TSTP Solution File: ALG383-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG383-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n031.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 16:43:08 EDT 2023
% Result : Unsatisfiable 150.04s 19.53s
% Output : Proof 150.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ALG383-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 04:31:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 150.04/19.53 Command-line arguments: --flatten
% 150.04/19.53
% 150.04/19.53 % SZS status Unsatisfiable
% 150.04/19.53
% 150.04/19.54 % SZS output start Proof
% 150.04/19.54 Take the following subset of the input axioms:
% 150.04/19.55 fof(cls_conjecture_0, negated_conjecture, ~c_lessequals(v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)).
% 150.04/19.55 fof(cls_order__trans_0, axiom, ![T_a, V_x, V_y, V_z]: (~class_Orderings_Opreorder(T_a) | (c_lessequals(V_x, V_z, T_a) | (~c_lessequals(V_y, V_z, T_a) | ~c_lessequals(V_x, V_y, T_a))))).
% 150.04/19.55 fof(cls_th1_0, axiom, c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 150.04/19.55 fof(cls_th2_0, axiom, c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)).
% 150.04/19.55 fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)).
% 150.04/19.55 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 150.04/19.55 fof(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs, axiom, class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)).
% 150.04/19.55 fof(clsarity_RealDef__Oreal__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_RealDef_Oreal)).
% 150.04/19.55 fof(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)).
% 150.04/19.55 fof(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)).
% 150.04/19.55 fof(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring, axiom, class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)).
% 150.04/19.55 fof(clsarity_nat__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_nat)).
% 150.04/19.55
% 150.04/19.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 150.04/19.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 150.04/19.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 150.04/19.55 fresh(y, y, x1...xn) = u
% 150.04/19.55 C => fresh(s, t, x1...xn) = v
% 150.04/19.55 where fresh is a fresh function symbol and x1..xn are the free
% 150.04/19.55 variables of u and v.
% 150.04/19.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 150.04/19.55 input problem has no model of domain size 1).
% 150.04/19.55
% 150.04/19.55 The encoding turns the above axioms into the following unit equations and goals:
% 150.04/19.55
% 150.04/19.55 Axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring): class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) = true2.
% 150.04/19.55 Axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs): class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) = true2.
% 150.04/19.55 Axiom 3 (clsarity_RealDef__Oreal__Orderings_Opreorder): class_Orderings_Opreorder(tc_RealDef_Oreal) = true2.
% 150.04/19.55 Axiom 4 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector): class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) = true2.
% 150.04/19.55 Axiom 5 (clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector): class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) = true2.
% 150.04/19.55 Axiom 6 (clsarity_nat__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_nat) = true2.
% 150.04/19.55 Axiom 7 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 150.04/19.55 Axiom 8 (clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) = true2.
% 150.04/19.55 Axiom 9 (cls_order__trans_0): fresh867(X, X, Y, Z, W) = true2.
% 150.04/19.55 Axiom 10 (cls_order__trans_0): fresh309(X, X, Y, Z, W, V) = c_lessequals(Z, W, Y).
% 150.04/19.55 Axiom 11 (cls_order__trans_0): fresh866(X, X, Y, Z, W, V) = fresh867(c_lessequals(Z, V, Y), true2, Y, Z, W).
% 150.04/19.55 Axiom 12 (cls_order__trans_0): fresh866(class_Orderings_Opreorder(X), true2, X, Y, Z, W) = fresh309(c_lessequals(W, Z, X), true2, X, Y, Z, W).
% 150.04/19.55 Axiom 13 (cls_th1_0): c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 150.04/19.55 Axiom 14 (cls_th2_0): c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) = true2.
% 150.04/19.55
% 150.04/19.55 Lemma 15: class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) = class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal).
% 150.04/19.55 Proof:
% 150.04/19.55 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 150.04/19.55 = { by axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) }
% 150.04/19.55 true2
% 150.04/19.55 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.55 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 150.04/19.55
% 150.04/19.55 Lemma 16: class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) = class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal).
% 150.04/19.55 Proof:
% 150.04/19.55 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 150.04/19.55 = { by axiom 4 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) }
% 150.04/19.55 true2
% 150.04/19.55 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.55 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 15 R->L }
% 150.04/19.55 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 150.04/19.55
% 150.04/19.55 Lemma 17: class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) = class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 150.04/19.55 Proof:
% 150.04/19.55 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
% 150.04/19.55 = { by axiom 5 (clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) }
% 150.04/19.55 true2
% 150.04/19.55 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.55 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 15 R->L }
% 150.04/19.55 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 16 R->L }
% 150.04/19.55 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 150.04/19.55
% 150.04/19.55 Lemma 18: class_Ring__and__Field_Ocomm__semiring__1(tc_nat) = class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal).
% 150.04/19.55 Proof:
% 150.04/19.55 class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
% 150.04/19.55 = { by axiom 6 (clsarity_nat__Ring__and__Field_Ocomm__semiring__1) }
% 150.04/19.55 true2
% 150.04/19.55 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.55 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 15 R->L }
% 150.04/19.55 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 16 R->L }
% 150.04/19.55 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 150.04/19.55 = { by lemma 17 R->L }
% 150.04/19.55 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
% 150.04/19.55
% 150.04/19.55 Lemma 19: class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 150.04/19.55 Proof:
% 150.04/19.55 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
% 150.04/19.55 = { by axiom 7 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) }
% 150.04/19.55 true2
% 150.04/19.55 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.55 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 15 R->L }
% 150.04/19.55 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 16 R->L }
% 150.04/19.55 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 150.04/19.55 = { by lemma 17 R->L }
% 150.04/19.55 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 18 R->L }
% 150.04/19.55 class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
% 150.04/19.55
% 150.04/19.55 Lemma 20: class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) = class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 150.04/19.55 Proof:
% 150.04/19.55 class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
% 150.04/19.55 = { by axiom 8 (clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) }
% 150.04/19.55 true2
% 150.04/19.55 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.55 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 15 R->L }
% 150.04/19.55 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 16 R->L }
% 150.04/19.55 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
% 150.04/19.55 = { by lemma 17 R->L }
% 150.04/19.55 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
% 150.04/19.55 = { by lemma 18 R->L }
% 150.04/19.55 class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
% 150.04/19.55 = { by lemma 19 R->L }
% 150.04/19.55 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
% 150.04/19.55
% 150.04/19.55 Goal 1 (cls_conjecture_0): c_lessequals(v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal) = true2.
% 150.04/19.55 Proof:
% 150.04/19.55 c_lessequals(v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal)
% 150.04/19.55 = { by axiom 10 (cls_order__trans_0) R->L }
% 150.04/19.55 fresh309(class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 20 }
% 150.04/19.55 fresh309(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 19 }
% 150.04/19.55 fresh309(class_Ring__and__Field_Ocomm__semiring__1(tc_nat), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 18 }
% 150.04/19.55 fresh309(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 17 }
% 150.04/19.55 fresh309(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 16 }
% 150.04/19.55 fresh309(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 15 }
% 150.04/19.55 fresh309(class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) }
% 150.04/19.55 fresh309(true2, class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by axiom 14 (cls_th2_0) R->L }
% 150.04/19.55 fresh309(c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 20 }
% 150.04/19.55 fresh309(c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 19 }
% 150.04/19.55 fresh309(c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_nat), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 18 }
% 150.04/19.55 fresh309(c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 17 }
% 150.04/19.55 fresh309(c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 16 }
% 150.04/19.55 fresh309(c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by lemma 15 }
% 150.04/19.55 fresh309(c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.55 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) }
% 150.04/19.56 fresh309(c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by axiom 12 (cls_order__trans_0) R->L }
% 150.04/19.56 fresh866(class_Orderings_Opreorder(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.56 fresh866(class_Orderings_Opreorder(tc_RealDef_Oreal), class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 15 R->L }
% 150.04/19.56 fresh866(class_Orderings_Opreorder(tc_RealDef_Oreal), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 16 R->L }
% 150.04/19.56 fresh866(class_Orderings_Opreorder(tc_RealDef_Oreal), class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 17 R->L }
% 150.04/19.56 fresh866(class_Orderings_Opreorder(tc_RealDef_Oreal), class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 18 R->L }
% 150.04/19.56 fresh866(class_Orderings_Opreorder(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_nat), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 19 R->L }
% 150.04/19.56 fresh866(class_Orderings_Opreorder(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 20 R->L }
% 150.04/19.56 fresh866(class_Orderings_Opreorder(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by axiom 3 (clsarity_RealDef__Oreal__Orderings_Opreorder) }
% 150.04/19.56 fresh866(true2, class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.56 fresh866(class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 15 R->L }
% 150.04/19.56 fresh866(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 16 R->L }
% 150.04/19.56 fresh866(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 17 R->L }
% 150.04/19.56 fresh866(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 18 R->L }
% 150.04/19.56 fresh866(class_Ring__and__Field_Ocomm__semiring__1(tc_nat), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 19 R->L }
% 150.04/19.56 fresh866(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by lemma 20 R->L }
% 150.04/19.56 fresh866(class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal))
% 150.04/19.56 = { by axiom 11 (cls_order__trans_0) }
% 150.04/19.56 fresh867(c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.56 fresh867(c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 15 R->L }
% 150.04/19.56 fresh867(c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 16 R->L }
% 150.04/19.56 fresh867(c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 17 R->L }
% 150.04/19.56 fresh867(c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 18 R->L }
% 150.04/19.56 fresh867(c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_nat), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 19 R->L }
% 150.04/19.56 fresh867(c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 20 R->L }
% 150.04/19.56 fresh867(c_lessequals(v_da____, c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v_z____, c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_RealVector_Onorm__class_Onorm(v_aa____, tc_Complex_Ocomplex), tc_RealDef_Oreal), tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by axiom 13 (cls_th1_0) }
% 150.04/19.56 fresh867(true2, class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 150.04/19.56 fresh867(class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 15 R->L }
% 150.04/19.56 fresh867(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 16 R->L }
% 150.04/19.56 fresh867(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 17 R->L }
% 150.04/19.56 fresh867(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 18 R->L }
% 150.04/19.56 fresh867(class_Ring__and__Field_Ocomm__semiring__1(tc_nat), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 19 R->L }
% 150.04/19.56 fresh867(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by lemma 20 R->L }
% 150.04/19.56 fresh867(class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_aa____, c_Polynomial_OpCons(v_c____, v_cs____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_z____, tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 150.04/19.56 = { by axiom 9 (cls_order__trans_0) }
% 150.04/19.56 true2
% 150.04/19.56 % SZS output end Proof
% 150.04/19.56
% 150.04/19.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------