TSTP Solution File: ALG378-1 by cvc5---1.0.5

%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ALG378-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.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 16:09:26 EDT 2023

% Result   : Unsatisfiable 0.56s 1.30s
% Output   : Proof 0.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.18  % Problem    : ALG378-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.19  % Command    : do_cvc5 %s %d
% 0.20/0.40  % Computer : n006.cluster.edu
% 0.20/0.40  % Model    : x86_64 x86_64
% 0.20/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.40  % Memory   : 8042.1875MB
% 0.20/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.40  % CPULimit   : 300
% 0.20/0.40  % WCLimit    : 300
% 0.20/0.40  % DateTime   : Mon Aug 28 03:51:36 EDT 2023
% 0.20/0.40  % CPUTime    : 
% 0.26/0.60  %----Proving TF0_NAR, FOF, or CNF
% 0.26/0.60  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.yw8j1076Fu/cvc5---1.0.5_5390.p...
% 0.26/0.71  ------- get file name : TPTP file name is ALG378-1
% 0.26/0.71  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_5390.smt2...
% 0.26/0.71  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.56/1.30  % SZS status Unsatisfiable for ALG378-1
% 0.56/1.30  % SZS output start Proof for ALG378-1
% 0.56/1.32  (
% 0.56/1.32  (let ((_let_1 (tptp.class_RealVector_Odist__norm tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.class_RealVector_Ometric__space tptp.tc_RealDef_Oreal))) (let ((_let_3 (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_RealDef_Oreal))) (let ((_let_4 (tptp.class_OrderedGroup_Opordered__ab__group__add__abs tptp.tc_RealDef_Oreal))) (let ((_let_5 (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus tptp.v_a tptp.v_m tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (let ((_let_6 (tptp.c_HOL_Ominus__class_Ominus tptp.v_b tptp.v_m tptp.tc_RealDef_Oreal))) (let ((_let_7 (tptp.c_HOL_Oabs__class_Oabs _let_6 tptp.tc_RealDef_Oreal))) (let ((_let_8 (tptp.c_lessequals _let_7 (tptp.c_HOL_Oplus__class_Oplus _let_5 tptp.v_c tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus tptp.v_a tptp.v_b tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (let ((_let_11 (tptp.c_lessequals _let_10 tptp.v_c tptp.tc_RealDef_Oreal))) (let ((_let_12 (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a)))))) (let ((_let_13 (forall ((T_a $$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)))))) (let ((_let_14 (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_RealVector_Odist__class_Odist V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))))) (let ((_let_15 (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))))) (let ((_let_16 (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)))))) (let ((_let_17 (tptp.c_RealVector_Odist__class_Odist tptp.v_a tptp.v_b tptp.tc_RealDef_Oreal))) (let ((_let_18 (= _let_10 _let_17))) (let ((_let_19 (tptp.c_RealVector_Odist__class_Odist tptp.v_a tptp.v_m tptp.tc_RealDef_Oreal))) (let ((_let_20 (= _let_5 _let_19))) (let ((_let_21 (tptp.c_RealVector_Odist__class_Odist tptp.v_b tptp.v_m tptp.tc_RealDef_Oreal))) (let ((_let_22 (= _let_7 _let_21))) (let ((_let_23 (= (tptp.c_RealVector_Onorm__class_Onorm _let_6 tptp.tc_RealDef_Oreal) _let_21))) (let ((_let_24 (tptp.c_lessequals _let_7 (tptp.c_HOL_Oplus__class_Oplus _let_5 _let_10 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (let ((_let_25 (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus tptp.v_b tptp.v_a tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (let ((_let_26 (= _let_10 _let_25))) (let ((_let_27 (= _let_5 (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus tptp.v_m tptp.v_a tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (let ((_let_28 (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus tptp.v_m tptp.v_b tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (let ((_let_29 (= _let_7 _let_28))) (let ((_let_30 (tptp.c_RealVector_Odist__class_Odist tptp.v_m tptp.v_b tptp.tc_RealDef_Oreal))) (let ((_let_31 (= _let_28 _let_30))) (let ((_let_32 (tptp.c_lessequals _let_30 (tptp.c_HOL_Oplus__class_Oplus _let_19 _let_17 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (let ((_let_33 (_let_14))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 ((tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal)))) (let ((_let_36 (not _let_1))) (let ((_let_37 (or _let_36 _let_23))) (let ((_let_38 (_let_16))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (not _let_24))) (let ((_let_41 (not _let_11))) (let ((_let_42 (not _let_3))) (let ((_let_43 (or _let_42 _let_8 _let_41 _let_40))) (let ((_let_44 (_let_13))) (let ((_let_45 (ASSUME :args _let_44))) (let ((_let_46 (not _let_4))) (let ((_let_47 (or _let_46 _let_26))) (let ((_let_48 (_let_12))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 ((tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a)))) (let ((_let_51 (ASSUME :args (_let_4)))) (let ((_let_52 (or _let_46 _let_27))) (let ((_let_53 (or _let_46 _let_29))) (let ((_let_54 (not _let_2))) (let ((_let_55 (or _let_54 _let_32))) (let ((_let_56 (_let_15))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 (not _let_31))) (let ((_let_59 (not _let_32))) (let ((_let_60 (not _let_29))) (let ((_let_61 (not _let_27))) (let ((_let_62 (not _let_26))) (let ((_let_63 (not _let_22))) (let ((_let_64 (not _let_20))) (let ((_let_65 (not _let_18))) (let ((_let_66 (not _let_23))) (let ((_let_67 (and _let_23 _let_18 _let_20 _let_22 _let_40 _let_26 _let_27 _let_29 _let_31))) (let ((_let_68 (ASSUME :args (_let_40)))) (let ((_let_69 (APPLY_UF tptp.c_lessequals))) (let ((_let_70 (REFL :args (tptp.tc_RealDef_Oreal)))) (let ((_let_71 (APPLY_UF tptp.c_HOL_Oplus__class_Oplus))) (let ((_let_72 (ASSUME :args (_let_26)))) (let ((_let_73 (ASSUME :args (_let_27)))) (let ((_let_74 (CONG (SYMM _let_73) (SYMM _let_72) _let_70 :args _let_71))) (let ((_let_75 (TRANS (CONG _let_73 (REFL :args (_let_25)) _let_70 :args _let_71) _let_74))) (let ((_let_76 (ASSUME :args (_let_18)))) (let ((_let_77 (ASSUME :args (_let_20)))) (let ((_let_78 (ASSUME :args (_let_22)))) (let ((_let_79 (ASSUME :args (_let_23)))) (let ((_let_80 (SYMM _let_79))) (let ((_let_81 (ASSUME :args (_let_29)))) (let ((_let_82 (ASSUME :args (_let_31)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_67)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_68 _let_78 _let_79 _let_73 _let_72 _let_81 _let_82 _let_77 _let_76) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (TRANS (SYMM _let_82) (SYMM _let_81) _let_78 _let_80) (TRANS (SYMM _let_80) (SYMM _let_78))) (TRANS (TRANS (CONG (TRANS (SYMM _let_77) _let_73) (TRANS (SYMM _let_76) _let_72) _let_70 :args _let_71) _let_74) (SYMM _let_75)) _let_70 :args _let_69) (CONG (REFL :args (_let_7)) _let_75 _let_70 :args _let_69) (FALSE_INTRO _let_68))) :args (_let_40 _let_22 _let_23 _let_27 _let_26 _let_29 _let_31 _let_20 _let_18))) :args (_let_23 _let_18 _let_20 _let_22 _let_40 _let_26 _let_27 _let_29 _let_31))) :args (true _let_67)) (CONG (REFL :args (_let_66)) (REFL :args (_let_65)) (REFL :args (_let_64)) (REFL :args (_let_63)) (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_24))) (REFL :args (_let_62)) (REFL :args (_let_61)) (REFL :args (_let_60)) (REFL :args (_let_58)) (REFL :args (_let_59)) :args (or))) :args ((or _let_24 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_54 _let_32 (not _let_55)))) (ASSUME :args (_let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (tptp.tc_RealDef_Oreal tptp.v_m tptp.v_b tptp.v_a QUANTIFIERS_INST_E_MATCHING ((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)))) :args _let_56)) _let_57 :args (_let_55 false _let_15)) :args (_let_32 false _let_2 false _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.v_m tptp.v_b QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33))) _let_34 :args (_let_31 false _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_46 _let_29 (not _let_53)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.tc_RealDef_Oreal tptp.v_b tptp.v_m QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_48)) _let_49 :args (_let_53 false _let_12)) :args (_let_29 false _let_4 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_46 _let_27 (not _let_52)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.tc_RealDef_Oreal tptp.v_a tptp.v_m QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_48)) _let_49 :args (_let_52 false _let_12)) :args (_let_27 false _let_4 false _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_26 (not _let_47)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.tc_RealDef_Oreal tptp.v_a tptp.v_b QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_48)) _let_49 :args (_let_47 false _let_12)) :args (_let_26 false _let_4 false _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_8 _let_41 _let_42 _let_40 (not _let_43)))) (ASSUME :args (_let_9)) (ASSUME :args (_let_11)) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (tptp.tc_RealDef_Oreal _let_7 _let_5 tptp.v_c _let_10 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) true)) (not (= (tptp.c_lessequals V_c V_d T_a) false))))) :args _let_44)) _let_45 :args (_let_43 false _let_13)) :args (_let_40 true _let_8 false _let_11 false _let_3 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_23 (not _let_37)))) (ASSUME :args (_let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_39 :args (tptp.tc_RealDef_Oreal tptp.v_b tptp.v_m QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a)))) :args _let_38))) _let_39 :args (_let_37 false _let_16)) :args (_let_23 false _let_1 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.v_b tptp.v_m QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33))) _let_34 :args (_let_22 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.v_a tptp.v_m QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33))) _let_34 :args (_let_20 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.v_a tptp.v_b QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_35)) :args _let_33))) _let_34 :args (_let_18 false _let_14)) :args (false false _let_32 false _let_31 false _let_29 false _let_27 false _let_26 true _let_24 false _let_23 false _let_22 false _let_20 false _let_18)) :args ((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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (let ((_let_2 (tptp.c_HOL_Oabs__class_Oabs V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_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_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 $$unsorted) (V_c $$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 $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (not (= (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_RealVector_Oof__real V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ouminus__class_Ouminus V_a tptp.tc_RealDef_Oreal) V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) V_xa T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_x V_xa T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((T_a $$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_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Oof__real V_r T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((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 $$unsorted) (V_b $$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)) (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 $$unsorted) (V_x $$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_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((V_x $$unsorted)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (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_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (= (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_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_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)) (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 $$unsorted) (V_c $$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 $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus 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(tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_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 $$unsorted) (V_x $$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 $$unsorted) (V_x $$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 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(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 $$unsorted)) (or (not (tptp.class_Orderings_Oorder 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(V_y $$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 $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not 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$$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$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 $$unsorted) (V_x $$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_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_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)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$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 $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a) (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$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 $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ouminus__class_Ouminus V_a tptp.tc_RealDef_Oreal) V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Odist__class_Odist V_x V_x T_a) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_a $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_a tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_x V_a))) (forall ((T_a $$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 $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (= V_a V_b))) (forall ((V_r $$unsorted)) (or (= (tptp.c_HOL_Oabs__class_Oabs V_r tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ouminus__class_Ouminus V_r tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_r (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oabs__if T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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_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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_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)) (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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$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 $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_lx $$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)) (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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_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_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) tptp.tc_RealDef_Oreal) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$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 $$unsorted) (V_c $$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_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_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 $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (not (= (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$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 $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a)))) (forall ((T_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_w V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_w V_z T_a) (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a))) (= V_y V_z) (= V_w V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted) (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_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 $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$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 $$unsorted) (V_a_H $$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_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (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) (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)) (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) (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) (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_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) V_y)) (= V_x (tptp.c_HOL_Ouminus__class_Ouminus V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Omonoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$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_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_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_y T_a) V_x T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_x_H $$unsorted) (V_y_H $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Ominus__class_Ominus V_x_H V_y_H T_a))) (tptp.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_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_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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 $$unsorted) (V_xa $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_xa V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_b_H $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ominus__class_Ominus V_b V_b_H T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b_H T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_a_H $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_a V_a_H T_a) V_b T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_ya $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) V_ya T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_ya T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_ya T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Ominus__class_Ominus V_b V_a T_a)))) (forall ((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) (= V_x V_y) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_r V_s tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) V_s tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) V_r tptp.tc_RealDef_Oreal)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals V_y (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_y (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$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)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_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) (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_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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Oplus__class_Oplus V_a V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_y _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) _let_1)) (not (tptp.c_lessequals _let_1 V_y T_a)) (not (tptp.c_lessequals _let_1 V_x T_a)) (= V_x _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_a T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le T_a)) (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) T_a) (not (tptp.c_lessequals V_b V_c T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (not (tptp.c_lessequals _let_1 _let_1 T_a)))) (or (not (tptp.class_OrderedGroup_Opordered__comm__monoid__add T_a)) _let_2 _let_2 (= (tptp.c_HOL_Oplus__class_Oplus _let_1 _let_1 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_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 $$unsorted) (V_e $$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 $$unsorted) (V_e $$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)) (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_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_x V_y T_a) (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$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_x $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ominus__class_Ominus V_y V_b T_a))) (let ((_let_2 (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Otimes__class_Otimes _let_2 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes _let_2 V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) T_a)))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1 T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_Oof__real V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_Oof__real V_x 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 $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)))) (forall ((V_S $$unsorted) (V_W $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus V_S (tptp.c_HOL_Ouminus__class_Ouminus V_W tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_W V_S tptp.tc_RealDef_Oreal)))) (forall ((V_W $$unsorted) (V_S $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_W V_S tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus V_S (tptp.c_HOL_Ouminus__class_Ouminus V_W tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Ometric__space T_a)) (= (tptp.c_RealVector_Odist__class_Odist V_x V_y T_a) (tptp.c_RealVector_Odist__class_Odist V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$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_r $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_a T_a) V_b T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) V_y T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_b T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) V_y T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_y T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_RealVector_Oof__real V_r T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs V_r tptp.tc_RealDef_Oreal)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_y (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$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)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_y (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$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)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_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 $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$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_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((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_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oabs__if T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted)) (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 $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR _let_1 V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR _let_1 V_y T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a _let_1 T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (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 $$unsorted) (V_a $$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 $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (= (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_2 T_a) _let_1))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) _let_16 (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((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)) (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 ((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__vector T_a)) (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_RealVector_Oof__real V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_RealVector_Oof__real V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (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_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 $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Oplus__class_Oplus V_a V_a_H tptp.tc_RealDef_Oreal) V_b T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a_H V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ominus__class_Ominus V_a V_r T_a) V_x T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_a T_a) T_a) V_r T_a)))) _let_15 (forall ((T_a $$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 $$unsorted) (V_z $$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)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_RealVector_Oof__real V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_RealVector_Oof__real V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (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 $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ominus__class_Ominus V_a V_a_H tptp.tc_RealDef_Oreal) V_b T_a) (tptp.c_HOL_Ominus__class_Ominus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a_H V_b T_a) T_a)))) (forall ((V_x $$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 $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Ominus__class_Ominus V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_r $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) V_r tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_r tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_r tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_r $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_r tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) V_r tptp.tc_RealDef_Oreal)))) (forall ((V_r $$unsorted) (V_s $$unsorted)) (= (tptp.c_HOL_Ominus__class_Ominus V_r V_s tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus V_r (tptp.c_HOL_Ouminus__class_Ouminus V_s tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Ouminus__class_Ouminus V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) _let_14 (forall ((T_a $$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 $$unsorted) (V_a $$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_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 ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) (tptp.c_RealVector_Onorm__class_Onorm V_b T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$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 $$unsorted) (V_a $$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_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))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_l $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_m tptp.tc_RealDef_Oreal))) (let ((_let_2 (tptp.c_HOL_Ouminus__class_Ouminus V_l tptp.tc_RealDef_Oreal))) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_x V_y tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus _let_2 _let_1 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oplus__class_Oplus V_x _let_2 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Oplus__class_Oplus V_y _let_1 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_a V_c T_a) T_a) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ominus__class_Ominus V_b V_d T_a) T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (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.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))) (forall ((V_x $$unsorted) (V_m $$unsorted) (V_e $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_x V_m tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) V_e tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oplus__class_Oplus V_m V_e tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_m V_x tptp.tc_RealDef_Oreal)))) (forall ((V_w $$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_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_z $$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_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)))) _let_13 (forall ((V_w $$unsorted)) (tptp.c_lessequals V_w V_w tptp.tc_RealDef_Oreal)) (forall ((V_i $$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 ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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)) (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 $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_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_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_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__semigroup__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$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 $$unsorted) (V_b $$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 $$unsorted) (V_a $$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 $$unsorted) (V_a $$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 $$unsorted) (V_x $$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) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_b V_d T_a) T_a)))) _let_12 (forall ((T_a $$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 $$unsorted) (V_x $$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 $$unsorted) (V_a $$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_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (= V_z V_w) (not (tptp.c_lessequals V_w V_z tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_z V_w tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((V_x $$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 (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Ominus__class_Ominus V_a V_b T_a) V_b T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$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_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Ocomm__monoid__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__group__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_x (tptp.c_HOL_Oplus__class_Oplus V_y V_z T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_y (tptp.c_HOL_Oplus__class_Oplus V_x V_z T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__add T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_d T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_c T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_c V_d T_a) T_a) (tptp.c_HOL_Oplus__class_Oplus V_c (tptp.c_HOL_Oplus__class_Oplus V_a V_d T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Oplus__class_Oplus (tptp.c_HOL_Oplus__class_Oplus V_a V_b T_a) V_c T_a) (tptp.c_HOL_Oplus__class_Oplus V_a (tptp.c_HOL_Oplus__class_Oplus V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_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 $$unsorted) (V_x $$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_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))) _let_11 _let_9 (tptp.class_OrderedGroup_Opordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__semigroup__add tptp.tc_RealDef_Oreal) _let_4 (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) _let_3 (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocancel__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__ring__abs tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__vector 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_Olordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__semiring tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ocomm__monoid__add 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_Osemiring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__algebra tptp.tc_RealDef_Oreal) _let_2 (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_Oabs__if tptp.tc_RealDef_Oreal) _let_1 (tptp.class_Ring__and__Field_Oring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oidom tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.56/1.32  )
% 0.56/1.32  % SZS output end Proof for ALG378-1
% 0.56/1.32  % cvc5---1.0.5 exiting
% 0.56/1.33  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------