TSTP Solution File: SWW290+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWW290+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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:54:37 EDT 2023
% Result : Theorem 227.35s 29.61s
% Output : Proof 227.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW290+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 22:20:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 227.35/29.61 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 227.35/29.61
% 227.35/29.61 % SZS status Theorem
% 227.35/29.61
% 227.35/29.62 % SZS output start Proof
% 227.35/29.62 Take the following subset of the input axioms:
% 227.35/29.62 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, axiom, class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)).
% 227.35/29.62 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, axiom, class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 227.35/29.63 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, axiom, ![T_1]: (class_Rings_Ocomm__semiring__1(T_1) => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)))).
% 227.35/29.63 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, axiom, ![T_1_2]: (class_Rings_Ocomm__semiring__1(T_1_2) => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1_2)))).
% 227.35/29.63 fof(conj_0, conjecture, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, v_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))).
% 227.35/29.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, axiom, ![V_a, T_a]: (class_Rings_Ocomm__semiring__1(T_a) => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a), V_a), c_Groups_Oone__class_Oone(T_a))=V_a)).
% 227.35/29.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, axiom, ![V_b, V_a2, T_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))).
% 227.35/29.63 fof(fact_mult__1, axiom, ![V_a2, T_a2]: (class_Groups_Ocomm__monoid__mult(T_a2) => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a2), c_Groups_Oone__class_Oone(T_a2)), V_a2)=V_a2)).
% 227.35/29.63 fof(fact_mult__smult__left, axiom, ![V_p, V_q, V_a2, T_a2]: (class_Rings_Ocomm__semiring__0(T_a2) => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a2)), c_Polynomial_Osmult(T_a2, V_a2, V_p)), V_q)=c_Polynomial_Osmult(T_a2, V_a2, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a2)), V_p), V_q)))).
% 227.35/29.63 fof(fact_mult__smult__right, axiom, ![V_q2, V_a2, V_p2, T_a2]: (class_Rings_Ocomm__semiring__0(T_a2) => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a2)), V_p2), c_Polynomial_Osmult(T_a2, V_a2, V_q2))=c_Polynomial_Osmult(T_a2, V_a2, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a2)), V_p2), V_q2)))).
% 227.35/29.63 fof(fact_one__poly__def, axiom, ![T_a2]: (class_Rings_Ocomm__semiring__1(T_a2) => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a2))=c_Polynomial_OpCons(T_a2, c_Groups_Oone__class_Oone(T_a2), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2))))).
% 227.35/29.63 fof(fact_smult__0__right, axiom, ![V_a2, T_a2]: (class_Rings_Ocomm__semiring__0(T_a2) => c_Polynomial_Osmult(T_a2, V_a2, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)))).
% 227.35/29.63 fof(fact_smult__pCons, axiom, ![V_a2, V_p2, T_a2, V_b2]: (class_Rings_Ocomm__semiring__0(T_a2) => c_Polynomial_Osmult(T_a2, V_a2, c_Polynomial_OpCons(T_a2, V_b2, V_p2))=c_Polynomial_OpCons(T_a2, hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a2), V_a2), V_b2), c_Polynomial_Osmult(T_a2, V_a2, V_p2)))).
% 227.35/29.63
% 227.35/29.63 Now clausify the problem and encode Horn clauses using encoding 3 of
% 227.35/29.63 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 227.35/29.63 We repeatedly replace C & s=t => u=v by the two clauses:
% 227.35/29.63 fresh(y, y, x1...xn) = u
% 227.35/29.63 C => fresh(s, t, x1...xn) = v
% 227.35/29.63 where fresh is a fresh function symbol and x1..xn are the free
% 227.35/29.63 variables of u and v.
% 227.35/29.63 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 227.35/29.63 input problem has no model of domain size 1).
% 227.35/29.63
% 227.35/29.63 The encoding turns the above axioms into the following unit equations and goals:
% 227.35/29.63
% 227.35/29.63 Axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1): class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 227.35/29.63 Axiom 2 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0): class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) = true2.
% 227.35/29.63 Axiom 3 (arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult): fresh1144(X, X, Y) = true2.
% 227.35/29.63 Axiom 4 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__1): fresh1120(X, X, Y) = true2.
% 227.35/29.63 Axiom 5 (fact_one__poly__def): fresh423(X, X, Y) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(Y)).
% 227.35/29.63 Axiom 6 (arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult): fresh1144(class_Rings_Ocomm__semiring__1(X), true2, X) = class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X)).
% 227.35/29.63 Axiom 7 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__1): fresh1120(class_Rings_Ocomm__semiring__1(X), true2, X) = class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X)).
% 227.35/29.63 Axiom 8 (fact_smult__0__right): fresh307(X, X, Y, Z) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(Z)).
% 227.35/29.63 Axiom 9 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J): fresh148(X, X, Y, Z) = Y.
% 227.35/29.63 Axiom 10 (fact_mult__1): fresh144(X, X, Y, Z) = Y.
% 227.35/29.63 Axiom 11 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J): fresh947(X, X, Y, Z, W) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(W), Y), Z).
% 227.35/29.63 Axiom 12 (fact_smult__0__right): fresh307(class_Rings_Ocomm__semiring__0(X), true2, Y, X) = c_Polynomial_Osmult(X, Y, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X))).
% 227.35/29.63 Axiom 13 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J): fresh148(class_Rings_Ocomm__semiring__1(X), true2, Y, X) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X), Y), c_Groups_Oone__class_Oone(X)).
% 227.35/29.63 Axiom 14 (fact_mult__1): fresh144(class_Groups_Ocomm__monoid__mult(X), true2, Y, X) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X), c_Groups_Oone__class_Oone(X)), Y).
% 227.35/29.63 Axiom 15 (fact_one__poly__def): fresh423(class_Rings_Ocomm__semiring__1(X), true2, X) = c_Polynomial_OpCons(X, c_Groups_Oone__class_Oone(X), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X))).
% 227.35/29.63 Axiom 16 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J): fresh947(class_Rings_Ocomm__semiring__1(X), true2, Y, Z, X) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X), Z), Y).
% 227.35/29.63 Axiom 17 (fact_smult__pCons): fresh290(X, X, Y, Z, W, V) = c_Polynomial_Osmult(V, W, c_Polynomial_OpCons(V, Z, Y)).
% 227.35/29.63 Axiom 18 (fact_mult__smult__right): fresh541(X, X, Y, Z, W, V) = c_Polynomial_Osmult(V, Z, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(V)), W), Y)).
% 227.35/29.63 Axiom 19 (fact_mult__smult__left): fresh542(X, X, Y, Z, W, V) = c_Polynomial_Osmult(V, W, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(V)), Z), Y)).
% 227.35/29.63 Axiom 20 (fact_mult__smult__left): fresh542(class_Rings_Ocomm__semiring__0(X), true2, Y, Z, W, X) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X)), c_Polynomial_Osmult(X, W, Z)), Y).
% 227.35/29.63 Axiom 21 (fact_mult__smult__right): fresh541(class_Rings_Ocomm__semiring__0(X), true2, Y, Z, W, X) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X)), W), c_Polynomial_Osmult(X, Z, Y)).
% 227.35/29.63 Axiom 22 (fact_smult__pCons): fresh290(class_Rings_Ocomm__semiring__0(X), true2, Y, Z, W, X) = c_Polynomial_OpCons(X, hAPP(hAPP(c_Groups_Otimes__class_Otimes(X), W), Z), c_Polynomial_Osmult(X, W, Y)).
% 227.35/29.63
% 227.35/29.63 Goal 1 (conj_0): c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, v_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))).
% 227.35/29.63 Proof:
% 227.35/29.63 c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, v_q)
% 227.35/29.63 = { by axiom 10 (fact_mult__1) R->L }
% 227.35/29.63 fresh144(true2, true2, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, v_q), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 3 (arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) R->L }
% 227.35/29.63 fresh144(fresh1144(true2, true2, tc_Complex_Ocomplex), true2, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, v_q), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) R->L }
% 227.35/29.63 fresh144(fresh1144(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), true2, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, v_q), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 6 (arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) }
% 227.35/29.63 fresh144(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, v_q), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 14 (fact_mult__1) }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, v_q))
% 227.35/29.63 = { by axiom 21 (fact_mult__smult__right) R->L }
% 227.35/29.63 fresh541(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, v_q, v_a, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex)
% 227.35/29.63 = { by axiom 2 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) }
% 227.35/29.63 fresh541(true2, true2, v_q, v_a, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), tc_Complex_Ocomplex)
% 227.35/29.63 = { by axiom 18 (fact_mult__smult__right) }
% 227.35/29.63 c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), v_q))
% 227.35/29.63 = { by axiom 19 (fact_mult__smult__left) R->L }
% 227.35/29.63 fresh542(true2, true2, v_q, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_a, tc_Complex_Ocomplex)
% 227.35/29.63 = { by axiom 2 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) R->L }
% 227.35/29.63 fresh542(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, v_q, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_a, tc_Complex_Ocomplex)
% 227.35/29.63 = { by axiom 20 (fact_mult__smult__left) }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), v_q)
% 227.35/29.63 = { by axiom 16 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) R->L }
% 227.35/29.63 fresh947(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), true2, v_q, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 7 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) R->L }
% 227.35/29.63 fresh947(fresh1120(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), true2, v_q, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) }
% 227.35/29.63 fresh947(fresh1120(true2, true2, tc_Complex_Ocomplex), true2, v_q, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 4 (arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) }
% 227.35/29.63 fresh947(true2, true2, v_q, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), tc_Polynomial_Opoly(tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 11 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))
% 227.35/29.63 = { by axiom 5 (fact_one__poly__def) R->L }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, fresh423(true2, true2, tc_Complex_Ocomplex)))
% 227.35/29.63 = { by axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) R->L }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, fresh423(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex)))
% 227.35/29.63 = { by axiom 15 (fact_one__poly__def) }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))
% 227.35/29.63 = { by axiom 17 (fact_smult__pCons) R->L }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), fresh290(true2, true2, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_a, tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 2 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) R->L }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), fresh290(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), v_a, tc_Complex_Ocomplex))
% 227.35/29.63 = { by axiom 22 (fact_smult__pCons) }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_OpCons(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_a), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))
% 227.35/29.63 = { by axiom 13 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) R->L }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_OpCons(tc_Complex_Ocomplex, fresh148(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, v_a, tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))
% 227.35/29.63 = { by axiom 1 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_OpCons(tc_Complex_Ocomplex, fresh148(true2, true2, v_a, tc_Complex_Ocomplex), c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))
% 227.35/29.63 = { by axiom 9 (fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a, c_Polynomial_Osmult(tc_Complex_Ocomplex, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))
% 227.35/29.63 = { by axiom 12 (fact_smult__0__right) R->L }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a, fresh307(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, v_a, tc_Complex_Ocomplex)))
% 227.35/29.63 = { by axiom 2 (arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a, fresh307(true2, true2, v_a, tc_Complex_Ocomplex)))
% 227.35/29.63 = { by axiom 8 (fact_smult__0__right) }
% 227.35/29.63 hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_q), c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))
% 227.35/29.63 % SZS output end Proof
% 227.35/29.63
% 227.35/29.63 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------