%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW222+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n002.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 : Fri Sep  1 00:20:01 EDT 2023

% Result   : Theorem 1.34s 1.53s
% Output   : Proof 1.34s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.25  % Problem    : SWW222+1 : TPTP v8.1.2. Released v5.2.0.
% 0.26/0.26  % Command    : do_cvc5 %s %d
% 0.26/0.47  % Computer : n002.cluster.edu
% 0.26/0.47  % Model    : x86_64 x86_64
% 0.26/0.47  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.47  % Memory   : 8042.1875MB
% 0.26/0.47  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.26/0.47  % CPULimit   : 300
% 0.26/0.47  % WCLimit    : 300
% 0.26/0.47  % DateTime   : Sun Aug 27 18:20:19 EDT 2023
% 0.26/0.48  % CPUTime    : 
% 0.50/0.74  %----Proving TF0_NAR, FOF, or CNF
% 1.34/1.53  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YqY0fCsmeT/cvc5---1.0.5_8937.p...
% 1.34/1.53  ------- get file name : TPTP file name is SWW222+1
% 1.34/1.53  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8937.smt2...
% 1.34/1.53  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.34/1.53  % SZS status Theorem for SWW222+1
% 1.34/1.53  % SZS output start Proof for SWW222+1
% 1.34/1.53  (
% 1.34/1.53  (let ((_let_1 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) (let ((_let_2 (tptp.c_Int_OBit0 _let_1))) (let ((_let_3 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal _let_2))) (let ((_let_4 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____))) (let ((_let_5 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p))) (let ((_let_6 (tptp.hAPP _let_5 tptp.v_z____))) (let ((_let_7 (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex _let_6) _let_4)))) (let ((_let_8 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal _let_7 _let_3))) (let ((_let_9 (tptp.hAPP _let_5 tptp.v_wa____))) (let ((_let_10 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex _let_9 _let_6))) (let ((_let_11 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex _let_10))) (let ((_let_12 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_11 _let_8))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.class_Groups_Oab__group__add tptp.tc_Complex_Ocomplex))) (let ((_let_15 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex))) (let ((_let_16 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_17 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_18 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_19 (tptp.c_Int_OBit1 _let_1))) (let ((_let_20 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 _let_2)))) (let ((_let_21 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi _let_20))) (let ((_let_22 (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_17 tptp.v_r))) (let ((_let_23 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint tptp.c_Int_OPls))) (let ((_let_24 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (let ((_let_25 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (let ((_let_26 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (let ((_let_27 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP _let_5 _let_26)))) (let ((_let_28 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex _let_26))) (let ((_let_29 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi _let_3))) (let ((_let_30 (tptp.c_Nat_OSuc _let_16))) (let ((_let_31 (tptp.c_Nat_OSuc _let_30))) (let ((_let_32 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_2))) (let ((_let_33 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (let ((_let_34 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_1))) (let ((_let_35 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))) (let ((_let_36 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat tptp.c_Int_OPls))) (let ((_let_37 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))) (let ((_let_38 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2)) (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (let ((_let_39 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))) (let ((_let_40 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_17 _let_8))) (let ((_let_41 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex tptp.v_wa____ tptp.v_z____))) (let ((_let_42 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex _let_41))) (let ((_let_43 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_42 tptp.v_d____))) (let ((_let_44 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_17 _let_42))) (let ((_let_45 (and _let_44 _let_43))) (let ((_let_46 (=> _let_45 _let_12))) (let ((_let_47 (= _let_17 _let_28))) (let ((_let_48 (= _let_11 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex _let_6 _let_9))))) (let ((_let_49 (= tptp.v_wa____ tptp.v_z____))) (let ((_let_50 (= _let_10 _let_26))) (let ((_let_51 (ASSUME :args (_let_40)))) (let ((_let_52 (ASSUME :args (_let_13)))) (let ((_let_53 (not _let_15))) (let ((_let_54 (or _let_53 _let_47))) (let ((_let_55 (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_39)) (MACRO_SR_EQ_INTRO :args (_let_39 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (ASSUME :args (_let_15)))) (let ((_let_58 (or _let_53 _let_48))) (let ((_let_59 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_37)) (MACRO_SR_EQ_INTRO :args (_let_37 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (= _let_41 _let_26))) (let ((_let_62 (= _let_61 _let_49))) (let ((_let_63 (not _let_14))) (let ((_let_64 (or _let_63 _let_62))) (let ((_let_65 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Oab__group__add T_a)) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 V_a_2)))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (_let_65))) (let ((_let_68 ((tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2)))) (let ((_let_69 (ASSUME :args (_let_14)))) (let ((_let_70 (not _let_61))) (let ((_let_71 (= _let_44 _let_70))) (let ((_let_72 (or _let_53 _let_71))) (let ((_let_73 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2)) (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_38)) (MACRO_SR_EQ_INTRO :args (_let_38 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (not _let_44))) (let ((_let_76 (not _let_45))) (let ((_let_77 (not _let_71))) (let ((_let_78 (or))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_62)) :args ((or _let_70 _let_49 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_71)) (CONG (REFL :args (_let_77)) (REFL :args (_let_44)) (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_61))) :args _let_78)) :args ((or _let_44 _let_61 _let_77))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_45)) :args ((or _let_45 (not _let_43) _let_75))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (ASSUME :args (_let_46))) :args ((or _let_12 _let_76))) _let_52 :args (_let_76 true _let_12)) (ASSUME :args (_let_43)) :args (_let_75 true _let_45 false _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_53 _let_71 (not _let_72)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (_let_41 tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2)))) :args (_let_73))) _let_74 :args (_let_72 false _let_73)) :args (_let_71 false _let_15 false _let_72)) :args (_let_61 true _let_44 false _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_63 _let_62 (not _let_64)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (tptp.v_z____ tptp.v_wa____ tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_68)) :args _let_67))) _let_66 :args (_let_64 false _let_65)) :args (_let_62 false _let_14 false _let_64)) :args (_let_49 false _let_61 false _let_62)))) (let ((_let_80 (= _let_6 _let_9))) (let ((_let_81 (= _let_50 _let_80))) (let ((_let_82 (or _let_63 _let_81))) (let ((_let_83 (not _let_49))) (let ((_let_84 (_let_49))) (let ((_let_85 (ASSUME :args _let_84))) (let ((_let_86 (CONG (REFL :args (_let_5)) (SYMM _let_85) :args (APPLY_UF tptp.hAPP)))) (let ((_let_87 (not _let_48))) (let ((_let_88 (not _let_47))) (let ((_let_89 (not _let_50))) (let ((_let_90 (not _let_40))) (let ((_let_91 (APPLY_UF tptp.c_Orderings_Oord__class_Oless))) (let ((_let_92 (REFL :args (_let_8)))) (let ((_let_93 (ASSUME :args (_let_47)))) (let ((_let_94 (APPLY_UF tptp.c_RealVector_Onorm__class_Onorm))) (let ((_let_95 (ASSUME :args (_let_50)))) (let ((_let_96 (REFL :args (tptp.tc_Complex_Ocomplex)))) (let ((_let_97 (ASSUME :args (_let_48)))) (let ((_let_98 (TRANS (CONG _let_96 (CONG _let_96 (REFL :args (_let_6)) _let_86 :args (APPLY_UF tptp.c_Groups_Ominus__class_Ominus)) :args _let_94) (SYMM _let_97)))) (let ((_let_99 (REFL :args (tptp.tc_RealDef_Oreal)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_51 _let_93 _let_95 _let_97 _let_85 _let_52) :args (_let_40 _let_13 _let_47 _let_50 _let_48 _let_49)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_52)) (CONG _let_99 (SYMM _let_98) _let_92 :args _let_91) (CONG _let_99 (TRANS _let_98 (TRANS (CONG _let_96 (SYMM (SYMM _let_95)) :args _let_94) (SYMM _let_93))) _let_92 :args _let_91) (TRUE_INTRO _let_51))) :args (_let_40 _let_47 _let_50 _let_48 _let_49 _let_13)) :args ((not (and _let_40 _let_13 _let_47 _let_50 _let_48 _let_49)) SB_LITERAL))) (CONG (REFL :args (_let_90)) (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) (REFL :args (_let_88)) (REFL :args (_let_89)) (REFL :args (_let_87)) (REFL :args (_let_83)) :args _let_78)) :args ((or _let_12 _let_90 _let_89 _let_88 _let_87 _let_83))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_81)) :args ((or _let_50 (not _let_80) (not _let_81)))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (MODUS_PONENS _let_85 (SCOPE _let_86 :args _let_84)) :args _let_84)) :args ((or _let_80 _let_83))) _let_79 :args (_let_80 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_63 _let_81 (not _let_82)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_6 _let_9 tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_68)) :args _let_67)) _let_66 :args (_let_82 false _let_65)) :args (_let_81 false _let_14 false _let_82)) :args (_let_50 false _let_80 false _let_81)) _let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_53 _let_48 (not _let_58)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (_let_6 _let_9 tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)))) :args (_let_59))) _let_60 :args (_let_58 false _let_59)) :args (_let_48 false _let_15 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_47 (not _let_54)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.tc_Complex_Ocomplex QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.class_RealVector_Oreal__normed__vector T_a) false))))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_47 false _let_15 false _let_54)) _let_52 _let_51 :args (false false _let_50 false _let_49 false _let_48 false _let_47 true _let_12 false _let_40)) :args ((forall ((V_ga_2 $$unsorted) (V_fa_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_fa_2 B_x) (tptp.hAPP V_ga_2 B_x))) (= V_fa_2 V_ga_2))) (tptp.c_SEQ_Osubseq tptp.v_f____) _let_43 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_17 _let_7) _let_46 (forall ((B_w $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p))) (let ((_let_2 (tptp.hAPP _let_1 tptp.v_z____))) (let ((_let_3 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex B_w tptp.v_z____)))) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) _let_3) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_3 tptp.v_d____)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 B_w) _let_2)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex _let_2) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____))) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))))) _let_40 (exists ((B_d $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_d) (forall ((B_w $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p))) (let ((_let_2 (tptp.hAPP _let_1 tptp.v_z____))) (let ((_let_3 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex B_w tptp.v_z____)))) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) _let_3) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_3 B_d)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 B_w) _let_2)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex _let_2) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____))) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_w))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_x (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_x))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_RealVector_Oreal__normed__field T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2) V_b_2) (and (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2))))) (not (forall ((B_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_d) (not (forall ((B_w $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p))) (let ((_let_2 (tptp.hAPP _let_1 tptp.v_z____))) (let ((_let_3 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex B_w tptp.v_z____)))) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) _let_3) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_3 B_d)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 B_w) _let_2)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex _let_2) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____))) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_RealVector_Onorm__class_Onorm T_a V_a))) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal _let_1) _let_1)))) (forall ((V_x $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_p)) V_x) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x))))) (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_x) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_17 tptp.v_d____) _let_39 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_x) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (= (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k tptp.c_Int_OPls) V_k)) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k V_l)))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint tptp.c_Int_OPls) tptp.c_Int_OPls) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k)) (tptp.c_Int_OBit0 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_k)))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls tptp.c_Int_OPls)) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a _let_1) _let_1)))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 V_y) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a _let_1 V_a) _let_1)))) _let_38 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit1 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_l $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint tptp.c_Int_OPls V_l)))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 tptp.c_Int_OPls)))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_y_2)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_x (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_x))) (let ((_let_2 (tptp.c_Groups_Oabs__class_Oabs T_a _let_1))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (and (=> _let_3 (= _let_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (= V_x_2 V_y_2)))) (forall ((V_x_2 $$unsorted) (V_wb_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (=> (tptp.class_Int_Onumber T_a) (= (= _let_1 V_x_2) (= V_x_2 _let_1))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (= V_k_2 V_l_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (= V_k_2 V_l_2))) (forall ((V_q_2 $$unsorted) (V_pa_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Oring__char__0 T_a) (tptp.class_Rings_Oidom T_a)) (= (= (tptp.c_Polynomial_Opoly T_a V_pa_2) (tptp.c_Polynomial_Opoly T_a V_q_2)) (= V_pa_2 V_q_2)))) (forall ((V_r $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_r) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_r (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))) (forall ((V_ra_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_ra_2 (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_ra_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 V_y_2)))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w))))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y) V_ya) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_ya) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_ya))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c))))) (forall ((V_k $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) tptp.c_Int_OPls))) (forall ((V_l $$unsorted)) (not (= tptp.c_Int_OPls (tptp.c_Int_OBit1 V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit1 V_l)))) (forall ((V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (= V_k_2 tptp.c_Int_OPls))) (forall ((V_l_2 $$unsorted)) (= (= tptp.c_Int_OPls (tptp.c_Int_OBit0 V_l_2)) (= tptp.c_Int_OPls V_l_2))) (= (tptp.c_Int_OBit0 tptp.c_Int_OPls) tptp.c_Int_OPls) _let_37 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)))) (forall ((V_r $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_r))) (=> (not _let_2) (= _let_1 V_r)))))) (forall ((V_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_a))) (=> (not _let_2) (= _let_1 V_a)))))) (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_x) V_y) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oabs__class_Oabs T_a V_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (=> (tptp.class_Groups_Oabs__if T_a) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))) (=> (not _let_2) (= _let_1 V_a))))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2)) (not (= V_a_2 _let_1)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint _let_24) _let_24) (forall ((V_i $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_i))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_i))) (=> (not _let_2) (= _let_1 V_i)))))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z)) V_z)) (forall ((V_w $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_x))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_v_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_v_2))) (= _let_36 _let_16) (= _let_16 _let_36) (forall ((V_wb_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_wb_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wb_2 _let_1)))) (= tptp.c_Int_OPls _let_24) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls _let_24)) (= _let_24 _let_23) (forall ((V_wb_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_wb_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wb_2 _let_1)))) (forall ((V_pa_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (and (tptp.class_Int_Oring__char__0 T_a) (tptp.class_Rings_Oidom T_a)) (= (= (tptp.c_Polynomial_Opoly T_a V_pa_2) (tptp.c_Polynomial_Opoly T_a _let_1)) (= V_pa_2 _let_1))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Groups_Oabs__class_Oabs _let_1 V_x))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless _let_1 V_x (tptp.c_Groups_Ozero__class_Ozero _let_1)))) (=> (tptp.class_Rings_Olinordered__idom T_a) (and (=> _let_3 (= _let_2 (tptp.c_Groups_Ouminus__class_Ouminus _let_1 V_x))) (=> (not _let_3) (= _let_2 V_x)))))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero _let_1))) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus _let_1 _let_2) _let_2))))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 V_p (tptp.c_Groups_Ozero__class_Ozero _let_1)) V_p)))) (forall ((V_q $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus _let_1 (tptp.c_Groups_Ozero__class_Ozero _let_1) V_q) (tptp.c_Groups_Ouminus__class_Ouminus _let_1 V_q))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ozero T_a) (= (= _let_1 V_x_2) (= V_x_2 _let_1))))) (forall ((V_da_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_da_2)) (= (= V_a_2 V_b_2) (= V_c_2 V_da_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_a))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= V_a_2 V_b_2)))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (let ((_let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_2 V_v_H_2))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H_2)) (and (=> _let_1 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_v_H_2)) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oabs__class_Oabs T_a V_a))) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) _let_35 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 V_b_2)))) (forall ((V_da_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_da_2)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_da_2))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (= _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_a_2) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_a_2)))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a _let_1) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_1))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2) _let_1) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_1)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b_2))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_16 _let_32) (forall ((B_e $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_e) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_N B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.v_g____ (tptp.hAPP tptp.v_f____ B_n)) tptp.v_z____)) B_e)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))) (forall ((V_p $$unsorted) (V_z $$unsorted) (V_e $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_e) (exists ((B_d $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_d) (forall ((B_w $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_p))) (let ((_let_2 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex B_w V_z)))) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) _let_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_2 B_d)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 B_w) (tptp.hAPP _let_1 V_z))) V_e))))))))) (forall ((V_a_2 $$unsorted) (V_pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pa_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_y))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_29) _let_17) (forall ((V_pa_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_a V_pa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))) (forall ((T_a $$unsorted)) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber__ring T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (= _let_24 _let_25)) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_y_2) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x_2 V_y_2) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2)) (= V_b_2 V_c_2)))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2)) (= V_b_2 V_c_2)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Groups_Oone T_a) (= (= _let_1 V_x_2) (= V_x_2 _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_z)))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2 V_y_2)))) (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k) V_k)) (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_x) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_x) (tptp.c_Groups_Oone__class_Oone T_a)))) (not (= tptp.c_Transcendental_Opi _let_17)) (forall ((V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_w))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_y_2)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1))))) (forall ((V_c $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_c)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_c)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1)) V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1))))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) _let_1) _let_1))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))) (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_y) V_s) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_r V_s)))))) (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (= V_a_2 _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_b))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)) V_b))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_ya) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_ya))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c))))) (forall ((V_da_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_da_2)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 V_da_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2) V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)))) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a _let_1) _let_1)))) (not (= _let_17 _let_18)) (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_za_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_za_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_24 _let_25) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi _let_17)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_17 tptp.c_Transcendental_Opi) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2 tptp.c_Int_OPls)))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_y_2)))) (forall ((V_w $$unsorted) (V_c $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Ominus__class_Ominus T_a V_c (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w))) V_c)))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) _let_1)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)) V_a))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_wb_2 $$unsorted) (V_v_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_v_2))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (=> (and (tptp.class_Int_Onumber T_a) (tptp.class_Orderings_Olinorder T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 _let_2) (not (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2) _let_1) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (= V_a _let_2))) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 (tptp.c_Groups_Oone__class_Oone T_a))))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a_2 V_b_2) (tptp.c_Groups_Oone__class_Oone T_a)) (= V_a_2 V_b_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2) V_b_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_2) V_b_2))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)))) (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_a_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 V_a_2))) (= _let_34 _let_33) (= _let_33 _let_34) (= _let_25 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint _let_1)) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_y)))) (forall ((V_s $$unsorted) (V_r $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_r V_s) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_r (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_s)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_y))) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_y (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) _let_1) _let_1))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_w V_z) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_w))))))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_w V_z) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_w))))))))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_w) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_w V_z) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_w))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls)) (tptp.c_Groups_Oone__class_Oone T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2) V_y_2))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi _let_20) (not (= _let_29 _let_3)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_29 _let_3) (not (= _let_29 _let_17)) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) V_y_2)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_17 _let_29) (forall ((V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_b V_a) _let_1) V_a) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_b V_a) _let_1)))) (forall ((V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b) _let_1) V_a) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_b V_a) _let_1)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_1 _let_1) V_x))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) (tptp.v_g____ B_n))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_n)))))) (forall ((V_ra_2 $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x_2 V_a_2)) V_ra_2) (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ra_2) V_x_2) (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_ra_2)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y) (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y))))) _let_22 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_n))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_n))) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.v_g____ B_n)) tptp.v_r)) (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))) (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_nat_H)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_nat_H_1 $$unsorted)) (not (= (tptp.c_Nat_OSuc V_nat_H_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_i))) (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_i))) (= _let_33 _let_30) (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_m)))) (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_i)))) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_30) _let_18) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)))) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) V_n)) (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc V_m))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k)))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) V_j)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))) (let ((_let_2 (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (and (=> _let_2 (= _let_1 V_n)) (=> (not _let_2) (= _let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))) (forall ((V_za_2 $$unsorted) (V_wb_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wb_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_wb_2 V_za_2))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (= (= _let_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (and (= V_m_2 _let_2) (= V_n_2 _let_1)) (and (= V_m_2 _let_1) (= V_n_2 _let_2))))))) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_za_2 $$unsorted) (V_wb_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_wb_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wb_2 V_za_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted) (V_j_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2) V_i_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) _let_2) (or (and (= V_m_2 _let_2) (= V_n_2 _let_1)) (and (= V_m_2 _let_1) (= V_n_2 _let_2))))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_m)) (= V_m V_n)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))) (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_k)))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w V_z) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Nat_OSuc V_j))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k)))) (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_j_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_j) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n) V_m))) (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2 V_j_2) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2) V_k_2) (= V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_i_2))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k))))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k)))) (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_j) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_m))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (not (= _let_1 V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_i) V_k)))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))) (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_H V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_H V_z_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= V_m V_n)))) (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_k))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))) (forall ((V_n $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n))) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_33) _let_18) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_n_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 _let_1) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 _let_1))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) (tptp.c_Nat_OSuc V_m_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))) (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_n))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m _let_1) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n)) (= V_m _let_1))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) V_n) (not (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n)))))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z) (= V_z V_w)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_k)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_i) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_j)))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_z3) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z2 V_z3)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_z)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_z))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))) (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w V_w)) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Nat_OSuc V_x) (tptp.c_Nat_OSuc V_y)) (= V_x V_y))) (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= (tptp.c_Nat_OSuc V_nat_2) (tptp.c_Nat_OSuc V_nat_H_2)) (= V_nat_2 V_nat_H_2))) (forall ((V_n $$unsorted)) (not (= (tptp.c_Nat_OSuc V_n) V_n))) (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Nat_OSuc V_n)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (= V_n_2 V_m_2))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_k))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n)))) (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)))) (forall ((V_z $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z))))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_w V_z)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z)))) (forall ((V_k $$unsorted)) (= (tptp.c_Int_OBit1 V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_k) V_k))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) V_z)) (forall ((V_z $$unsorted)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint tptp.c_Int_OPls V_k) V_k)) (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k tptp.c_Int_OPls) V_k)) (forall ((V_k $$unsorted)) (= (tptp.c_Int_OBit0 V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_k))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal _let_1) _let_1))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j V_k)))) (forall ((V_za_2 $$unsorted) (V_wb_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wb_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wb_2 V_za_2) (= V_wb_2 V_za_2)))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls tptp.c_Int_OPls) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_l_2) (exists ((B_n $$unsorted)) (= V_l_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 B_n))))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (not (= V_x_2 V_y_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (= V_x_2 V_y_2)))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)))) (forall ((V_wb_2 $$unsorted) (V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 V_wb_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_za_2 V_wb_2) (not (= V_za_2 V_wb_2))))) (forall ((V_q $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus _let_1 (tptp.c_Groups_Ozero__class_Ozero _let_1) V_q) V_q)))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus _let_1 V_p (tptp.c_Groups_Ozero__class_Ozero _let_1)) V_p)))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_y)))) (forall ((V_i $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_i)) V_n))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc _let_1))) V_n)))) (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_j $$unsorted)) (and (= V_m_2 (tptp.c_Nat_OSuc B_j)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_n_2)))))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc _let_1)) (= V_n_2 _let_1)))) (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (exists ((B_m $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc B_m))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((B_d $$unsorted)) (=> (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (not (or (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (exists ((B_d $$unsorted)) (and (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2) V_m_2))) (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc V_n))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_n))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v))) (let ((_let_3 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat _let_2 _let_1))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_H tptp.c_Int_OPls))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_v_H))))))))))))) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc V_n)))) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_n) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc V_n)))) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat _let_16) _let_17) (forall ((V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))))) (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= V_n (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit1 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))) (forall ((V_za_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) V_za_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 _let_1)))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_za_2))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x_2 V_y_2)) (and (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_1 V_x_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_y_2 _let_1)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_17 tptp.c_Transcendental_Opi) (forall ((V_za_2 $$unsorted) (V_wb_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_wb_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_wb_2 V_za_2))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z V_w))) (forall ((V_ra_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x_2) V_ra_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_ra_2) V_x_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_ra_2)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (forall ((V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) _let_1) (= _let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_v_2 $$unsorted)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 tptp.c_Int_OPls))) (forall ((V_v_2 $$unsorted)) (= (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 tptp.c_Int_OPls))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))) (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))) (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))) (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H_2)) (=> (not (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 V_v_H_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2 tptp.c_Int_OPls)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2) V_y_2))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) _let_1) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_m) _let_1) (= V_m V_n))))) (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat _let_1 V_n) _let_1))) (forall ((V_P_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2)))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (=> (=> (= V_m_2 V_n_2) _let_1) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) _let_1) _let_1))))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m))))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_n) V_k))) (forall ((V_t $$unsorted) (V_s $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_s V_t) (not (= V_s V_t)))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m) (not (= V_m V_n)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))) (forall ((V_m $$unsorted) (V_l $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_m))) (let ((_let_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_l))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_2 _let_1))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x _let_2)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_y _let_1))))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m) (= V_m V_n)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_m))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n V_n)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_m) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))))) (forall ((V_n $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_i)) V_i))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_l)))) (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_m)) (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2))) (= _let_34 _let_30) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat _let_19) (tptp.c_Nat_OSuc _let_31)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat tptp.c_Int_OPls) V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat _let_33 _let_33) _let_32) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))) (= _let_31 _let_32) (= _let_32 _let_31) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_3 tptp.c_Transcendental_Opi) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (or (= V_n _let_1) (= V_n (tptp.c_Nat_OSuc _let_1)))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))))) (forall ((V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_29 _let_3) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Ominus__class_Ominus T_a V_c V_d))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_n _let_1)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_m $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_m))))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (not (= V_n_2 _let_1)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2)))) (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2))) (forall ((V_n_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 _let_1) (= V_n_2 _let_1)))) (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_m_2) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2 V_n_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_c V_a) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a V_c) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_b V_c))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n) (=> (not (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2) (not (= V_m_2 V_n_2))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_17 _let_29) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (or (= V_x _let_1) (= V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_24 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint _let_2)) (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) B_K)))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))) (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) B_K)))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_N)))))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_n)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_n))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_n))))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_24 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint _let_19)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex tptp.v_w____) tptp.v_r) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal _let_28 tptp.v_r) (= _let_27 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_27)))) (forall ((V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z) tptp.v_r) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) V_z))))) (forall ((V_x_2 $$unsorted) (V_z_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z_2) tptp.v_r) (=> (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) V_z_2)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (forall ((B_y $$unsorted)) (= (exists ((B_x $$unsorted)) (and (exists ((B_z $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z) tptp.v_r) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) B_z)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal B_x)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_y B_x))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_y tptp.v_s____))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n) V_m)) (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_n) V_m)) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z) (= V_z V_w)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_j V_k) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i V_k)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_z))) (forall ((V_w $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w V_w)) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x V_z)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (= V_m_2 V_n_2))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_k) V_j))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_24 _let_24) (forall ((V_fa_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_fa_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m B_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_fa_2 B_m) (tptp.hAPP V_fa_2 B_n)))))) (forall ((V_n_2 $$unsorted) (V_fa_2 $$unsorted)) (=> (tptp.c_SEQ_Osubseq V_fa_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2 (tptp.hAPP V_fa_2 V_n_2)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (let ((_let_2 (tptp.c_Nat_OSuc _let_1))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Nat_OSuc _let_2)) (or (= V_x _let_1) (= V_x _let_2)))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_24 _let_25) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y)))))) (forall ((V_fa_2 $$unsorted)) (= (tptp.c_SEQ_Osubseq V_fa_2) (forall ((B_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP V_fa_2 B_n) (tptp.hAPP V_fa_2 (tptp.c_Nat_OSuc B_n)))))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_24 _let_23) (forall ((V_n_2 $$unsorted)) (exists ((B_z $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z) tptp.v_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) B_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n_2)))))))) (exists ((B_f $$unsorted)) (forall ((B_x $$unsorted)) (let ((_let_1 (tptp.hAPP B_f B_x))) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex _let_1) tptp.v_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) _let_1)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_x))))))))) (forall ((B_n $$unsorted)) (exists ((B_z $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z) tptp.v_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) B_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Nat_OSuc B_n)))))))) (forall ((V_y_2 $$unsorted)) (= (exists ((B_z $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z) tptp.v_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) B_z)))) V_y_2))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____) V_y_2))) (forall ((V_y_2 $$unsorted)) (= (exists ((B_z $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z) tptp.v_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) B_z)) V_y_2))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____) V_y_2))) (= (exists ((B_z $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z) tptp.v_r) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) B_z)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.v_s____)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_4 _let_4)) (exists ((B_z $$unsorted)) (forall ((B_x $$unsorted)) (=> (exists ((B_za $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_za) tptp.v_r) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p) B_za)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal B_x)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_x B_z)))) (=> (not _let_22) (exists ((B_z $$unsorted)) (forall ((B_w $$unsorted)) (let ((_let_1 (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_w) tptp.v_r) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 B_z)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP _let_1 B_w)))))))) (forall ((V_a $$unsorted) (V_b $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_b V_a)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_b)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_a))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_x V_y) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_x (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Complex_Ocomplex V_y)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_x))) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) _let_1))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_y_2))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) (forall ((V_y $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Transcendental_Oarctan V_y))) (= (tptp.c_Transcendental_Oarctan _let_17) _let_17) (forall ((V_za_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.c_Int_Oiszero T_a V_za_2) (= V_za_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (tptp.c_Int_Oiszero T_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (not (tptp.c_Int_Oiszero T_a (tptp.c_Groups_Oone__class_Oone T_a))))) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Oarctan (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oarctan V_x)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oarctan V_x) (tptp.c_Transcendental_Oarctan V_y)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oarctan V_x) (tptp.c_Transcendental_Oarctan V_y)))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (not (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 V_w)))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)))) (forall ((V_wb_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (= (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_wb_2))) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))))) (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (not (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_y_2))))))) (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_y_2))))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Int_Oiszero T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint tptp.c_Int_OPls))))))) (forall ((V_y $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oarctan V_y) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= (tptp.c_Transcendental_Oarctan _let_18) _let_21) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (let ((_let_2 (tptp.c_Transcendental_Oarctan V_y))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) _let_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_2 _let_1))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x _let_1) (= (tptp.c_Transcendental_Oarctan (tptp.c_Transcendental_Otan V_x)) V_x))))) (forall ((V_y $$unsorted)) (let ((_let_1 (tptp.c_Transcendental_Oarctan V_y))) (let ((_let_2 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_2) _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 _let_2) (= (tptp.c_Transcendental_Otan _let_1) V_y))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Otan V_x) _let_1))))) (forall ((V_y $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_Transcendental_Oarctan V_y)) V_y)) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Otan V_x)))) (= (tptp.c_Transcendental_Otan _let_17) _let_17) (= (tptp.c_Transcendental_Otan tptp.c_Transcendental_Opi) _let_17) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi)) (tptp.c_Transcendental_Otan V_x))) (= (tptp.c_Transcendental_Otan _let_21) _let_18) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.c_Transcendental_Otan V_x)))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) V_y) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Otan V_y) (tptp.c_Transcendental_Otan V_x))))))) (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (let ((_let_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_2 V_y_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y_2 _let_1) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_2 V_x_2) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 _let_1) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y_2 V_x_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Otan V_y_2) (tptp.c_Transcendental_Otan V_x_2)))))))))) (forall ((V_y $$unsorted)) (= (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Otan V_y)) (tptp.c_Transcendental_Otan (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_y)))) (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (exists ((B_z $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) B_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_z _let_1) (= (tptp.c_Transcendental_Otan B_z) V_x)))))) (forall ((V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (exists ((B_x $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_x (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.c_Transcendental_Otan B_x) V_y))))) (forall ((V_y $$unsorted)) (exists ((B_x $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) B_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_x _let_1) (= (tptp.c_Transcendental_Otan B_x) V_y))))) (forall ((V_y $$unsorted)) (exists ((B_x $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) B_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_x _let_1) (= (tptp.c_Transcendental_Otan B_x) V_y) (forall ((B_y $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) B_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_y _let_1) (= (tptp.c_Transcendental_Otan B_y) V_y)) (= B_y B_x)))))))) (forall ((V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (exists ((B_x $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal B_x (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_y (tptp.c_Transcendental_Otan B_x)))))) (= _let_21 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal _let_20 (tptp.c_Transcendental_Oarctan (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal _let_18 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit1 _let_2))))) (tptp.c_Transcendental_Oarctan (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal _let_18 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 _let_19))))))))))) (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (let ((_let_2 (tptp.c_Groups_Oabs__class_Oabs T_a V_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a _let_2 _let_1) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_d)))))))) (forall ((V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x_2 V_x_2))) (= V_x_2 _let_1)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x_2 V_za_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_y_2 V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2)))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x V_y)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z V_x) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b))))) (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_xa (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_xa V_x))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b) (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_b_2)) (or (= V_a_2 V_b_2) (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b_2)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y)) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_e) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_e) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_e) V_c)))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_ya) (tptp.c_Groups_Otimes__class_Otimes T_a V_y V_ya))))) (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_a_H) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) (tptp.c_Groups_Otimes__class_Otimes T_a V_a_H V_b))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_xa (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_xa V_x) (tptp.c_Groups_Otimes__class_Otimes T_a V_xa V_y))))) (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_b_H)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b_H))))) (forall ((V_za_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (V_wb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_wb_2 V_y_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2 V_za_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_wb_2 V_za_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2 V_y_2))) (or (= V_wb_2 V_x_2) (= V_y_2 V_za_2))))) (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_m) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_m)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_m)))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c))))) (forall ((V_da_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (and (not (= V_a_2 V_b_2)) (not (= V_c_2 V_da_2))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_da_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_da_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_c_2))))))) (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_x (tptp.c_Groups_Oplus__class_Oplus T_a V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y) (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_z))))) (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y) V_ya) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_ya) (tptp.c_Groups_Otimes__class_Otimes T_a V_y V_ya))))) (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a_H) V_b) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) (tptp.c_Groups_Otimes__class_Otimes T_a V_a_H V_b))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_xa (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_xa V_x) (tptp.c_Groups_Otimes__class_Otimes T_a V_xa V_y))))) (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_b_H)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b_H))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) V_a))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) V_c)))) (forall ((V_w $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a V_z V_w)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_z) (tptp.c_Groups_Otimes__class_Otimes T_a V_y V_w))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oabs__class_Oabs T_a V_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 _let_1) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_z) V_z)) (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_r V_a) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_r V_r)) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_a V_r))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z1 V_z2) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z1 V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z2 V_w)))) (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_z)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w)) V_z)))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w))))) (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))) (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_x) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y)) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_w V_z))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c))))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z1 V_z2) V_z3) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_z2 V_z3)))) (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_y) V_s) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y)) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_r V_s)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_a)))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_lx (tptp.c_Groups_Otimes__class_Otimes T_a V_rx V_ry)) (tptp.c_Groups_Otimes__class_Otimes T_a V_rx (tptp.c_Groups_Otimes__class_Otimes T_a V_lx V_ry))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_lx (tptp.c_Groups_Otimes__class_Otimes T_a V_rx V_ry)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_lx V_rx) V_ry)))) (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_lx V_ly) V_rx) (tptp.c_Groups_Otimes__class_Otimes T_a V_lx (tptp.c_Groups_Otimes__class_Otimes T_a V_ly V_rx))))) (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_lx V_ly) V_rx) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_lx V_rx) V_ly)))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_rx V_ry))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_lx V_ly) _let_1) (tptp.c_Groups_Otimes__class_Otimes T_a V_lx (tptp.c_Groups_Otimes__class_Otimes T_a V_ly _let_1)))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_lx V_ly))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_rx V_ry)) (tptp.c_Groups_Otimes__class_Otimes T_a V_rx (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 V_ry)))))) (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_lx V_ly) (tptp.c_Groups_Otimes__class_Otimes T_a V_rx V_ry)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_lx V_rx) (tptp.c_Groups_Otimes__class_Otimes T_a V_ly V_ry))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_c_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_c_2 V_b_2)) (= V_a_2 V_b_2)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_a_2 V_c_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_b_2 V_c_2)) (= V_a_2 V_b_2)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 V_a) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a _let_1) _let_1)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1) (or (= V_a _let_1) (= V_b _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a _let_1)) (=> (not (= V_b _let_1)) (not (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oring__no__zero__divisors T_a) (= (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_b_2) _let_1) (or (= V_a_2 _let_1) (= V_b_2 _let_1)))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_x _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a _let_1) _let_1)))) (forall ((V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 V_y) _let_1)))) (forall ((V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 V_b) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 V_a) _let_1)))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (= (= (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2 V_x_2) _let_1) (or (= V_x_2 _let_1) (= V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus T_a _let_1))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_x)))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2) V_b_2))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (= V_b_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (= V_b (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c) V_a))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) V_b) (= V_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (= V_c_2 _let_1))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> (not _let_2) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2) V_b_2)) (=> _let_2 (= V_a_2 _let_1)))))))) (forall ((V_a_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (= V_c_2 _let_1))) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (and (=> (not _let_2) (= V_b_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2))) (=> _let_2 (= V_a_2 _let_1)))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b))))) (forall ((V_wb_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y_2 _let_1)) (=> (not (= V_za_2 _let_1)) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_x_2 V_y_2) (tptp.c_Rings_Oinverse__class_Odivide T_a V_wb_2 V_za_2)) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2 V_za_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_wb_2 V_y_2)))))))) (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Oring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Groups_Ominus__class_Ominus T_b V_a V_b) _let_1) (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.c_Groups_Otimes__class_Otimes T_b V_a _let_1) (tptp.c_Groups_Otimes__class_Otimes T_b V_b _let_1)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Oring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 (tptp.c_Groups_Ominus__class_Ominus T_b V_b V_c)) (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 V_b) (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 V_c)))))) (forall ((V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m V_m) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1) V_m))))) (forall ((V_a $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_m)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_m)))) (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_m) V_m) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_m)))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a) V_b))))) (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_da_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) V_e_2) V_c_2) V_da_2)))) (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_da_2)) (= V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_a_2) V_e_2) V_da_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b))) (let ((_let_2 (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a _let_2 _let_1) (tptp.c_Groups_Otimes__class_Otimes T_a _let_2 V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a V_a _let_1))))))) (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b (tptp.c_Groups_Oplus__class_Oplus T_b V_a V_b) _let_1) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.c_Groups_Otimes__class_Otimes T_b V_a _let_1) (tptp.c_Groups_Otimes__class_Otimes T_b V_b _let_1)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_b V_v))) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 (tptp.c_Groups_Oplus__class_Oplus T_b V_b V_c)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 V_b) (tptp.c_Groups_Otimes__class_Otimes T_b _let_1 V_c)))))) (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_m) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_n) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_m V_n))))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2 V_x_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_y_2 V_y_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (=> (not (= V_r (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (= V_a V_b) (not (= V_c V_d))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Otimes__class_Otimes T_a V_r V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b (tptp.c_Groups_Otimes__class_Otimes T_a V_r V_d)))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_c_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_b_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_a) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b)))))) (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 V_a_2))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__comm__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b))) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1))) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_d))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_d))))))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__comm__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_a) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) _let_1)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_b_2) _let_1) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_1))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_a)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x_2 V_x_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_y_2 V_y_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1))))) (forall ((V_x $$unsorted) (V_u $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_u V_u)) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x V_x))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_fa_2 $$unsorted)) (let ((_let_1 (tptp.hAPP V_fa_2 V_a_2))) (let ((_let_2 (tptp.hAPP V_fa_2 V_b_2))) (let ((_let_3 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal _let_2 _let_1) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_b_2 V_a_2)))) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal _let_3 V_a_2)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal _let_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal _let_3 V_b_2))))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_a) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_d))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_d))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_d))))))))) (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_c) (tptp.c_Groups_Otimes__class_Otimes T_a V_b V_d))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 V_a_2))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_a_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_c_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 V_b_2))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2 V_x_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_y_2 V_y_2)) _let_1) (and (= V_x_2 _let_1) (= V_y_2 _let_1)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_x) (tptp.c_Groups_Otimes__class_Otimes T_a V_y V_y))))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x_2 V_x_2) (tptp.c_Groups_Otimes__class_Otimes T_a V_y_2 V_y_2))) (or (not (= V_x_2 _let_1)) (not (= V_y_2 _let_1))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_x) (tptp.c_Groups_Otimes__class_Otimes T_a V_y V_y)) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_y V_x) V_x))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y) V_x))))))) (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_da_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) V_e_2) V_c_2) V_da_2)))) (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_da_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_a_2) V_e_2) V_da_2))))) (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_da_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b_2 V_a_2) V_e_2) V_da_2))))) (forall ((V_da_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_b_2 V_e_2) V_da_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_b_2) V_e_2) V_c_2) V_da_2)))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_3 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_3 V_b_2)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_3)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1)))))))))))) (forall ((V_a_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_3 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_3)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless T_a _let_3 V_b_2)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2)))))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2) V_b_2))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2)))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_y)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_y) V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2) V_b_2))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_x) _let_1) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x _let_1) (tptp.c_Groups_Ominus__class_Ominus T_a V_x _let_1)))))) (forall ((V_w $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y _let_1)) (=> (not (= V_z _let_1)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a V_w V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_z) (tptp.c_Groups_Otimes__class_Otimes T_a V_w V_y)) (tptp.c_Groups_Otimes__class_Otimes T_a V_y V_z)))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_y)) V_z))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_y)) V_y))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_x) V_y) V_z))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_y)) V_y))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Oordered__ring__abs T_a) (=> (and (or (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a _let_1)) (or (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b _let_1))) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_y) V_x) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_y V_x)))))) (forall ((V_wb_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (= _let_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2)) (and (=> (not _let_3) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 _let_2) V_b_2)) (=> _let_3 (= V_a_2 _let_1))))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_wb_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (= V_c_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> (not _let_3) (= (tptp.c_Groups_Otimes__class_Otimes T_a _let_2 V_c_2) V_b_2)) (=> _let_3 (= _let_2 _let_1))))))))) (forall ((V_wb_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (= V_c_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) _let_2) (and (=> (not _let_3) (= V_b_2 (tptp.c_Groups_Otimes__class_Otimes T_a _let_2 V_c_2))) (=> _let_3 (= _let_2 _let_1))))))))) (forall ((V_a_2 $$unsorted) (V_wb_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (= _let_2 _let_1))) (=> (and (tptp.class_Fields_Ofield__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2) V_a_2) (and (=> (not _let_3) (= V_b_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 _let_2))) (=> _let_3 (= V_a_2 _let_1))))))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_x (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_x) V_y) V_z))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_y)) V_z))))) (forall ((V_w $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y _let_1)) (=> (not (= V_z _let_1)) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a V_w V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_z) (tptp.c_Groups_Otimes__class_Otimes T_a V_w V_y)) (tptp.c_Groups_Otimes__class_Otimes T_a V_y V_z)))))))) (forall ((V_h $$unsorted) (V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b) (tptp.c_Groups_Otimes__class_Otimes T_a V_c V_d)) V_h) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d) V_h)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c) V_h) V_d))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls)) V_a) V_a))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_za_2 V_x_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_za_2 V_y_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))) (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x_2 V_za_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_y_2 V_za_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2 V_y_2)))) (forall ((V_z $$unsorted) (V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) V_z) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)) V_z)))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c _let_1) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_c (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y))) (= V_x _let_1))))) (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__1 T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_u V_x) (tptp.c_Groups_Otimes__class_Otimes T_a V_v V_y)) V_a))))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_3 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_3 V_b_2)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_3)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1)))))))))))) (forall ((V_a_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_3 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2))) (let ((_let_4 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (and (=> _let_4 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_3)) (=> (not _let_4) (and (=> _let_2 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_3 V_b_2)) (=> (not _let_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2)))))))))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2) V_b_2))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2)))))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_y)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z))))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_z V_y) V_x) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))) (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2)))))) (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 V_c_2) V_b_2))))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c _let_1) (=> (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b)))))))) (forall ((V_wb_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))))))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_wb_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a _let_2 V_c_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))))))))) (forall ((V_wb_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_2))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 V_c_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_c_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) _let_1) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))))))))))))) (forall ((V_a_2 $$unsorted) (V_wb_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2) V_a_2) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))))))))))) (forall ((V_w $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Oplus__class_Oplus T_a _let_1 _let_1) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_w)))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_c (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))) (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)))))) (forall ((V_n $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) tptp.c_Transcendental_Opi)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n) tptp.c_Transcendental_Opi))) (tptp.c_Transcendental_Otan V_x))) (forall ((V_n $$unsorted) (V_x $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n) tptp.c_Transcendental_Opi))) (tptp.c_Transcendental_Otan V_x))) (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__semiring__1__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_u) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_v) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_u V_x) (tptp.c_Groups_Otimes__class_Otimes T_a V_v V_y)) V_a))))))))) (forall ((V_wb_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2 _let_1))))))))))))) (forall ((V_c_2 $$unsorted) (V_b_2 $$unsorted) (V_wb_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_1))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a _let_2 V_c_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_c_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2)) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 _let_1))))))))))))) (forall ((V_wb_2 $$unsorted) (V_c_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 _let_2))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a _let_1 V_c_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 V_c_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 V_c_2) _let_1) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_2 _let_1))))))))))))) (forall ((V_a_2 $$unsorted) (V_wb_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_wb_2))) (let ((_let_3 (tptp.c_Orderings_Oord__class_Oless T_a _let_2 _let_1))) (let ((_let_4 (tptp.c_Groups_Otimes__class_Otimes T_a V_a_2 _let_2))) (let ((_let_5 (tptp.c_Orderings_Oord__class_Oless T_a _let_1 _let_2))) (=> (and (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (tptp.class_Int_Onumber T_a)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b_2 _let_2) V_a_2) (and (=> _let_5 (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2 _let_4)) (=> (not _let_5) (and (=> _let_3 (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_4 V_b_2)) (=> (not _let_3) (tptp.c_Orderings_Oord__class_Oless__eq T_a _let_1 V_a_2))))))))))))) (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a V_z (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oplus__class_Oplus T_a V_z V_z)))) (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_z) (tptp.c_Groups_Oplus__class_Oplus T_a V_z V_z)))) (forall ((V_za_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (= V_x_2 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_y_2 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal _let_1 V_za_2))) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal _let_1 V_x_2) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_y_2 V_za_2))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal _let_3 tptp.c_Transcendental_Opi)) tptp.c_Transcendental_Opi) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Otan (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) tptp.c_Transcendental_Opi))) (tptp.c_Transcendental_Otan V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) _let_1) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y) _let_1) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oarctan V_x) (tptp.c_Transcendental_Oarctan V_y)) (tptp.c_Transcendental_Oarctan (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal V_x V_y))))))))) (forall ((V_x $$unsorted)) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_Transcendental_Oarctan (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) tptp.c_Transcendental_Opi) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Transcendental_Oarctan V_x))))) (forall ((V_x $$unsorted) (V_n $$unsorted)) (let ((_let_1 (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal _let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal tptp.c_Transcendental_Opi (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal _let_1) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x _let_1) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Ocos V_x)))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat _let_1 V_n_2))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n_2 V_k_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j V_k))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_i) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_j))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_k_2))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) V_w) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z V_w)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_n)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n V_k)))) (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n V_k)))) (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_n)))) (forall ((V_w $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint tptp.c_Int_OPls V_w) tptp.c_Int_OPls)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_k_2))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_n_2)) (= V_m_2 V_n_2)))) (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) V_l) (tptp.c_Int_OBit0 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k V_l)))) (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j V_l))))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_i) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k V_j)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_j V_k)))) (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_m)))) (forall ((V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_m))) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z) V_z)) (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)) (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z1) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z2)))) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1 V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z2 V_w)))) (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_w)))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (= _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2)) (and (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n) V_n)) (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1 V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z2 V_w)))) (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z1) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z2)))) (forall ((V_r $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Groups_Otimes__class_Otimes _let_1 (tptp.c_Groups_Oplus__class_Oplus _let_1 V_p V_q) V_r) (tptp.c_Groups_Oplus__class_Oplus _let_1 (tptp.c_Groups_Otimes__class_Otimes _let_1 V_p V_r) (tptp.c_Groups_Otimes__class_Otimes _let_1 V_q V_r)))))) (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_a V_b)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_b))))) (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Otimes__class_Otimes T_a V_x V_y)) (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x) (tptp.c_Groups_Osgn__class_Osgn T_a V_y))))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_w V_z))) (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1 V_z2) V_z3) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_z2 V_z3)))) (forall ((V_k $$unsorted) (V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H) V_k)))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not _let_2) (= _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_v_H)) V_k))))))) (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)))) (let ((_let_2 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls))) (and (=> _let_2 (= _let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not _let_2) (= _let_1 (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_v V_v_H)))))))) (forall ((V_q $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero _let_1))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Groups_Otimes__class_Otimes _let_1 _let_2 V_q) _let_2))))) (forall ((V_p $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.tc_Polynomial_Opoly T_a))) (let ((_let_2 (tptp.c_Groups_Ozero__class_Ozero _let_1))) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Groups_Otimes__class_Otimes _let_1 V_p _let_2) _let_2))))) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_n) _let_1))) (forall ((V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m _let_1) _let_1))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_n_2) _let_1) (or (= V_m_2 _let_1) (= V_n_2 _let_1))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_k_2 V_n_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_n_2 V_k_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint _let_1 (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_x V_y)))))) (forall ((V_x $$unsorted)) (not (= (tptp.c_Transcendental_Ocos (tptp.c_Transcendental_Oarctan V_x)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)))) (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k V_i) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_k V_j))))) (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (let ((_let_1 (tptp.c_Nat_OSuc V_k_2))) (= (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_m_2) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat _let_1 V_n_2)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2 V_n_2)))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a _let_1) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2) _let_1) (= V_a_2 _let_1))))) (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x_2) _let_1) (= V_x_2 _let_1))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Groups_Osgn__if T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a _let_1) _let_1)))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Osgn__class_Osgn T_a V_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a _let_1) _let_1)))) (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone T_a))) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a _let_1) _let_1)))) (= (tptp.c_Transcendental_Ocos _let_17) _let_18) (forall ((V_x $$unsorted)) (= (tptp.c_Transcendental_Ocos (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_RealDef_Oreal V_x)) (tptp.c_Transcendental_Ocos V_x))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)) (or (= V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (let ((_let_1 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (=> (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint V_m V_n)) _let_1) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_m) _let_1)))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a _let_1 (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a _let_1 V_a_2))))) (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (let ((_let_1 (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_a_2) _let_1) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 _let_1))))) (forall ((V_x $$unsorted)) (= (tptp.c_Groups_Osgn__class_Osgn tptp.tc_RealDef_Oreal V_x) (tptp.c_Rings_Oinverse__class_Odivide tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))) (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Otimes__class_Otimes T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x) (tptp.c_Groups_Oabs__class_Oabs T_a V_x)) V_x))) (forall ((V_k $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_k) (tptp.c_Groups_Otimes__class_Otimes T_a V_k (tptp.c_Groups_Osgn__class_Osgn T_a V_k))))) (= (tptp.c_RComplete_Onatceiling _let_17) _let_16) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) (tptp.c_RComplete_Onatceiling V_y)))) (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)))) (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_n))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x tptp.c_Transcendental_Opi) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Ocos V_x) (tptp.c_Transcendental_Ocos V_y)))))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))) (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Int_Oint) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint) (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_Int_Oint) (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__semiring tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__ring__abs tptp.tc_Int_Oint) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint) (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint) (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint) (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint) (tptp.class_Rings_Oordered__ring tptp.tc_Int_Oint) (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint) (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Int_Oint) (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint) (tptp.class_Rings_Osemiring__1 tptp.tc_Int_Oint) (tptp.class_Groups_Ogroup__add tptp.tc_Int_Oint) (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint) (tptp.class_Rings_Ocomm__ring tptp.tc_Int_Oint) (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint) (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint) (tptp.class_Rings_Osemiring tptp.tc_Int_Oint) (tptp.class_Groups_Osgn__if tptp.tc_Int_Oint) (tptp.class_Groups_Oabs__if tptp.tc_Int_Oint) (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint) (tptp.class_Groups_Ozero tptp.tc_Int_Oint) (tptp.class_Rings_Oring tptp.tc_Int_Oint) (tptp.class_Rings_Oidom tptp.tc_Int_Oint) (tptp.class_Int_Onumber tptp.tc_Int_Oint) (tptp.class_Groups_Oone tptp.tc_Int_Oint) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Nat_Onat) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat) (tptp.class_Rings_Oordered__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Nat_Onat) (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat) (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat) (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat) (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat) (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring__1 tptp.tc_Nat_Onat) (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat) (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat) (tptp.class_Groups_Ozero tptp.tc_Nat_Onat) (tptp.class_Int_Onumber tptp.tc_Nat_Onat) (tptp.class_Groups_Oone tptp.tc_Nat_Onat) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Fields_Olinordered__field__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__field tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__comm__semiring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Fields_Ofield__inverse__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal) (tptp.class_Fields_Olinordered__field tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__ring__abs tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__field tptp.tc_RealDef_Oreal) (tptp.class_Rings_Odivision__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal) (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring__1 tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal) (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Ocomm__ring tptp.tc_RealDef_Oreal) (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal) (tptp.class_Groups_Osgn__if tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oabs__if tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal) (tptp.class_Fields_Ofield tptp.tc_RealDef_Oreal) (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal) (tptp.class_Rings_Oidom tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber tptp.tc_RealDef_Oreal) (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex) _let_15 (tptp.class_RealVector_Oreal__normed__field tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Fields_Ofield__inverse__zero tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oab__semigroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__field tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__semiring tptp.tc_Complex_Ocomplex) _let_14 (tptp.class_Rings_Ozero__neq__one tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Omonoid__mult tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Omonoid__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ogroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Ocomm__ring tptp.tc_Complex_Ocomplex) (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Osemiring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Fields_Ofield tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oring tptp.tc_Complex_Ocomplex) (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber tptp.tc_Complex_Ocomplex) (tptp.class_Groups_Oone tptp.tc_Complex_Ocomplex) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__1__strict (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add__abs (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Olinordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__1__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__cancel__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__comm__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semidom (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Groups_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__ring__abs (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__idom (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__ring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Osemiring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Ogroup__add (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Omult__zero (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Int_Oring__char__0 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Int_Onumber__ring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Osgn__if (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oabs__if (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Oring__1 (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ozero T_1) (tptp.class_Groups_Ozero (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Oring (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oidom (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Int_Onumber (tptp.tc_Polynomial_Opoly T_1)))) (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Oone (tptp.tc_Polynomial_Opoly T_1)))) _let_13 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.34/1.54  )
% 1.34/1.54  % SZS output end Proof for SWW222+1
% 1.34/1.54  % cvc5---1.0.5 exiting
% 1.34/1.54  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------