TSTP Solution File: SWW285+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW285+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:54:36 EDT 2023
% Result : Timeout 292.46s 38.13s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWW285+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Sun Aug 27 20:40:00 EDT 2023
% 0.09/0.28 % CPUTime :
% 292.46/38.13 Command-line arguments: --flatten
% 292.46/38.13
% 292.46/38.13 % SZS status Theorem
% 292.46/38.13
% 293.14/38.30 % SZS output start Proof
% 293.14/38.30 Take the following subset of the input axioms:
% 293.14/38.31 fof(arity_Complex__Ocomplex__Fields_Ofield, axiom, class_Fields_Ofield(tc_Complex_Ocomplex)).
% 293.14/38.31 fof(arity_Complex__Ocomplex__Groups_Ozero, axiom, class_Groups_Ozero(tc_Complex_Ocomplex)).
% 293.14/38.31 fof(arity_Complex__Ocomplex__Int_Oring__char__0, axiom, class_Int_Oring__char__0(tc_Complex_Ocomplex)).
% 293.14/38.31 fof(arity_Complex__Ocomplex__RealVector_Oreal__field, axiom, class_RealVector_Oreal__field(tc_Complex_Ocomplex)).
% 293.14/38.31 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, axiom, class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)).
% 293.14/38.31 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 293.14/38.31 fof(arity_Complex__Ocomplex__Rings_Oidom, axiom, class_Rings_Oidom(tc_Complex_Ocomplex)).
% 293.14/38.31 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, axiom, class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)).
% 293.14/38.31 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)).
% 293.14/38.31 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, axiom, class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)).
% 293.14/38.31 fof(arity_Polynomial__Opoly__Divides_Osemiring__div, axiom, ![T_1]: (class_Fields_Ofield(T_1) => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)))).
% 293.14/38.31 fof(arity_Polynomial__Opoly__Power_Opower, axiom, ![T_1_2]: (class_Rings_Ocomm__semiring__1(T_1_2) => class_Power_Opower(tc_Polynomial_Opoly(T_1_2)))).
% 293.14/38.31 fof(arity_Polynomial__Opoly__Rings_Omult__zero, axiom, ![T_1_2]: (class_Rings_Ocomm__semiring__0(T_1_2) => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1_2)))).
% 293.14/38.31 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors, axiom, ![T_1_2]: (class_Rings_Oidom(T_1_2) => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1_2)))).
% 293.14/38.31 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one, axiom, ![T_1_2]: (class_Rings_Ocomm__semiring__1(T_1_2) => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1_2)))).
% 293.14/38.31 fof(fact_Suc__n__not__n, axiom, ![V_n]: c_Nat_OSuc(V_n)!=V_n).
% 293.14/38.31 fof(fact_Suc__neq__Zero, axiom, ![V_m]: c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 293.14/38.31 fof(fact_Suc__not__Zero, axiom, ![V_m2]: c_Nat_OSuc(V_m2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 293.14/38.31 fof(fact_Zero__neq__Suc, axiom, ![V_m2]: c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m2)).
% 293.14/38.31 fof(fact_Zero__not__Suc, axiom, ![V_m2]: c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m2)).
% 293.14/38.31 fof(fact__096p_Advd_Aq_A_094_Adegree_Ap_096, axiom, c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_p, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)))).
% 293.14/38.31 fof(fact_degree__0, axiom, ![T_a]: (class_Groups_Ozero(T_a) => c_Polynomial_Odegree(T_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 293.14/38.31 fof(fact_dvd__eq__mod__eq__0, axiom, ![V_a_2, V_b_2, T_a2]: (class_Divides_Osemiring__div(T_a2) => (c_Rings_Odvd__class_Odvd(T_a2, V_a_2, V_b_2) <=> c_Divides_Odiv__class_Omod(T_a2, V_b_2, V_a_2)=c_Groups_Ozero__class_Ozero(T_a2)))).
% 293.14/38.31 fof(fact_gr__implies__not0, axiom, ![V_n2, V_m2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m2, V_n2) => V_n2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 293.14/38.31 fof(fact_less__irrefl__nat, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, V_n2)).
% 293.14/38.31 fof(fact_less__nat__zero__code, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 293.14/38.31 fof(fact_less__not__refl, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, V_n2)).
% 293.14/38.31 fof(fact_less__not__refl2, axiom, ![V_n2, V_m2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, V_m2) => V_m2!=V_n2)).
% 293.14/38.31 fof(fact_less__not__refl3, axiom, ![V_t, V_s]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_s, V_t) => V_s!=V_t)).
% 293.14/38.31 fof(fact_less__zeroE, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 293.14/38.31 fof(fact_mod__by__0, axiom, ![V_a, T_a2]: (class_Divides_Osemiring__div(T_a2) => c_Divides_Odiv__class_Omod(T_a2, V_a, c_Groups_Ozero__class_Ozero(T_a2))=V_a)).
% 293.14/38.31 fof(fact_n__not__Suc__n, axiom, ![V_n2]: V_n2!=c_Nat_OSuc(V_n2)).
% 293.14/38.31 fof(fact_nat_Osimps_I2_J, axiom, ![V_nat_H]: c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H)).
% 293.14/38.31 fof(fact_nat_Osimps_I3_J, axiom, ![V_nat_H_1]: c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 293.14/38.31 fof(fact_nat__dvd__not__less, axiom, ![V_n2, V_m2]: (c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_m2) => (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m2, V_n2) => ~c_Rings_Odvd__class_Odvd(tc_Nat_Onat, V_n2, V_m2)))).
% 293.14/38.31 fof(fact_nat__less__cases, axiom, ![V_n_2, V_P_2, V_m_2]: ((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2, V_n_2) => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2))) => ((V_m_2=V_n_2 => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2))) => ((c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2, V_m_2) => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2))) => hBOOL(hAPP(hAPP(V_P_2, V_n_2), V_m_2)))))).
% 293.14/38.31 fof(fact_nat__neq__iff, axiom, ![V_n_2_2, V_m_2_2]: (V_m_2_2!=V_n_2_2 <=> (c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2_2, V_n_2_2) | c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2_2, V_m_2_2)))).
% 293.14/38.31 fof(fact_neq0__conv, axiom, ![V_n_2_2]: (V_n_2_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), V_n_2_2))).
% 293.14/38.31 fof(fact_not__add__less1, axiom, ![V_j, V_i]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_i, V_j), V_i)).
% 293.14/38.31 fof(fact_not__add__less2, axiom, ![V_j2, V_i2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, V_j2, V_i2), V_i2)).
% 293.14/38.31 fof(fact_not__less0, axiom, ![V_n2]: ~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n2, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 293.14/38.31 fof(fact_not__less__eq, axiom, ![V_n_2_2, V_m_2_2]: (~c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_m_2_2, V_n_2_2) <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat, V_n_2_2, c_Nat_OSuc(V_m_2_2)))).
% 293.14/38.31 fof(fact_not__one__le__zero, axiom, ![T_a2]: (class_Rings_Olinordered__semidom(T_a2) => ~c_Orderings_Oord__class_Oless__eq(T_a2, c_Groups_Oone__class_Oone(T_a2), c_Groups_Ozero__class_Ozero(T_a2)))).
% 293.14/38.31 fof(fact_not__one__less__zero, axiom, ![T_a2]: (class_Rings_Olinordered__semidom(T_a2) => ~c_Orderings_Oord__class_Oless(T_a2, c_Groups_Oone__class_Oone(T_a2), c_Groups_Ozero__class_Ozero(T_a2)))).
% 293.14/38.31 fof(fact_not__pos__poly__0, axiom, ![T_a2]: (class_Rings_Olinordered__idom(T_a2) => ~c_Polynomial_Opos__poly(T_a2, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2))))).
% 293.14/38.31 fof(fact_not__square__less__zero, axiom, ![T_a2, V_a2]: (class_Rings_Olinordered__ring(T_a2) => ~c_Orderings_Oord__class_Oless(T_a2, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a2), V_a2), V_a2), c_Groups_Ozero__class_Ozero(T_a2)))).
% 293.14/38.32 fof(fact_not__sum__squares__lt__zero, axiom, ![V_x, V_y, T_a2]: (class_Rings_Olinordered__ring(T_a2) => ~c_Orderings_Oord__class_Oless(T_a2, c_Groups_Oplus__class_Oplus(T_a2, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a2), V_x), V_x), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a2), V_y), V_y)), c_Groups_Ozero__class_Ozero(T_a2)))).
% 293.14/38.32 fof(fact_odd__nonzero, axiom, ![V_z]: c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), V_z), V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 293.14/38.32 fof(fact_one__neq__zero, axiom, ![T_a2]: (class_Rings_Ozero__neq__one(T_a2) => c_Groups_Oone__class_Oone(T_a2)!=c_Groups_Ozero__class_Ozero(T_a2))).
% 293.14/38.32 fof(fact_pe, axiom, v_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 293.14/38.32 fof(fact_poly__gcd__unique, axiom, ![V_d, T_a2, V_x2, V_y2]: (class_Fields_Ofield(T_a2) => (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a2), V_d, V_x2) => (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a2), V_d, V_y2) => (![B_k]: (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a2), B_k, V_x2) => (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a2), B_k, V_y2) => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a2), B_k, V_d))) => ((((V_x2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)) & V_y2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2))) => hAPP(c_Polynomial_Ocoeff(T_a2, V_d), c_Polynomial_Odegree(T_a2, V_d))=c_Groups_Ozero__class_Ozero(T_a2)) & (~(V_x2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)) & V_y2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2))) => hAPP(c_Polynomial_Ocoeff(T_a2, V_d), c_Polynomial_Odegree(T_a2, V_d))=c_Groups_Oone__class_Oone(T_a2))) => c_Polynomial_Opoly__gcd(T_a2, V_x2, V_y2)=V_d)))))).
% 293.14/38.32 fof(fact_power__eq__0__iff, axiom, ![T_a2, V_n_2_2, V_a_2_2]: ((class_Power_Opower(T_a2) & (class_Rings_Omult__zero(T_a2) & (class_Rings_Ono__zero__divisors(T_a2) & class_Rings_Ozero__neq__one(T_a2)))) => (hAPP(hAPP(c_Power_Opower__class_Opower(T_a2), V_a_2_2), V_n_2_2)=c_Groups_Ozero__class_Ozero(T_a2) <=> (V_a_2_2=c_Groups_Ozero__class_Ozero(T_a2) & V_n_2_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))).
% 293.14/38.32 fof(fact_sum__squares__gt__zero__iff, axiom, ![V_x_2, V_y_2, T_a2]: (class_Rings_Olinordered__ring__strict(T_a2) => (c_Orderings_Oord__class_Oless(T_a2, c_Groups_Ozero__class_Ozero(T_a2), c_Groups_Oplus__class_Oplus(T_a2, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a2), V_x_2), V_x_2), hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a2), V_y_2), V_y_2))) <=> (V_x_2!=c_Groups_Ozero__class_Ozero(T_a2) | V_y_2!=c_Groups_Ozero__class_Ozero(T_a2))))).
% 293.14/38.32 fof(fact_zdvd__not__zless, axiom, ![V_n2, V_m2]: (c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), V_m2) => (c_Orderings_Oord__class_Oless(tc_Int_Oint, V_m2, V_n2) => ~c_Rings_Odvd__class_Odvd(tc_Int_Oint, V_n2, V_m2)))).
% 293.14/38.32 fof(fact_zero__neq__one, axiom, ![T_a2]: (class_Rings_Ozero__neq__one(T_a2) => c_Groups_Ozero__class_Ozero(T_a2)!=c_Groups_Oone__class_Oone(T_a2))).
% 293.14/38.32 fof(fact_zless__le, axiom, ![V_z_2, V_w_2]: (c_Orderings_Oord__class_Oless(tc_Int_Oint, V_z_2, V_w_2) <=> (c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, V_z_2, V_w_2) & V_z_2!=V_w_2))).
% 293.14/38.32
% 293.14/38.32 Now clausify the problem and encode Horn clauses using encoding 3 of
% 293.14/38.32 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 293.14/38.32 We repeatedly replace C & s=t => u=v by the two clauses:
% 293.14/38.32 fresh(y, y, x1...xn) = u
% 293.14/38.32 C => fresh(s, t, x1...xn) = v
% 293.14/38.32 where fresh is a fresh function symbol and x1..xn are the free
% 293.14/38.32 variables of u and v.
% 293.14/38.32 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 293.14/38.32 input problem has no model of domain size 1).
% 293.14/38.32
% 293.14/38.32 The encoding turns the above axioms into the following unit equations and goals:
% 293.14/38.32
% 293.14/38.32 Axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field): class_RealVector_Oreal__field(tc_Complex_Ocomplex) = true2.
% 293.14/38.32 Axiom 2 (arity_Int__Oint__Rings_Olinordered__comm__semiring__strict): class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) = true2.
% 293.14/38.32 Axiom 3 (arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict): class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) = true2.
% 293.14/38.32 Axiom 4 (arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors): class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) = true2.
% 293.14/38.32 Axiom 5 (arity_Complex__Ocomplex__Int_Oring__char__0): class_Int_Oring__char__0(tc_Complex_Ocomplex) = true2.
% 293.14/38.32 Axiom 6 (arity_Complex__Ocomplex__Rings_Oidom): class_Rings_Oidom(tc_Complex_Ocomplex) = true2.
% 293.14/38.32 Axiom 7 (arity_Complex__Ocomplex__Groups_Ozero): class_Groups_Ozero(tc_Complex_Ocomplex) = true2.
% 293.14/38.32 Axiom 8 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0): class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) = true2.
% 293.14/38.32 Axiom 9 (arity_Complex__Ocomplex__Fields_Ofield): class_Fields_Ofield(tc_Complex_Ocomplex) = true2.
% 293.14/38.32 Axiom 10 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1): class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 293.14/38.32 Axiom 11 (fact_pe): v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 293.14/38.32 Axiom 12 (arity_Polynomial__Opoly__Divides_Osemiring__div): fresh1164(X, X, Y) = true2.
% 293.14/38.32 Axiom 13 (arity_Polynomial__Opoly__Power_Opower): fresh1141(X, X, Y) = true2.
% 293.14/38.32 Axiom 14 (arity_Polynomial__Opoly__Rings_Omult__zero): fresh1126(X, X, Y) = true2.
% 293.14/38.32 Axiom 15 (arity_Polynomial__Opoly__Rings_Ono__zero__divisors): fresh1125(X, X, Y) = true2.
% 293.14/38.32 Axiom 16 (arity_Polynomial__Opoly__Rings_Ozero__neq__one): fresh1114(X, X, Y) = true2.
% 293.14/38.32 Axiom 17 (fact_degree__0): fresh985(X, X, Y) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 293.14/38.32 Axiom 18 (arity_Polynomial__Opoly__Divides_Osemiring__div): fresh1164(class_Fields_Ofield(X), true2, X) = class_Divides_Osemiring__div(tc_Polynomial_Opoly(X)).
% 293.14/38.32 Axiom 19 (arity_Polynomial__Opoly__Power_Opower): fresh1141(class_Rings_Ocomm__semiring__1(X), true2, X) = class_Power_Opower(tc_Polynomial_Opoly(X)).
% 293.14/38.32 Axiom 20 (arity_Polynomial__Opoly__Rings_Omult__zero): fresh1126(class_Rings_Ocomm__semiring__0(X), true2, X) = class_Rings_Omult__zero(tc_Polynomial_Opoly(X)).
% 293.14/38.32 Axiom 21 (arity_Polynomial__Opoly__Rings_Ono__zero__divisors): fresh1125(class_Rings_Oidom(X), true2, X) = class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X)).
% 293.14/38.32 Axiom 22 (arity_Polynomial__Opoly__Rings_Ozero__neq__one): fresh1114(class_Rings_Ocomm__semiring__1(X), true2, X) = class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X)).
% 293.14/38.32 Axiom 23 (fact_mod__by__0): fresh22(X, X, Y, Z) = Y.
% 293.14/38.32 Axiom 24 (fact_degree__0): fresh985(class_Groups_Ozero(X), true2, X) = c_Polynomial_Odegree(X, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X))).
% 293.14/38.32 Axiom 25 (fact_dvd__eq__mod__eq__0_1): fresh883(X, X, Y, Z, W) = c_Groups_Ozero__class_Ozero(W).
% 293.14/38.32 Axiom 26 (fact_dvd__eq__mod__eq__0_1): fresh882(X, X, Y, Z, W) = c_Divides_Odiv__class_Omod(W, Y, Z).
% 293.14/38.32 Axiom 27 (fact_mod__by__0): fresh22(class_Divides_Osemiring__div(X), true2, Y, X) = c_Divides_Odiv__class_Omod(X, Y, c_Groups_Ozero__class_Ozero(X)).
% 293.14/38.32 Axiom 28 (fact_realpow__minus__mult): fresh1671(X, X, Y, Z, W) = hAPP(hAPP(c_Power_Opower__class_Opower(W), Y), Z).
% 293.14/38.32 Axiom 29 (fact_dvd__eq__mod__eq__0_1): fresh882(class_Divides_Osemiring__div(X), true2, Y, Z, X) = fresh883(c_Rings_Odvd__class_Odvd(X, Z, Y), true2, Y, Z, X).
% 293.14/38.32 Axiom 30 (fact__096p_Advd_Aq_A_094_Adegree_Ap_096): c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_p, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))) = true2.
% 293.14/38.32
% 293.14/38.32 Lemma 31: class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) = class_RealVector_Oreal__field(tc_Complex_Ocomplex).
% 293.14/38.32 Proof:
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)
% 293.14/38.32 = { by axiom 2 (arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) }
% 293.14/38.32 true2
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 293.14/38.32
% 293.14/38.32 Lemma 32: class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) = class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 293.14/38.32 Proof:
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)
% 293.14/38.32 = { by axiom 3 (arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) }
% 293.14/38.32 true2
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 31 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)
% 293.14/38.32
% 293.14/38.32 Lemma 33: class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) = class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 293.14/38.32 Proof:
% 293.14/38.32 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
% 293.14/38.32 = { by axiom 4 (arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) }
% 293.14/38.32 true2
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 31 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)
% 293.14/38.32 = { by lemma 32 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)
% 293.14/38.32
% 293.14/38.32 Lemma 34: class_Int_Oring__char__0(tc_Complex_Ocomplex) = class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 293.14/38.32 Proof:
% 293.14/38.32 class_Int_Oring__char__0(tc_Complex_Ocomplex)
% 293.14/38.32 = { by axiom 5 (arity_Complex__Ocomplex__Int_Oring__char__0) }
% 293.14/38.32 true2
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 31 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)
% 293.14/38.32 = { by lemma 32 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)
% 293.14/38.32 = { by lemma 33 R->L }
% 293.14/38.32 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
% 293.14/38.32
% 293.14/38.32 Lemma 35: class_Rings_Oidom(tc_Complex_Ocomplex) = class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 293.14/38.32 Proof:
% 293.14/38.32 class_Rings_Oidom(tc_Complex_Ocomplex)
% 293.14/38.32 = { by axiom 6 (arity_Complex__Ocomplex__Rings_Oidom) }
% 293.14/38.32 true2
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 31 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)
% 293.14/38.32 = { by lemma 32 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)
% 293.14/38.32 = { by lemma 33 R->L }
% 293.14/38.32 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 34 R->L }
% 293.14/38.32 class_Int_Oring__char__0(tc_Complex_Ocomplex)
% 293.14/38.32
% 293.14/38.32 Lemma 36: class_Groups_Ozero(tc_Complex_Ocomplex) = class_Rings_Oidom(tc_Complex_Ocomplex).
% 293.14/38.32 Proof:
% 293.14/38.32 class_Groups_Ozero(tc_Complex_Ocomplex)
% 293.14/38.32 = { by axiom 7 (arity_Complex__Ocomplex__Groups_Ozero) }
% 293.14/38.32 true2
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 31 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)
% 293.14/38.32 = { by lemma 32 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)
% 293.14/38.32 = { by lemma 33 R->L }
% 293.14/38.32 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 34 R->L }
% 293.14/38.32 class_Int_Oring__char__0(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 35 R->L }
% 293.14/38.32 class_Rings_Oidom(tc_Complex_Ocomplex)
% 293.14/38.32
% 293.14/38.32 Lemma 37: class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) = class_Groups_Ozero(tc_Complex_Ocomplex).
% 293.14/38.32 Proof:
% 293.14/38.32 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)
% 293.14/38.32 = { by axiom 10 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) }
% 293.14/38.32 true2
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 31 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)
% 293.14/38.32 = { by lemma 32 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)
% 293.14/38.32 = { by lemma 33 R->L }
% 293.14/38.32 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 34 R->L }
% 293.14/38.32 class_Int_Oring__char__0(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 35 R->L }
% 293.14/38.32 class_Rings_Oidom(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 36 R->L }
% 293.14/38.32 class_Groups_Ozero(tc_Complex_Ocomplex)
% 293.14/38.32
% 293.14/38.32 Lemma 38: class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = class_Groups_Ozero(tc_Complex_Ocomplex).
% 293.14/38.32 Proof:
% 293.14/38.32 class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 293.14/38.32 = { by axiom 18 (arity_Polynomial__Opoly__Divides_Osemiring__div) R->L }
% 293.14/38.32 fresh1164(class_Fields_Ofield(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex)
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 fresh1164(class_Fields_Ofield(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 31 R->L }
% 293.14/38.32 fresh1164(class_Fields_Ofield(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 32 R->L }
% 293.14/38.32 fresh1164(class_Fields_Ofield(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 33 R->L }
% 293.14/38.32 fresh1164(class_Fields_Ofield(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 34 R->L }
% 293.14/38.32 fresh1164(class_Fields_Ofield(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 35 R->L }
% 293.14/38.32 fresh1164(class_Fields_Ofield(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 36 R->L }
% 293.14/38.32 fresh1164(class_Fields_Ofield(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by axiom 9 (arity_Complex__Ocomplex__Fields_Ofield) }
% 293.14/38.32 fresh1164(true2, class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 fresh1164(class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 31 R->L }
% 293.14/38.32 fresh1164(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 32 R->L }
% 293.14/38.32 fresh1164(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 33 R->L }
% 293.14/38.32 fresh1164(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 34 R->L }
% 293.14/38.32 fresh1164(class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 35 R->L }
% 293.14/38.32 fresh1164(class_Rings_Oidom(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 36 R->L }
% 293.14/38.32 fresh1164(class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 293.14/38.32 = { by axiom 12 (arity_Polynomial__Opoly__Divides_Osemiring__div) }
% 293.14/38.32 true2
% 293.14/38.32 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.32 class_RealVector_Oreal__field(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 31 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint)
% 293.14/38.32 = { by lemma 32 R->L }
% 293.14/38.32 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat)
% 293.14/38.32 = { by lemma 33 R->L }
% 293.14/38.32 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 34 R->L }
% 293.14/38.32 class_Int_Oring__char__0(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 35 R->L }
% 293.14/38.32 class_Rings_Oidom(tc_Complex_Ocomplex)
% 293.14/38.32 = { by lemma 36 R->L }
% 293.14/38.33 class_Groups_Ozero(tc_Complex_Ocomplex)
% 293.14/38.33
% 293.14/38.33 Goal 1 (fact_power__eq__0__iff): tuple4(X, hAPP(hAPP(c_Power_Opower__class_Opower(Y), Z), X), class_Power_Opower(Y), class_Rings_Omult__zero(Y), class_Rings_Ono__zero__divisors(Y), class_Rings_Ozero__neq__one(Y)) = tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(Y), true2, true2, true2, true2).
% 293.14/38.33 The goal is true when:
% 293.14/38.33 X = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 293.14/38.33 Y = tc_Polynomial_Opoly(tc_Complex_Ocomplex)
% 293.14/38.33 Z = v_q
% 293.14/38.33
% 293.14/38.33 Proof:
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 28 (fact_realpow__minus__mult) R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 17 (fact_degree__0) R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, fresh985(class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 36 }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, fresh985(class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 35 }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, fresh985(class_Groups_Ozero(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 34 }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, fresh985(class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 33 }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, fresh985(class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 32 }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, fresh985(class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 31 }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, fresh985(class_Groups_Ozero(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, fresh985(class_Groups_Ozero(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 24 (fact_degree__0) }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 11 (fact_pe) R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh1671(Y, Y, v_q, c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 28 (fact_realpow__minus__mult) }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Power_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 19 (arity_Polynomial__Opoly__Power_Opower) R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), fresh1141(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), fresh1141(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 31 R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), fresh1141(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 32 R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), fresh1141(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 33 R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), fresh1141(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 34 R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), fresh1141(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 35 R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), fresh1141(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 36 R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), fresh1141(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by lemma 37 }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), fresh1141(class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 13 (arity_Polynomial__Opoly__Power_Opower) }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), true2, class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.33 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.33 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 31 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 32 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 33 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 34 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 35 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 36 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by axiom 20 (arity_Polynomial__Opoly__Rings_Omult__zero) R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 31 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 32 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 33 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 34 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 35 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 36 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by axiom 8 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(true2, class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 31 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 32 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 33 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 34 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 35 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Rings_Oidom(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 36 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1126(class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by axiom 14 (arity_Polynomial__Opoly__Rings_Omult__zero) }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), true2, class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 31 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 32 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 33 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 34 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 35 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 36 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by axiom 21 (arity_Polynomial__Opoly__Rings_Ono__zero__divisors) R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1125(class_Rings_Oidom(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1125(class_Rings_Oidom(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 31 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1125(class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 32 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1125(class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 33 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1125(class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 34 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1125(class_Rings_Oidom(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 35 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1125(class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 36 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1125(class_Rings_Oidom(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by lemma 36 R->L }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1125(class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.34 = { by axiom 15 (arity_Polynomial__Opoly__Rings_Ono__zero__divisors) }
% 293.14/38.34 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), true2, class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.35 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.35 = { by lemma 31 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.35 = { by lemma 32 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.35 = { by lemma 33 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.35 = { by lemma 34 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.35 = { by lemma 35 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.35 = { by lemma 36 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
% 293.14/38.35 = { by axiom 22 (arity_Polynomial__Opoly__Rings_Ozero__neq__one) R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1114(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex))
% 293.14/38.35 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1114(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 31 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1114(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 32 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1114(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 33 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1114(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 34 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1114(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 35 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1114(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 36 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1114(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 37 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), fresh1114(class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 293.14/38.35 = { by axiom 16 (arity_Polynomial__Opoly__Rings_Ozero__neq__one) }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), true2)
% 293.14/38.35 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 31 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))
% 293.14/38.35 = { by lemma 32 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))
% 293.14/38.35 = { by lemma 33 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 34 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 35 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 36 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by axiom 23 (fact_mod__by__0) R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh22(class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 38 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh22(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 36 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh22(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oidom(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 35 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh22(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Int_Oring__char__0(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 34 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh22(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 33 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh22(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 32 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh22(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 31 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh22(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_RealVector_Oreal__field(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh22(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by axiom 27 (fact_mod__by__0) }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by axiom 26 (fact_dvd__eq__mod__eq__0_1) R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh882(class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 38 R->L }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh882(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 36 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh882(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oidom(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 35 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh882(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Int_Oring__char__0(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 34 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh882(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 33 }
% 293.14/38.35 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh882(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.35 = { by lemma 32 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh882(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 31 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh882(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_RealVector_Oreal__field(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh882(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 29 (fact_dvd__eq__mod__eq__0_1) }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))), class_RealVector_Oreal__field(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 31 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 32 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 33 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 34 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))), class_Int_Oring__char__0(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 35 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))), class_Rings_Oidom(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 36 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 28 (fact_realpow__minus__mult) R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), fresh1671(X, X, v_q, c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p), tc_Polynomial_Opoly(tc_Complex_Ocomplex))), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 11 (fact_pe) }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), fresh1671(X, X, v_q, c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), tc_Polynomial_Opoly(tc_Complex_Ocomplex))), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 28 (fact_realpow__minus__mult) }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 11 (fact_pe) R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_p, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 11 (fact_pe) R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_p, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p))), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 30 (fact__096p_Advd_Aq_A_094_Adegree_Ap_096) }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(true2, class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 31 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 32 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 33 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 34 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 35 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(class_Rings_Oidom(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 36 R->L }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), fresh883(class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by axiom 25 (fact_dvd__eq__mod__eq__0_1) }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 36 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oidom(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 36 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 36 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Groups_Ozero(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 36 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 35 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 35 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 35 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Rings_Oidom(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 35 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 34 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 34 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 34 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Int_Oring__char__0(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 34 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 33 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 33 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 33 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))
% 293.14/38.36 = { by lemma 33 }
% 293.14/38.36 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))
% 293.14/38.36 = { by lemma 32 }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))
% 293.14/38.37 = { by lemma 32 }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))
% 293.14/38.37 = { by lemma 32 }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))
% 293.14/38.37 = { by lemma 32 }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))
% 293.14/38.37 = { by lemma 31 }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))
% 293.14/38.37 = { by lemma 31 }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))
% 293.14/38.37 = { by lemma 31 }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))
% 293.14/38.37 = { by lemma 31 }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex))
% 293.14/38.37 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex))
% 293.14/38.37 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, true2, class_RealVector_Oreal__field(tc_Complex_Ocomplex), class_RealVector_Oreal__field(tc_Complex_Ocomplex))
% 293.14/38.37 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, true2, true2, class_RealVector_Oreal__field(tc_Complex_Ocomplex))
% 293.14/38.37 = { by axiom 1 (arity_Complex__Ocomplex__RealVector_Oreal__field) }
% 293.14/38.37 tuple4(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, true2, true2, true2)
% 293.14/38.37 % SZS output end Proof
% 293.14/38.37
% 293.14/38.37 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------