TSTP Solution File: SWW260+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW260+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 : n015.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 00:54:32 EDT 2023
% Result : Theorem 136.34s 18.08s
% Output : Proof 137.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW260+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 19:34:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 136.34/18.08 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 136.34/18.08
% 136.34/18.08 % SZS status Theorem
% 136.34/18.08
% 136.34/18.09 % SZS output start Proof
% 136.34/18.09 Take the following subset of the input axioms:
% 136.34/18.10 fof(arity_Complex__Ocomplex__Groups_Ogroup__add, axiom, class_Groups_Ogroup__add(tc_Complex_Ocomplex)).
% 136.34/18.10 fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1, axiom, class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)).
% 136.34/18.10 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1, axiom, class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex)).
% 136.34/18.10 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 136.34/18.10 fof(arity_RealDef__Oreal__Groups_Ogroup__add, axiom, class_Groups_Ogroup__add(tc_RealDef_Oreal)).
% 136.34/18.10 fof(conj_0, conjecture, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))).
% 136.34/18.10 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, axiom, ![V_x, T_a]: (class_Rings_Ocomm__ring__1(T_a) => c_Groups_Ouminus__class_Ouminus(T_a, V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), c_Groups_Ouminus__class_Ouminus(T_a, c_Groups_Oone__class_Oone(T_a))), V_x))).
% 136.34/18.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, axiom, ![V_a, V_c, T_a2]: (class_Rings_Ocomm__semiring__1(T_a2) => c_Groups_Oplus__class_Oplus(T_a2, V_a, V_c)=c_Groups_Oplus__class_Oplus(T_a2, V_c, V_a))).
% 136.34/18.10 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, axiom, ![V_b, T_a2, V_a2]: (class_Rings_Ocomm__semiring__1(T_a2) => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a2), V_a2), V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a2), V_b), V_a2))).
% 136.34/18.10 fof(fact_complex__of__real__power, axiom, ![V_n, V_x2]: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, V_x2)), V_n)=c_RealVector_Oof__real(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), V_x2), V_n))).
% 136.34/18.10 fof(fact_diff__add__cancel, axiom, ![T_a2, V_a2, V_b2]: (class_Groups_Ogroup__add(T_a2) => c_Groups_Oplus__class_Oplus(T_a2, c_Groups_Ominus__class_Ominus(T_a2, V_a2, V_b2), V_b2)=V_a2)).
% 136.34/18.10 fof(fact_minus__add__cancel, axiom, ![T_a2, V_a2, V_b2]: (class_Groups_Ogroup__add(T_a2) => c_Groups_Oplus__class_Oplus(T_a2, c_Groups_Ouminus__class_Ouminus(T_a2, V_a2), c_Groups_Oplus__class_Oplus(T_a2, V_a2, V_b2))=V_b2)).
% 136.34/18.10 fof(fact_of__real__1, axiom, ![T_a2]: (class_RealVector_Oreal__algebra__1(T_a2) => c_RealVector_Oof__real(T_a2, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(T_a2))).
% 136.34/18.10 fof(fact_of__real__add, axiom, ![V_y, V_x2, T_a2]: (class_RealVector_Oreal__algebra__1(T_a2) => c_RealVector_Oof__real(T_a2, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, V_x2, V_y))=c_Groups_Oplus__class_Oplus(T_a2, c_RealVector_Oof__real(T_a2, V_x2), c_RealVector_Oof__real(T_a2, V_y)))).
% 136.34/18.10
% 136.34/18.10 Now clausify the problem and encode Horn clauses using encoding 3 of
% 136.34/18.10 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 136.34/18.10 We repeatedly replace C & s=t => u=v by the two clauses:
% 136.34/18.10 fresh(y, y, x1...xn) = u
% 136.34/18.10 C => fresh(s, t, x1...xn) = v
% 136.34/18.10 where fresh is a fresh function symbol and x1..xn are the free
% 136.34/18.10 variables of u and v.
% 136.34/18.10 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 136.34/18.10 input problem has no model of domain size 1).
% 136.34/18.10
% 136.34/18.10 The encoding turns the above axioms into the following unit equations and goals:
% 136.34/18.10
% 136.34/18.10 Axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1): class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 136.34/18.10 Axiom 2 (arity_Complex__Ocomplex__Groups_Ogroup__add): class_Groups_Ogroup__add(tc_Complex_Ocomplex) = true2.
% 136.34/18.10 Axiom 3 (arity_RealDef__Oreal__Groups_Ogroup__add): class_Groups_Ogroup__add(tc_RealDef_Oreal) = true2.
% 136.34/18.10 Axiom 4 (arity_Complex__Ocomplex__RealVector_Oreal__algebra__1): class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) = true2.
% 136.34/18.10 Axiom 5 (arity_Complex__Ocomplex__Rings_Ocomm__ring__1): class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) = true2.
% 136.34/18.10 Axiom 6 (fact_of__real__1): fresh472(X, X, Y) = c_Groups_Oone__class_Oone(Y).
% 136.34/18.10 Axiom 7 (fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J): fresh996(X, X, Y, Z) = c_Groups_Ouminus__class_Ouminus(Z, Y).
% 136.34/18.10 Axiom 8 (fact_of__real__1): fresh472(class_RealVector_Oreal__algebra__1(X), true2, X) = c_RealVector_Oof__real(X, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 136.34/18.10 Axiom 9 (fact_complex__of__real__power): hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, X)), Y) = c_RealVector_Oof__real(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), X), Y)).
% 136.34/18.10 Axiom 10 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J): fresh981(X, X, Y, Z, W) = c_Groups_Oplus__class_Oplus(W, Y, Z).
% 136.34/18.10 Axiom 11 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J): fresh971(X, X, Y, Z, W) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(W), Y), Z).
% 136.34/18.10 Axiom 12 (fact_of__real__add): fresh471(X, X, Y, Z, W) = c_RealVector_Oof__real(W, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, Z, Y)).
% 136.34/18.10 Axiom 13 (fact_diff__add__cancel): fresh125(X, X, Y, Z, W) = Z.
% 136.34/18.10 Axiom 14 (fact_minus__add__cancel): fresh124(X, X, Y, Z, W) = Y.
% 136.34/18.10 Axiom 15 (fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J): fresh996(class_Rings_Ocomm__ring__1(X), true2, Y, X) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X), c_Groups_Ouminus__class_Ouminus(X, c_Groups_Oone__class_Oone(X))), Y).
% 136.34/18.10 Axiom 16 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J): fresh981(class_Rings_Ocomm__semiring__1(X), true2, Y, Z, X) = c_Groups_Oplus__class_Oplus(X, Z, Y).
% 136.34/18.10 Axiom 17 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J): fresh971(class_Rings_Ocomm__semiring__1(X), true2, Y, Z, X) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X), Z), Y).
% 136.34/18.10 Axiom 18 (fact_of__real__add): fresh471(class_RealVector_Oreal__algebra__1(X), true2, Y, Z, X) = c_Groups_Oplus__class_Oplus(X, c_RealVector_Oof__real(X, Z), c_RealVector_Oof__real(X, Y)).
% 136.34/18.10 Axiom 19 (fact_diff__add__cancel): fresh125(class_Groups_Ogroup__add(X), true2, Y, Z, X) = c_Groups_Oplus__class_Oplus(X, c_Groups_Ominus__class_Ominus(X, Z, Y), Y).
% 136.34/18.10 Axiom 20 (fact_minus__add__cancel): fresh124(class_Groups_Ogroup__add(X), true2, Y, Z, X) = c_Groups_Oplus__class_Oplus(X, c_Groups_Ouminus__class_Ouminus(X, Z), c_Groups_Oplus__class_Oplus(X, Z, Y)).
% 136.34/18.10
% 136.34/18.10 Lemma 21: c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, X, Y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, Y, X).
% 136.34/18.10 Proof:
% 136.34/18.10 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, X, Y)
% 136.34/18.10 = { by axiom 16 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) R->L }
% 136.34/18.10 fresh981(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, Y, X, tc_Complex_Ocomplex)
% 136.34/18.10 = { by axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) }
% 136.34/18.10 fresh981(true2, true2, Y, X, tc_Complex_Ocomplex)
% 136.34/18.10 = { by axiom 10 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) }
% 136.34/18.10 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, Y, X)
% 136.34/18.10
% 136.34/18.10 Goal 1 (conj_0): c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))).
% 136.34/18.10 Proof:
% 136.34/18.10 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))
% 136.34/18.10 = { by lemma 21 }
% 136.34/18.10 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))))
% 136.34/18.10 = { by axiom 17 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) R->L }
% 136.34/18.10 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), fresh971(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____), tc_Complex_Ocomplex)))
% 136.34/18.10 = { by axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) }
% 136.34/18.10 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), fresh971(true2, true2, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____), tc_Complex_Ocomplex)))
% 136.34/18.11 = { by axiom 11 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____))))
% 136.34/18.11 = { by axiom 15 (fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) R->L }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), fresh996(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____), tc_Complex_Ocomplex)))
% 136.34/18.11 = { by axiom 5 (arity_Complex__Ocomplex__Rings_Ocomm__ring__1) }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), fresh996(true2, true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____), tc_Complex_Ocomplex)))
% 136.34/18.11 = { by axiom 7 (fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____))))
% 136.34/18.11 = { by lemma 21 }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))
% 136.34/18.11 = { by axiom 6 (fact_of__real__1) R->L }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), fresh472(true2, true2, tc_Complex_Ocomplex)))
% 136.34/18.11 = { by axiom 4 (arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) R->L }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), fresh472(class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex)))
% 136.34/18.11 = { by axiom 8 (fact_of__real__1) }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
% 136.34/18.11 = { by axiom 13 (fact_diff__add__cancel) R->L }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_RealVector_Oof__real(tc_Complex_Ocomplex, fresh125(true2, true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))))
% 136.34/18.11 = { by axiom 3 (arity_RealDef__Oreal__Groups_Ogroup__add) R->L }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_RealVector_Oof__real(tc_Complex_Ocomplex, fresh125(class_Groups_Ogroup__add(tc_RealDef_Oreal), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____), c_Groups_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal))))
% 136.34/18.11 = { by axiom 19 (fact_diff__add__cancel) }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))))
% 136.34/18.11 = { by axiom 12 (fact_of__real__add) R->L }
% 136.34/18.11 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), fresh471(true2, true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), tc_Complex_Ocomplex)))
% 136.34/18.12 = { by axiom 4 (arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) R->L }
% 136.34/18.12 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), fresh471(class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex), true2, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), tc_Complex_Ocomplex)))
% 136.34/18.12 = { by axiom 18 (fact_of__real__add) }
% 136.34/18.12 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), c_RealVector_Oof__real(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))))
% 136.34/18.12 = { by axiom 9 (fact_complex__of__real__power) R->L }
% 136.34/18.12 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____))))
% 136.34/18.12 = { by lemma 21 }
% 136.34/18.12 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____), c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))))))
% 136.34/18.12 = { by axiom 20 (fact_minus__add__cancel) R->L }
% 136.34/18.12 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), fresh124(class_Groups_Ogroup__add(tc_Complex_Ocomplex), true2, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____), tc_Complex_Ocomplex))
% 136.34/18.12 = { by axiom 2 (arity_Complex__Ocomplex__Groups_Ogroup__add) }
% 136.34/18.12 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), fresh124(true2, true2, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____), tc_Complex_Ocomplex))
% 136.34/18.12 = { by axiom 14 (fact_minus__add__cancel) }
% 136.34/18.12 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))))
% 136.34/18.12 = { by lemma 21 R->L }
% 137.06/18.12 c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))
% 137.06/18.12 % SZS output end Proof
% 137.06/18.12
% 137.06/18.12 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------