%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : ALG373-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 16:09:25 EDT 2023

% Result   : Unsatisfiable 23.82s 24.02s
% Output   : Proof 23.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16  % Problem    : ALG373-1 : TPTP v8.1.2. Released v4.1.0.
% 0.18/0.18  % Command    : do_cvc5 %s %d
% 0.18/0.39  % Computer : n019.cluster.edu
% 0.18/0.39  % Model    : x86_64 x86_64
% 0.18/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39  % Memory   : 8042.1875MB
% 0.18/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39  % CPULimit   : 300
% 0.18/0.39  % WCLimit    : 300
% 0.18/0.39  % DateTime   : Mon Aug 28 05:56:13 EDT 2023
% 0.18/0.39  % CPUTime    : 
% 0.26/0.56  %----Proving TF0_NAR, FOF, or CNF
% 0.26/0.57  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.KEzWWMS5yY/cvc5---1.0.5_31381.p...
% 0.26/0.64  ------- get file name : TPTP file name is ALG373-1
% 0.26/0.65  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31381.smt2...
% 0.26/0.65  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.57/10.74  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.57/15.79  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.63/20.84  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 23.82/24.02  % SZS status Unsatisfiable for ALG373-1
% 23.82/24.02  % SZS output start Proof for ALG373-1
% 23.82/24.02  (
% 23.82/24.02  (let ((_let_1 (forall ((V_xb $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless (tptp.v_x V_xb) V_xb tptp.tc_RealDef_Oreal))))) (let ((_let_2 (forall ((V_xb $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_p (tptp.v_xa V_xb) tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.v_x V_xb) tptp.tc_RealDef_Oreal))))) (let ((_let_3 (forall ((V_xb $$unsorted)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.v_xa V_xb) tptp.tc_Complex_Ocomplex) tptp.v_r tptp.tc_RealDef_Oreal)))) (let ((_let_4 (forall ((V_z $$unsorted) (V_x $$unsorted)) (or (not (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_p V_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal))) (not (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm V_z tptp.tc_Complex_Ocomplex) tptp.v_r tptp.tc_RealDef_Oreal)) (tptp.c_HOL_Oord__class_Oless V_x (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))))) (let ((_let_5 (tptp.v_sko__local__Xmth1__2 tptp.v_p tptp.v_r))) (let ((_let_6 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (let ((_let_7 (tptp.c_HOL_Oone__class_Oone tptp.tc_RealDef_Oreal))) (let ((_let_8 (tptp.v_x _let_7))) (let ((_let_9 (tptp.c_HOL_Oord__class_Oless _let_8 _let_7 tptp.tc_RealDef_Oreal))) (let ((_let_10 (tptp.v_xa _let_7))) (let ((_let_11 (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm _let_10 tptp.tc_Complex_Ocomplex) tptp.v_r tptp.tc_RealDef_Oreal))) (let ((_let_12 (not _let_11))) (let ((_let_13 (= (tptp.c_HOL_Ouminus__class_Ouminus _let_8 tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_p _let_10 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex)))) (let ((_let_14 (not _let_13))) (let ((_let_15 (or _let_14 _let_12 _let_9))) (let ((_let_16 (_let_4))) (let ((_let_17 (ASSUME :args _let_16))) (let ((_let_18 (not _let_15))) (let ((_let_19 (_let_3))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 (_let_2))) (let ((_let_22 (ASSUME :args _let_21))) (let ((_let_23 (_let_7 QUANTIFIERS_INST_FMF_FMC_EXH))) (let ((_let_24 (_let_1))) (let ((_let_25 (ASSUME :args _let_24))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_17 :args (_let_10 _let_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_16))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_15)) :args ((or _let_9 _let_14 _let_12 _let_18))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args _let_23) :args _let_24)) _let_25 :args ((not _let_9) false _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_22 :args _let_23) :args _let_21))) _let_22 :args (_let_13 false _let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (_let_7 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_19)) _let_20 :args (_let_11 false _let_3)) :args (_let_18 true _let_9 false _let_13 false _let_11)) _let_17 :args (false true _let_15 false _let_4)) :args ((forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_vskULt $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 V_vskULt V_r T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_vskULn $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 V_vskULn T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_vskULp $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 V_vskULp T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_vskULu $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1 V_vskULu V_r T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_v $$unsorted) (V_w $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (tptp.c_lessequals _let_1 _let_2 T_a) (tptp.c_HOL_Oord__class_Oless _let_2 _let_1 T_a))))) (forall ((T_a $$unsorted) (V_w $$unsorted) (V_v $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_w T_a))) (let ((_let_2 (tptp.c_Int_Onumber__class_Onumber__of V_v T_a))) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_Int_Onumber T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 _let_2 T_a)) (not (tptp.c_lessequals _let_2 _let_1 T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Int_Oring__char__0 T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (not (= (tptp.c_Int_Onumber__class_Onumber__of V_x T_a) (tptp.c_Int_Onumber__class_Onumber__of V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_x T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (not (= (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_RealVector_Oof__real V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (= (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_a _let_1) (= V_b _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ono__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1)) (= V_b _let_1) (= V_a _let_1)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_x tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a))))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_ly V_ry T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes _let_1 V_ry T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= V_a _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a)) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_K $$unsorted) (V_vskULu $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1 V_vskULu V_r T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_K $$unsorted) (V_vskULt $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 V_vskULt V_r T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_K $$unsorted) (V_vskULm $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1 V_vskULm V_r T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_K $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_K V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_K $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_vskULp $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) (tptp.c_RealVector_Onorm__class_Onorm V_b T_a) tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 V_vskULp T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_K $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_K $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_K V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_vskULn $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) (tptp.c_RealVector_Onorm__class_Onorm V_b T_a) tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 V_vskULn T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_K $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_K T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 V_x T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_K $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_K V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_K T_a) (tptp.c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1 V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_vskULj $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_a T_a) (tptp.c_RealVector_Onorm__class_Onorm V_b T_a) tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1 V_vskULj T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_Int_Onumber__class_Onumber__of V_x T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (not (tptp.class_Int_Onumber__ring T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Olordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_b T_a) T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (let ((_let_2 (tptp.c_HOL_Oabs__class_Oabs V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_2 T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_d T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless _let_2 V_d T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a)))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a)))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes V_z V_w tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_w V_z tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Oof__real V_r T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_RealVector_OscaleR__class_OscaleR V_b V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Otimes__class_Otimes V_a V_b tptp.tc_RealDef_Oreal) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_b T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not 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(tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a)) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a)) (= V_a (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oring T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oidom T_a)) (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_b T_a))) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a))) (= _let_1 V_a)))) (forall ((V_x $$unsorted) (V_r $$unsorted)) (or (tptp.c_lessequals V_x V_r tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) V_r tptp.tc_RealDef_Oreal)))) (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_z V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_z V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_z V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_z V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_z tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_x V_z tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_y V_z tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_s $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_r V_s tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) V_s tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) V_r tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) tptp.tc_RealDef_Oreal) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) tptp.tc_RealDef_Oreal)))) (forall ((V_r $$unsorted)) (or (= (tptp.c_HOL_Oabs__class_Oabs V_r tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ouminus__class_Ouminus V_r tptp.tc_RealDef_Oreal)) (not (tptp.c_HOL_Oord__class_Oless V_r (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_RealVector_Onorm__class_Onorm V_a T_a))) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 tptp.tc_RealDef_Oreal) _let_1)))) (forall ((V_x $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs (tptp.c_Complex_ORe V_x) tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm V_x tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Oordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a))) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 V_b T_a) (tptp.c_lessequals V_b _let_1 T_a) (not (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__semiring__strict T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_HOL_Oord__class_Oless V_b _let_1 T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono1 T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Omult__mono T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__idem__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x T_a) V_x))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (not (= (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_HOL_Ozero__class_Ozero T_a))) (= V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Otimes__class_Otimes V_x V_y tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Oof__real V_x T_a) (tptp.c_RealVector_Oof__real V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__ring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_OrderedGroup_Oab__semigroup__mult T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ly T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_ly $$unsorted) (V_rx $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a) (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_ly V_rx T_a) T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ry T_a)))) (forall ((T_a $$unsorted) (V_lx $$unsorted) (V_rx $$unsorted) (V_ry $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_lx (tptp.c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes V_rx (tptp.c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a)))) (forall ((V_z1 $$unsorted) (V_z2 $$unsorted) (V_z3 $$unsorted)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_z1 V_z2 tptp.tc_RealDef_Oreal) V_z3 tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_z1 (tptp.c_HOL_Otimes__class_Otimes V_z2 V_z3 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (V_z $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) V_z T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_a _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals V_b _let_1 T_a) (tptp.c_lessequals _let_1 V_b T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_d $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) (not (tptp.c_lessequals _let_1 V_c T_a)) (not (tptp.c_lessequals _let_1 V_a T_a)) (not (tptp.c_lessequals V_c V_d T_a)) (not (tptp.c_lessequals V_a V_b T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a))))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c _let_1 T_a) (tptp.c_HOL_Oord__class_Oless _let_1 V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a))))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_y V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (= V_x (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_y V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (= V_y (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((V_p $$unsorted) (V_r $$unsorted)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 V_p V_r) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_b T_a)) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Opordered__cancel__semiring T_a)) (tptp.c_lessequals (tptp.c_HOL_Otimes__class_Otimes V_b V_a T_a) _let_1 T_a) (not (tptp.c_lessequals V_b _let_1 T_a)) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1 T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (not (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) _let_1)) (= V_x _let_1) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_a T_a) V_b T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) V_y T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_b T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_xa $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_xa (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) V_y T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_y T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_a tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) tptp.tc_RealDef_Oreal)))) (forall ((V_x $$unsorted) (V_c $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= V_x _let_1) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_c (tptp.c_HOL_Oabs__class_Oabs V_y tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_c _let_1 tptp.tc_RealDef_Oreal))))) (forall ((T_a $$unsorted) (V_r $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_RealVector_Oof__real V_r T_a) T_a) (tptp.c_HOL_Oabs__class_Oabs V_r tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a) (= V_a _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_b T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a (tptp.c_RealVector_OscaleR__class_OscaleR V_b V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_b (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_ra $$unsorted) (V_r $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_ra (tptp.c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_r (tptp.c_RealVector_OscaleR__class_OscaleR V_ra V_x T_a) T_a)))) (not (tptp.c_HOL_Oord__class_Oless _let_6 (tptp.c_HOL_Otimes__class_Otimes _let_6 _let_6 tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__div__algebra T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a) (tptp.c_HOL_Otimes__class_Otimes (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) tptp.tc_RealDef_Oreal)))) (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_c V_a tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_c V_b tptp.tc_RealDef_Oreal))) (= V_c (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_a V_b))) (forall ((V_a $$unsorted) (V_c $$unsorted) (V_b $$unsorted)) (or (not (= (tptp.c_HOL_Otimes__class_Otimes V_a V_c tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_b V_c tptp.tc_RealDef_Oreal))) (= V_c (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Oabs__class_Oabs V_a T_a))) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 _let_1 T_a) (tptp.c_HOL_Otimes__class_Otimes V_a V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_y T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__normed__algebra T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_x _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_x T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_a T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Omult__zero T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes _let_1 V_b T_a) _let_1)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_Ring__and__Field_Oring__no__zero__divisors T_a)) (= (tptp.c_HOL_Otimes__class_Otimes V_a _let_1 T_a) _let_1)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (= (tptp.c_HOL_Otimes__class_Otimes (tptp.c_HOL_Oabs__class_Oabs V_y T_a) V_x T_a) (tptp.c_HOL_Oabs__class_Oabs (tptp.c_HOL_Otimes__class_Otimes V_y V_x T_a) T_a)) (not (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Oabs__class_Oabs V_a T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((V_r $$unsorted)) (or (= (tptp.c_HOL_Oabs__class_Oabs V_r tptp.tc_RealDef_Oreal) V_r) (tptp.c_HOL_Oord__class_Oless V_r (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.class_OrderedGroup_Olordered__ab__group__add__abs T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oabs__if T_a)) (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_a) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (= (tptp.c_HOL_Oabs__class_Oabs V_a T_a) _let_1)) (= V_a _let_1)))) (forall ((T_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (not (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Oabs__class_Oabs _let_1 T_a) T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR _let_1 V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR _let_1 V_y T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a _let_1 T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_b _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (not (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_HOL_Otimes__class_Otimes V_c (tptp.c_RealVector_Onorm__class_Onorm V_y T_a) tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_c (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (not (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_y T_a))) (= V_a (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (not (= (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) (tptp.c_RealVector_OscaleR__class_OscaleR V_b V_x T_a))) (= V_x (tptp.c_HOL_Ozero__class_Ozero T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_c V_a T_a) (tptp.c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) V_c T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((T_a $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__ring__strict T_a)) (tptp.c_HOL_Oord__class_Oless V_c (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Otimes__class_Otimes V_a V_c T_a) (tptp.c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (or (= V_x _let_1) (tptp.c_HOL_Oord__class_Oless _let_1 (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_HOL_Oabs__class_Oabs V_a T_a) T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Olordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ozero__class_Ozero T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a _let_1 T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a _let_1 T_a) (not (tptp.c_lessequals _let_1 (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add__abs T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a) (not (tptp.c_lessequals _let_1 V_a T_a))))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero T_a))) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals _let_1 V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) _let_1 T_a))))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_RealVector_Onorm__class_Onorm V_x T_a) (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_Oof__real V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__algebra__1 T_a)) (= (tptp.c_RealVector_Oof__real (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_Oof__real V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ouminus__class_Ouminus V_a tptp.tc_RealDef_Oreal) V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_xa $$unsorted)) (or (not (tptp.class_RealVector_Oreal__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ouminus__class_Ouminus V_x tptp.tc_RealDef_Oreal) V_xa T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_x V_xa T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_OscaleR__class_OscaleR (tptp.c_HOL_Ouminus__class_Ouminus V_a tptp.tc_RealDef_Oreal) V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a)))) (forall ((V_x $$unsorted) (V_r $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) V_r tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_x V_r tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_r tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal)))) (forall ((V_r $$unsorted) (V_x $$unsorted)) (or (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_r tptp.tc_RealDef_Oreal) V_x tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_HOL_Oabs__class_Oabs V_x tptp.tc_RealDef_Oreal) V_r tptp.tc_RealDef_Oreal)))) (forall ((V_u $$unsorted) (V_x $$unsorted)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Otimes__class_Otimes V_u V_u tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal) (tptp.c_HOL_Otimes__class_Otimes V_x V_x tptp.tc_RealDef_Oreal) tptp.tc_RealDef_Oreal)) (forall ((V_x $$unsorted)) (tptp.c_lessequals (tptp.c_Complex_ORe V_x) (tptp.c_RealVector_Onorm__class_Onorm V_x tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal)) (forall ((T_a $$unsorted) (V_p $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Ocomm__ring T_a)) (= (tptp.c_Polynomial_Opoly (tptp.c_HOL_Ouminus__class_Ouminus V_p (tptp.tc_Polynomial_Opoly T_a)) V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_Polynomial_Opoly V_p V_x T_a) T_a)))) (tptp.c_lessequals _let_6 tptp.v_r tptp.tc_RealDef_Oreal) (forall ((V_w $$unsorted)) (or (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_p (tptp.v_sko__unknown__thm__rW8__1 tptp.v_p tptp.v_r) tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_p V_w tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm V_w tptp.tc_Complex_Ocomplex) tptp.v_r tptp.tc_RealDef_Oreal)) (tptp.c_lessequals (tptp.c_HOL_Ozero__class_Ozero tptp.tc_RealDef_Oreal) tptp.v_r tptp.tc_RealDef_Oreal))) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly tptp.v_p _let_5 tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.c_HOL_Ouminus__class_Ouminus (tptp.v_sko__local__Xmth1__1 tptp.v_p tptp.v_r) tptp.tc_RealDef_Oreal)) (forall ((V_p $$unsorted) (V_z $$unsorted) (V_r $$unsorted)) (or (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_Polynomial_Opoly V_p V_z tptp.tc_Complex_Ocomplex) tptp.tc_Complex_Ocomplex) (tptp.v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 V_p V_r) tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm V_z tptp.tc_Complex_Ocomplex) V_r tptp.tc_RealDef_Oreal)))) (tptp.c_lessequals (tptp.c_RealVector_Onorm__class_Onorm _let_5 tptp.tc_Complex_Ocomplex) tptp.v_r tptp.tc_RealDef_Oreal) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.c_lessequals V_w V_z tptp.tc_RealDef_Oreal) (tptp.c_lessequals V_z V_w tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_lessequals V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_lessequals V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_w $$unsorted)) (tptp.c_lessequals V_w V_w tptp.tc_RealDef_Oreal)) (forall ((V_i $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (or (tptp.c_lessequals V_i V_k tptp.tc_RealDef_Oreal) (not (tptp.c_lessequals V_j V_k tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_i V_j tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal) (not (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_lessequals V_x V_y T_a) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_RealVector_Oreal__normed__vector T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) (tptp.c_RealVector_Onorm__class_Onorm V_x T_a)))) (forall ((V_x $$unsorted)) (let ((_let_1 (tptp.c_RealVector_Onorm__class_Onorm V_x tptp.tc_Complex_Ocomplex))) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus _let_1 tptp.tc_RealDef_Oreal) _let_1 tptp.tc_RealDef_Oreal))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (= V_a V_b) (not (tptp.c_lessequals V_b V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_b V_a T_a) (not (tptp.c_lessequals V_b V_a T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_lessequals V_a V_b T_a)) (= V_a V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (= V_a V_b) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((V_x $$unsorted) (V_y $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_RealDef_Oreal) (= V_x V_y) (not (tptp.c_lessequals V_x V_y tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (= V_x V_y) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_lessequals V_x V_y T_a)))) (forall ((V_z $$unsorted) (V_w $$unsorted)) (or (= V_z V_w) (not (tptp.c_lessequals V_w V_z tptp.tc_RealDef_Oreal)) (not (tptp.c_lessequals V_z V_w tptp.tc_RealDef_Oreal)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_y T_a))) (= V_x V_y))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (not (= (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a))) (= V_a V_b))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_lessequals V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_lessequals V_y V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_x T_a) (tptp.c_lessequals V_x V_x T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_lessequals V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_lessequals V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_lessequals V_x V_y T_a))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_lessequals V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) V_b))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_a (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= V_b (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Lattices_Oboolean__algebra T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_x T_a) T_a) V_x))) (forall ((T_a $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Ogroup__add T_a)) (= (tptp.c_HOL_Ouminus__class_Ouminus (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) V_a))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_HOL_Oord__class_Oless V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a) (not (tptp.c_lessequals (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) (not (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_OrderedGroup_Opordered__ab__group__add T_a)) (tptp.c_lessequals V_b (tptp.c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) (not (tptp.c_lessequals V_a (tptp.c_HOL_Ouminus__class_Ouminus V_b T_a) T_a)))) _let_4 _let_3 _let_2 _let_1 (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Oab__group__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__semiring__0 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__group__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__ring__1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add__abs tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add__abs tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__ring__strict tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oordered__ab__group__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__ring__abs tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Opordered__ring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Olordered__ring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_Int_Oint) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oabs__if tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oring tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oidom tptp.tc_Int_Oint) (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint) (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint) (tptp.class_Orderings_Oorder tptp.tc_Int_Oint) (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint) (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint) (tptp.class_Int_Onumber tptp.tc_Int_Oint) (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__cancel__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semiring__strict tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__group__add__abs tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Olordered__ab__group__add__abs tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__ring__strict tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Opordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Olordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oordered__ab__group__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__ring__abs tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__semiring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Opordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Olordered__ring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oordered__idom tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Omult__mono1 tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__algebra__1 tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Omult__mono tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__algebra tptp.tc_RealDef_Oreal) (tptp.class_RealVector_Oreal__vector tptp.tc_RealDef_Oreal) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oabs__if tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oidom tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal) (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal) (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal) (tptp.class_Int_Onumber tptp.tc_RealDef_Oreal) (tptp.class_Ring__and__Field_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ono__zero__divisors tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Oab__semigroup__mult tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__algebra__1 tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Omult__zero tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Ocomm__ring tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__algebra tptp.tc_Complex_Ocomplex) (tptp.class_RealVector_Oreal__vector tptp.tc_Complex_Ocomplex) (tptp.class_OrderedGroup_Ogroup__add tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oring tptp.tc_Complex_Ocomplex) (tptp.class_Ring__and__Field_Oidom tptp.tc_Complex_Ocomplex) (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex) (tptp.class_Int_Onumber tptp.tc_Complex_Ocomplex) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__cancel__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__group__add__abs (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Opordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__ring__abs (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__semiring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Opordered__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oordered__idom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__mono1 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__zero (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__semiring__0 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Omult__mono (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_OrderedGroup_Ogroup__add (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_OrderedGroup_Oab__group__add T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oabs__if (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Ring__and__Field_Oidom (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oidom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Opreorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Orderings_Oorder (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Int_Oring__char__0 (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Oordered__idom T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Int_Onumber__ring (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1)))) (forall ((T_1 $$unsorted)) (or (tptp.class_Int_Onumber (tptp.tc_Polynomial_Opoly T_1)) (not (tptp.class_Ring__and__Field_Ocomm__ring__1 T_1))))))))))))))))))))))))))))))))
% 23.82/24.02  )
% 23.82/24.03  % SZS output end Proof for ALG373-1
% 23.82/24.03  % cvc5---1.0.5 exiting
% 23.82/24.03  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------