreal__of__preal V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_y (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted)) (or (= (tptp.c_Transcendental_Oexp (tptp.c_Transcendental_Oln V_x) 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 $$unsorted)) (or (not (= (tptp.c_Transcendental_Oexp (tptp.c_Transcendental_Oln V_x) tptp.tc_RealDef_Oreal) V_x)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal))) (forall ((V_z $$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 $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_z tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal) (= V_x V_y) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((V_x $$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_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)) (let ((_let_1 (tptp.c_RealVector_Onorm__class_Onorm V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 tptp.tc_RealDef_Oreal) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Osmult V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_OpCons V_a V_p T_a) _let_1)) (= V_p _let_1)))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_p (tptp.c_HOL_Ozero__class_Ozero _let_1) _let_1) V_p)))) (forall ((V_p $$unsorted) (V_z $$unsorted) (V_r $$unsorted)) (or (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly V_p V_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 V_p V_r) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm V_z tptp.tc_Complex_Ocomplex) V_r tptp.tc_RealDef_Oreal)))) (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 $$unsorted) (V_c $$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 $$unsorted) (V_b $$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_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_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) T_a))))) (forall ((T_a $$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_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 $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_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_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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Osgn__class_Osgn V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Osgn__class_Osgn V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_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_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)) (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))))) (forall ((T_a $$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 ((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 ((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 $$unsorted) (V_c $$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 ((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 $$unsorted) (V_b $$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_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 $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ozero__class_Ozero T_a) V_p T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly 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 ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_HOL_Ominus__class_Ominus V_p V_q (tptp.tc_Polynomial_Opoly T_a)) V_n T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Polynomial_Ocoeff V_p V_n T_a) (tptp.c_Polynomial_Ocoeff V_q V_n T_a) T_a)))) (forall ((T_a $$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_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_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)) (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$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 V_a _let_1 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 $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((V_y $$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 ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_lessequals _let_1 V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal))))) (forall ((V_x $$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 ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_b $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_OpCons V_a V_p T_a) (tptp.c_Polynomial_OpCons V_b V_q T_a))) (= V_p V_q))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_b $$unsorted) (V_q $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_OpCons V_a V_p T_a) (tptp.c_Polynomial_OpCons V_b V_q T_a))) (= V_a V_b))) (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 ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_y tptp.tc_RealDef_Oreal))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((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_a $$unsorted) (V_b $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a (tptp.c_Polynomial_OpCons V_b V_p T_a) T_a) (tptp.c_Polynomial_OpCons (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_Polynomial_Osmult V_a V_p T_a) T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_RealDef_Oreal V_x tptp.tc_nat))) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 tptp.tc_RealDef_Oreal) _let_1))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_p $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (not (= (tptp.c_Polynomial_Osmult V_c V_p T_a) (tptp.c_Polynomial_OpCons V_a V_p T_a))) (= V_p (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly 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 $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_b $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Polynomial_OpCons V_a V_p T_a) (tptp.c_Polynomial_OpCons V_b V_q T_a) _let_1) (tptp.c_Polynomial_OpCons (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ominus__class_Ominus V_p V_q _let_1) T_a))))) (forall ((T_a $$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_a $$unsorted) (V_b $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_a)) (= (tptp.c_Polynomial_Osmult V_a (tptp.c_Polynomial_Omonom V_b V_n T_a) T_a) (tptp.c_Polynomial_Omonom (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_n T_a)))) (forall ((T_a $$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 $$unsorted) (V_b $$unsorted) (V_vskULn $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) (tptp.c_RealVector_Onorm__class_Onorm V_b T_a) tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 V_vskULn T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_K $$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_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$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)) (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 ((V_y $$unsorted)) (= (tptp.c_Transcendental_Oln (tptp.c_Transcendental_Oexp V_y tptp.tc_RealDef_Oreal)) V_y)) (forall ((V_u $$unsorted)) (= (tptp.c_Transcendental_Oln (tptp.c_Transcendental_Oexp V_u tptp.tc_RealDef_Oreal)) V_u)) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Oln (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal)) V_x)) (forall ((T_a $$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) (V_x $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_Polynomial_Omonom V_a V_x T_a) V_x T_a) V_a))) (forall ((V_x $$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 ((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 ((V_x $$unsorted) (V_c $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= V_x _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_c (tptp.c_HOL_Oabs__class_Oabs V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_c _let_1 tptp.tc_RealDef_Oreal))))) (forall ((T_a $$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_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)) (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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (= (tptp.c_Polynomial_Osmult (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_p T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Polynomial_Osmult V_a V_p T_a) (tptp.c_Polynomial_Osmult V_b V_p T_a) (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (= (tptp.c_Polynomial_Osmult V_a (tptp.c_HOL_Ominus__class_Ominus V_p V_q _let_1) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Polynomial_Osmult V_a V_p T_a) (tptp.c_Polynomial_Osmult V_a V_q T_a) _let_1))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal))) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 tptp.tc_RealDef_Oreal) _let_1))) (forall ((T_a $$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_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 ((V_x $$unsorted)) (= (tptp.c_NthRoot_Osqrt (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Polynomial_Omonom V_a V_n T_a) (tptp.c_Polynomial_Omonom V_b V_n T_a) (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_n T_a)))) (tptp.c_lessequals _let_6 tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_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 $$unsorted) (V_y $$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_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_Omonom V_a V_n T_a) (tptp.c_Polynomial_Omonom V_b V_n T_a))) (= V_a V_b))) (forall ((T_a $$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 $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_OpCons V_a V_p T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_p $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_Polynomial_Osmult V_a V_p T_a) _let_1)) (= V_p _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_OpCons (tptp.c_HOL_Ozero__class_Ozero T_a) _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (not (= (tptp.c_Polynomial_Omonom V_a V_n T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Omonom (tptp.c_HOL_Ozero__class_Ozero T_a) V_n T_a) (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_HOL_Ozero T_a)) (= (tptp.c_Polynomial_Ocoeff (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_n T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y (tptp.c_RealDef_Oreal__of__preal V_x) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal))) (tptp.c_HOL_Oord__class_Oless _let_6 tptp.c_Transcendental_Opi tptp.tc_RealDef_Oreal) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= V_x _let_1) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_r $$unsorted)) (or (= (tptp.c_HOL_Oabs__class_Oabs V_r tptp.tc_RealDef_Oreal) V_r) (tptp.c_HOL_Oord__class_Oless V_r (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__algebra T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal))) (tptp.c_HOL_Oord__class_Oless _let_6 tptp.c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1 tptp.tc_RealDef_Oreal) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal))) (not (tptp.c_HOL_Oord__class_Oless _let_6 _let_10 tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__field T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal))) (forall ((V_m $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal__of__preal V_m) tptp.tc_RealDef_Oreal)) (forall ((V_xa $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal__of__preal V_xa) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_vskULt $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 V_vskULt V_r T_a) tptp.tc_RealDef_Oreal))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1 V_y) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal))))) (forall ((V_d1 $$unsorted) (V_d2 $$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_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1 V_d1 V_d2) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_d2 tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_d1 tptp.tc_RealDef_Oreal))))) (forall ((V_a $$unsorted) (V_n $$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_Osko__NthRoot__Xrealpow__pos__nth2__1__1 V_a V_n) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a tptp.tc_RealDef_Oreal))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Deriv_Osko__Deriv__Xlemma__interval__1__1 V_a V_b V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_b tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_a V_x tptp.tc_RealDef_Oreal)))) (forall ((V_x $$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 ((V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_NthRoot_Osqrt V_y) tptp.tc_RealDef_Oreal))))) (forall ((V_y $$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_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 (tptp.c_Transcendental_Oln V_x) (tptp.c_Transcendental_Oln V_y) 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_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (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 V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oln V_x) (tptp.c_Transcendental_Oln V_y) 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_p $$unsorted) (V_r $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 V_p V_r) tptp.tc_RealDef_Oreal)) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_Transcendental_Oln V_x) (tptp.c_Transcendental_Oln V_y))) (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)) (= V_x V_y)))) (forall ((V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oln V_x) V_x tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= (tptp.c_NthRoot_Oroot V_n V_x) _let_1) (tptp.c_HOL_Oord__class_Oless V_x _let_1 tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_vskULo $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1 V_vskULo T_a) tptp.tc_RealDef_Oreal))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1 V_a V_b V_x) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_b tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_a V_x tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) tptp.tc_RealDef_Oreal) (= V_x V_y))) (forall ((T_a $$unsorted) (V_vskULr $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1 V_vskULr T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.c_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)))) (tptp.c_HOL_Oord__class_Oless _let_6 tptp.c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1 tptp.tc_RealDef_Oreal) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (= (tptp.c_NthRoot_Osqrt V_x) _let_1)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (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 ((V_d1 $$unsorted) (V_d2 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1 V_d1 V_d2) V_d2 tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_d2 tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_d1 tptp.tc_RealDef_Oreal))))) (forall ((V_d1 $$unsorted) (V_d2 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1 V_d1 V_d2) V_d1 tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_d2 tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_d1 tptp.tc_RealDef_Oreal))))) (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 ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealDef_Oreal V_n tptp.tc_nat) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless 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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_NthRoot_Osqrt V_x) _let_1 tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x _let_1 tptp.tc_RealDef_Oreal))))) (not (tptp.c_HOL_Oord__class_Oless tptp.c_Transcendental_Opi _let_6 tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Oord__class_Oless _let_6 tptp.c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1 tptp.tc_RealDef_Oreal) (forall ((T_a $$unsorted) (V_vskULn $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 V_vskULn T_a) tptp.tc_RealDef_Oreal))) (forall ((V_z $$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 ((V_x $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oexp V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$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 $$unsorted) (V_x $$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 ((V_w $$unsorted)) (= (tptp.c_Polynomial_Opoly tptp.v_q____ (tptp.c_HOL_Ominus__class_Ominus V_w tptp.v_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_Polynomial_Opoly tptp.v_p V_w tptp.tc_Complex_Ocomplex))) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_q $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Ominus__class_Ominus V_p V_q (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_Polynomial_Opoly V_p V_x T_a) (tptp.c_Polynomial_Opoly V_q V_x T_a) T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_RealVector_Odist__class_Odist V_x V_y tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex))) _let_9 (forall ((T_a $$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 $$unsorted) (V_a $$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_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 $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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 $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder 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 $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$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)))) _let_8 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) _let_7 (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 $$unsorted) (V_x $$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 $$unsorted) (V_y $$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 $$unsorted) (V_y $$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)) (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 $$unsorted) (V_x $$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)) (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 $$unsorted) (V_x $$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 $$unsorted) (V_z $$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 $$unsorted) (V_x $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (= V_x_H V_y_H))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_xa V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a))) (= V_xa V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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)))) _let_7 (forall ((V_xa $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.v_x V_xa) tptp.v_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_xa tptp.tc_RealDef_Oreal))))) (forall ((V_xa $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus (tptp.hAPP tptp.v_x V_xa) tptp.v_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) V_xa tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_xa tptp.tc_RealDef_Oreal)))) _let_5 (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocancel__comm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (tptp.class_OrderedGroup_Ocancel__comm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocancel__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Opordered__comm__monoid__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_nat) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_nat) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_nat) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_nat) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_nat) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_nat) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_nat) (tptp.class_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_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat) (tptp.class_Power_Opower tptp.tc_nat) (tptp.class_HOL_Ozero tptp.tc_nat) (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_Oring__1__no__zero__divisors 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) _let_4 (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_Ring__and__Field_Ocomm__semiring__0 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 tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__field tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Olordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__field tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_RealDef_Oreal) (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_Ring__and__Field_Ocomm__ring 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_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) _let_3 (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal) (tptp.class_Power_Opower tptp.tc_RealDef_Oreal) (tptp.class_SEQ_Obanach tptp.tc_RealDef_Oreal) (tptp.class_HOL_Ozero tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Odivision__by__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) _let_2 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) _let_1 (tptp.class_OrderedGroup_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ocomm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_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_Int_Onumber__ring tptp.tc_Complex_Ocomplex) (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex) (tptp.class_SEQ_Obanach tptp.tc_Complex_Ocomplex) (tptp.class_HOL_Ozero tptp.tc_Complex_Ocomplex) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__cancel__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring__1__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__group__add__abs (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocancel__comm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocancel__comm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__ring__abs (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semidom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__idom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__mono1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Oab__group__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__zero (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__mono (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Osemiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ogroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Oab__group__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Osgn__if (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oabs__if (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oidom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Int_Onumber__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Power_Opower (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_HOL_Ozero (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_HOL_Ozero T_1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.61/1.88  )
% 1.70/1.88  % SZS output end Proof for ALG368-1
% 1.70/1.88  % cvc5---1.0.5 exiting
% 1.70/1.89  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------