TSTP Solution File: ALG413-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG413-1 : 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 : n024.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 16:43:13 EDT 2023
% Result : Unsatisfiable 147.35s 19.08s
% Output : Proof 147.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG413-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 05:38:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 147.35/19.08 Command-line arguments: --flatten
% 147.35/19.08
% 147.35/19.08 % SZS status Unsatisfiable
% 147.35/19.08
% 147.35/19.11 % SZS output start Proof
% 147.35/19.11 Take the following subset of the input axioms:
% 147.35/19.11 fof(cls_CHAINED_0, axiom, c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____, v_ds____, tc_Complex_Ocomplex), c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 147.35/19.11 fof(cls_add__diff__cancel_0, axiom, ![T_a, V_a, V_b]: (~class_OrderedGroup_Ogroup__add(T_a) | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a, V_b, T_a), V_b, T_a)=V_a)).
% 147.35/19.11 fof(cls_comm__monoid__add_Omult__commute_0, axiom, ![T_a2, V_a2, V_b2]: (~class_OrderedGroup_Ocomm__monoid__add(T_a2) | c_HOL_Oplus__class_Oplus(V_a2, V_b2, T_a2)=c_HOL_Oplus__class_Oplus(V_b2, V_a2, T_a2))).
% 147.35/19.11 fof(cls_conjecture_0, negated_conjecture, c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)!=c_RealVector_Onorm__class_Onorm(v_d____, tc_Complex_Ocomplex)).
% 147.35/19.11 fof(cls_group__add__class_Odiff__0_0, axiom, ![T_a2, V_a2]: (~class_OrderedGroup_Ogroup__add(T_a2) | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a2), V_a2, T_a2)=c_HOL_Ouminus__class_Ouminus(V_a2, T_a2))).
% 147.35/19.11 fof(cls_norm__minus__cancel_0, axiom, ![V_x, T_a2]: (~class_RealVector_Oreal__normed__vector(T_a2) | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x, T_a2), T_a2)=c_RealVector_Onorm__class_Onorm(V_x, T_a2))).
% 147.35/19.11 fof(cls_poly__pCons_0, axiom, ![V_p, T_a2, V_a2, V_x2]: (~class_Ring__and__Field_Ocomm__semiring__0(T_a2) | c_Polynomial_Opoly(c_Polynomial_OpCons(V_a2, V_p, T_a2), V_x2, T_a2)=c_HOL_Oplus__class_Oplus(V_a2, c_HOL_Otimes__class_Otimes(V_x2, c_Polynomial_Opoly(V_p, V_x2, T_a2), T_a2), T_a2))).
% 147.35/19.11 fof(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add, axiom, class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)).
% 147.35/19.11 fof(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, axiom, class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)).
% 147.35/19.11 fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field, axiom, class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)).
% 147.35/19.11 fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)).
% 147.35/19.11 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0, axiom, class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)).
% 147.35/19.11 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors, axiom, class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)).
% 147.35/19.11 fof(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs, axiom, class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)).
% 147.35/19.11 fof(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field, axiom, class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)).
% 147.35/19.11 fof(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring, axiom, class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)).
% 147.35/19.11 fof(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field, axiom, class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal)).
% 147.35/19.11 fof(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors, axiom, class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal)).
% 147.35/19.11
% 147.35/19.11 Now clausify the problem and encode Horn clauses using encoding 3 of
% 147.35/19.11 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 147.35/19.11 We repeatedly replace C & s=t => u=v by the two clauses:
% 147.35/19.11 fresh(y, y, x1...xn) = u
% 147.35/19.11 C => fresh(s, t, x1...xn) = v
% 147.35/19.11 where fresh is a fresh function symbol and x1..xn are the free
% 147.35/19.11 variables of u and v.
% 147.35/19.11 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 147.35/19.11 input problem has no model of domain size 1).
% 147.35/19.11
% 147.35/19.11 The encoding turns the above axioms into the following unit equations and goals:
% 147.35/19.11
% 147.35/19.11 Axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring): class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) = true2.
% 147.35/19.11 Axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs): class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) = true2.
% 147.35/19.11 Axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors): class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) = true2.
% 147.35/19.11 Axiom 4 (clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors): class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) = true2.
% 147.35/19.11 Axiom 5 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field): class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) = true2.
% 147.35/19.11 Axiom 6 (clsarity_RealDef__Oreal__RealVector_Oreal__normed__field): class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) = true2.
% 147.35/19.11 Axiom 7 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector): class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) = true2.
% 147.35/19.11 Axiom 8 (clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add): class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) = true2.
% 147.35/19.11 Axiom 9 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0): class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) = true2.
% 147.35/19.11 Axiom 10 (clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add): class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) = true2.
% 147.35/19.11 Axiom 11 (clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field): class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) = true2.
% 147.35/19.11 Axiom 12 (cls_group__add__class_Odiff__0_0): fresh552(X, X, Y, Z) = c_HOL_Ouminus__class_Ouminus(Z, Y).
% 147.35/19.11 Axiom 13 (cls_norm__minus__cancel_0): fresh291(X, X, Y, Z) = c_RealVector_Onorm__class_Onorm(Z, Y).
% 147.35/19.11 Axiom 14 (cls_comm__monoid__add_Omult__commute_0): fresh661(X, X, Y, Z, W) = c_HOL_Oplus__class_Oplus(W, Z, Y).
% 147.35/19.11 Axiom 15 (cls_group__add__class_Odiff__0_0): fresh552(class_OrderedGroup_Ogroup__add(X), true2, X, Y) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X), Y, X).
% 147.35/19.12 Axiom 16 (cls_norm__minus__cancel_0): fresh291(class_RealVector_Oreal__normed__vector(X), true2, X, Y) = c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(Y, X), X).
% 147.35/19.12 Axiom 17 (cls_add__diff__cancel_0): fresh26(X, X, Y, Z, W) = Z.
% 147.35/19.12 Axiom 18 (cls_comm__monoid__add_Omult__commute_0): fresh661(class_OrderedGroup_Ocomm__monoid__add(X), true2, X, Y, Z) = c_HOL_Oplus__class_Oplus(Y, Z, X).
% 147.35/19.12 Axiom 19 (cls_poly__pCons_0): fresh259(X, X, Y, Z, W, V) = c_Polynomial_Opoly(c_Polynomial_OpCons(Z, W, Y), V, Y).
% 147.35/19.12 Axiom 20 (cls_add__diff__cancel_0): fresh26(class_OrderedGroup_Ogroup__add(X), true2, X, Y, Z) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(Y, Z, X), Z, X).
% 147.35/19.12 Axiom 21 (cls_CHAINED_0): c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____, v_ds____, tc_Complex_Ocomplex), c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 147.35/19.12 Axiom 22 (cls_poly__pCons_0): fresh259(class_Ring__and__Field_Ocomm__semiring__0(X), true2, X, Y, Z, W) = c_HOL_Oplus__class_Oplus(Y, c_HOL_Otimes__class_Otimes(W, c_Polynomial_Opoly(Z, W, X), X), X).
% 147.35/19.12
% 147.35/19.12 Lemma 23: class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) = class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal).
% 147.35/19.12 Proof:
% 147.35/19.12 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 147.35/19.12 = { by axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) }
% 147.35/19.12 true2
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.12 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 147.35/19.12
% 147.35/19.12 Lemma 24: class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) = class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal).
% 147.35/19.12 Proof:
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) }
% 147.35/19.12 true2
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.12 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 23 R->L }
% 147.35/19.12 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 147.35/19.12
% 147.35/19.12 Lemma 25: class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) = class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 147.35/19.12 Proof:
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
% 147.35/19.12 = { by axiom 4 (clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) }
% 147.35/19.12 true2
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.12 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 23 R->L }
% 147.35/19.12 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 24 R->L }
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
% 147.35/19.12
% 147.35/19.12 Lemma 26: class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) = class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 147.35/19.12 Proof:
% 147.35/19.12 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 5 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) }
% 147.35/19.12 true2
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.12 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 23 R->L }
% 147.35/19.12 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 24 R->L }
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 25 R->L }
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
% 147.35/19.12
% 147.35/19.12 Lemma 27: class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) = class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 147.35/19.12 Proof:
% 147.35/19.12 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
% 147.35/19.12 = { by axiom 6 (clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) }
% 147.35/19.12 true2
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.12 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 23 R->L }
% 147.35/19.12 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 24 R->L }
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 25 R->L }
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 26 R->L }
% 147.35/19.12 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
% 147.35/19.12
% 147.35/19.12 Lemma 28: class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) = class_RealVector_Oreal__normed__field(tc_RealDef_Oreal).
% 147.35/19.12 Proof:
% 147.35/19.12 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal)
% 147.35/19.12 = { by axiom 11 (clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) }
% 147.35/19.12 true2
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.12 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 23 R->L }
% 147.35/19.12 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 24 R->L }
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 25 R->L }
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 26 R->L }
% 147.35/19.12 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 27 R->L }
% 147.35/19.12 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
% 147.35/19.12
% 147.35/19.12 Lemma 29: class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) = class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex).
% 147.35/19.12 Proof:
% 147.35/19.12 class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 28 }
% 147.35/19.12 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 27 }
% 147.35/19.12 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 26 }
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 25 }
% 147.35/19.12 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 24 }
% 147.35/19.12 class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
% 147.35/19.12 = { by lemma 23 }
% 147.35/19.12 class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal)
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) }
% 147.35/19.12 true2
% 147.35/19.12 = { by axiom 10 (clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) R->L }
% 147.35/19.12 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
% 147.35/19.12
% 147.35/19.12 Goal 1 (cls_conjecture_0): c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(v_d____, tc_Complex_Ocomplex).
% 147.35/19.12 Proof:
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 17 (cls_add__diff__cancel_0) R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(fresh26(class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 29 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(fresh26(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 28 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(fresh26(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 27 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(fresh26(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 26 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(fresh26(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal), tc_Complex_Ocomplex, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 25 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(fresh26(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 24 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(fresh26(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_Complex_Ocomplex, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 23 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(fresh26(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), tc_Complex_Ocomplex, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(fresh26(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 20 (cls_add__diff__cancel_0) }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____, tc_Complex_Ocomplex), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 14 (cls_comm__monoid__add_Omult__commute_0) R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 28 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_RealVector_Oreal__normed__field(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 27 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 26 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 25 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 24 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 23 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(true2, class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 8 (clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 28 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 27 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 26 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 25 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 24 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 23 }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex), class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh661(class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 18 (cls_comm__monoid__add_Omult__commute_0) }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_d____, c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), c_Polynomial_Opoly(v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 22 (cls_poly__pCons_0) R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 23 R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 24 R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 25 R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 26 R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 27 R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by lemma 28 R->L }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.12 = { by axiom 9 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) }
% 147.35/19.12 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(true2, class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 23 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 24 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 25 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 26 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 27 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_RealVector_Oreal__normed__field(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 28 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(fresh259(class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____, v_ds____, c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex)), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by axiom 19 (cls_poly__pCons_0) }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_Polynomial_OpCons(v_d____, v_ds____, tc_Complex_Ocomplex), c_RealVector_Oof__real(v_x____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by axiom 21 (cls_CHAINED_0) }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by axiom 15 (cls_group__add__class_Odiff__0_0) R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(fresh552(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_d____), tc_Complex_Ocomplex)
% 147.35/19.13 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(fresh552(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 23 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(fresh552(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 24 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(fresh552(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_d____), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 25 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(fresh552(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 26 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(fresh552(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_d____), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 27 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(fresh552(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 28 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(fresh552(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____), tc_Complex_Ocomplex)
% 147.35/19.13 = { by lemma 29 R->L }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(fresh552(class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____), tc_Complex_Ocomplex)
% 147.35/19.13 = { by axiom 12 (cls_group__add__class_Odiff__0_0) }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(v_d____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 147.35/19.13 = { by axiom 16 (cls_norm__minus__cancel_0) R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 23 R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 24 R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 25 R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 26 R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 27 R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_RealVector_Oreal__normed__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 28 R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by axiom 7 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) }
% 147.35/19.13 fresh291(true2, class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) R->L }
% 147.35/19.13 fresh291(class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 23 R->L }
% 147.35/19.13 fresh291(class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 24 R->L }
% 147.35/19.13 fresh291(class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 25 R->L }
% 147.35/19.13 fresh291(class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 26 R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 27 R->L }
% 147.35/19.13 fresh291(class_RealVector_Oreal__normed__field(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by lemma 28 R->L }
% 147.35/19.13 fresh291(class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal), tc_Complex_Ocomplex, v_d____)
% 147.35/19.13 = { by axiom 13 (cls_norm__minus__cancel_0) }
% 147.35/19.13 c_RealVector_Onorm__class_Onorm(v_d____, tc_Complex_Ocomplex)
% 147.35/19.13 % SZS output end Proof
% 147.35/19.13
% 147.35/19.13 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------