TSTP Solution File: ALG401-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG401-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : 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 : Wed Aug 30 16:43:11 EDT 2023
% Result : Unsatisfiable 100.09s 13.14s
% Output : Proof 100.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ALG401-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.09 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.27 % Computer : n032.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8042.1875MB
% 0.10/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Aug 28 04:31:00 EDT 2023
% 0.10/0.27 % CPUTime :
% 100.09/13.14 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 100.09/13.14
% 100.09/13.14 % SZS status Unsatisfiable
% 100.09/13.14
% 100.09/13.15 % SZS output start Proof
% 100.09/13.15 Take the following subset of the input axioms:
% 100.09/13.15 fof(cls_CHAINED_0_01, axiom, v_s____=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))).
% 100.09/13.15 fof(cls_class__semiring_Omul__c_0, axiom, ![T_a, V_x, V_y]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a) | c_HOL_Otimes__class_Otimes(V_x, V_y, T_a)=c_HOL_Otimes__class_Otimes(V_y, V_x, T_a))).
% 100.09/13.15 fof(cls_class__semiring_Osemiring__rules_I10_J_0, axiom, ![V_a, T_a2]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a2) | c_HOL_Otimes__class_Otimes(V_a, c_HOL_Ozero__class_Ozero(T_a2), T_a2)=c_HOL_Ozero__class_Ozero(T_a2))).
% 100.09/13.15 fof(cls_conjecture_0, negated_conjecture, c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)!=c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(v_a____, c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)).
% 100.09/13.15 fof(cls_kas_I4_J_0, axiom, ![V_z]: c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), V_z, tc_Complex_Ocomplex)=c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_z, v_k____, tc_Complex_Ocomplex), c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____, v_s____, tc_Complex_Ocomplex), V_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)).
% 100.09/13.15 fof(cls_monoid__add__class_Oadd__0__right_0, axiom, ![T_a2, V_a2]: (~class_OrderedGroup_Omonoid__add(T_a2) | c_HOL_Oplus__class_Oplus(V_a2, c_HOL_Ozero__class_Ozero(T_a2), T_a2)=V_a2)).
% 100.09/13.15 fof(cls_order__root_1, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Oidom(T_a2) | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)), V_a2, T_a2)=c_HOL_Ozero__class_Ozero(T_a2))).
% 100.09/13.15 fof(cls_poly__pCons_0, axiom, ![V_p, T_a2, V_a2, V_x2]: (~class_Ring__and__Field_Ocomm__semiring__0(T_a2) | c_Polynomial_Opoly(c_Polynomial_OpCons(V_a2, V_p, T_a2), V_x2, T_a2)=c_HOL_Oplus__class_Oplus(V_a2, c_HOL_Otimes__class_Otimes(V_x2, c_Polynomial_Opoly(V_p, V_x2, T_a2), T_a2), T_a2))).
% 100.09/13.15 fof(cls_r01_0, axiom, c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex)=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)).
% 100.09/13.15 fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add, axiom, class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)).
% 100.09/13.15 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0, axiom, class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)).
% 100.09/13.15 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 100.09/13.15 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, axiom, class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)).
% 100.09/13.15
% 100.09/13.15 Now clausify the problem and encode Horn clauses using encoding 3 of
% 100.09/13.15 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 100.09/13.15 We repeatedly replace C & s=t => u=v by the two clauses:
% 100.09/13.15 fresh(y, y, x1...xn) = u
% 100.09/13.15 C => fresh(s, t, x1...xn) = v
% 100.09/13.15 where fresh is a fresh function symbol and x1..xn are the free
% 100.09/13.15 variables of u and v.
% 100.09/13.15 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 100.09/13.15 input problem has no model of domain size 1).
% 100.09/13.15
% 100.09/13.15 The encoding turns the above axioms into the following unit equations and goals:
% 100.09/13.15
% 100.09/13.15 Axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 100.09/13.15 Axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0): class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) = true2.
% 100.09/13.15 Axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Oidom): class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) = true2.
% 100.09/13.15 Axiom 4 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add): class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) = true2.
% 100.09/13.15 Axiom 5 (cls_CHAINED_0_01): v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 100.09/13.15 Axiom 6 (cls_class__semiring_Osemiring__rules_I10_J_0): fresh742(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 100.09/13.15 Axiom 7 (cls_order__root_1): fresh294(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 100.09/13.15 Axiom 8 (cls_monoid__add__class_Oadd__0__right_0): fresh11(X, X, Y, Z) = Z.
% 100.09/13.15 Axiom 9 (cls_class__semiring_Omul__c_0): fresh747(X, X, Y, Z, W) = c_HOL_Otimes__class_Otimes(W, Z, Y).
% 100.09/13.15 Axiom 10 (cls_class__semiring_Osemiring__rules_I10_J_0): fresh742(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y) = c_HOL_Otimes__class_Otimes(Y, c_HOL_Ozero__class_Ozero(X), X).
% 100.09/13.15 Axiom 11 (cls_order__root_1): fresh294(class_Ring__and__Field_Oidom(X), true2, X, Y) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X)), Y, X).
% 100.09/13.15 Axiom 12 (cls_monoid__add__class_Oadd__0__right_0): fresh11(class_OrderedGroup_Omonoid__add(X), true2, X, Y) = c_HOL_Oplus__class_Oplus(Y, c_HOL_Ozero__class_Ozero(X), X).
% 100.09/13.15 Axiom 13 (cls_class__semiring_Omul__c_0): fresh747(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y, Z) = c_HOL_Otimes__class_Otimes(Y, Z, X).
% 100.09/13.15 Axiom 14 (cls_poly__pCons_0): fresh269(X, X, Y, Z, W, V) = c_Polynomial_Opoly(c_Polynomial_OpCons(Z, W, Y), V, Y).
% 100.09/13.15 Axiom 15 (cls_poly__pCons_0): fresh269(class_Ring__and__Field_Ocomm__semiring__0(X), true2, X, Y, Z, W) = c_HOL_Oplus__class_Oplus(Y, c_HOL_Otimes__class_Otimes(W, c_Polynomial_Opoly(Z, W, X), X), X).
% 100.09/13.15 Axiom 16 (cls_r01_0): c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 100.09/13.16 Axiom 17 (cls_kas_I4_J_0): c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), X, tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X, v_k____, tc_Complex_Ocomplex), c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____, v_s____, tc_Complex_Ocomplex), X, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex).
% 100.09/13.16
% 100.09/13.16 Goal 1 (cls_conjecture_0): c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(v_a____, c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex).
% 100.09/13.16 Proof:
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 17 (cls_kas_I4_J_0) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_q____, tc_Complex_Ocomplex), c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____, v_s____, tc_Complex_Ocomplex), v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 16 (cls_r01_0) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____, v_s____, tc_Complex_Ocomplex), v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 14 (cls_poly__pCons_0) R->L }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), fresh269(true2, true2, tc_Complex_Ocomplex, v_a____, v_s____, v_w____), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) R->L }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), fresh269(class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_a____, v_s____, v_w____), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 15 (cls_poly__pCons_0) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_a____, c_HOL_Otimes__class_Otimes(v_w____, c_Polynomial_Opoly(v_s____, v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 5 (cls_CHAINED_0_01) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_a____, c_HOL_Otimes__class_Otimes(v_w____, c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_w____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 11 (cls_order__root_1) R->L }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_a____, c_HOL_Otimes__class_Otimes(v_w____, fresh294(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_w____), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_a____, c_HOL_Otimes__class_Otimes(v_w____, fresh294(true2, true2, tc_Complex_Ocomplex, v_w____), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 7 (cls_order__root_1) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_a____, c_HOL_Otimes__class_Otimes(v_w____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 10 (cls_class__semiring_Osemiring__rules_I10_J_0) R->L }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_a____, fresh742(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_w____), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_a____, fresh742(true2, true2, tc_Complex_Ocomplex, v_w____), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 6 (cls_class__semiring_Osemiring__rules_I10_J_0) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(v_a____, c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 12 (cls_monoid__add__class_Oadd__0__right_0) R->L }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), fresh11(class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_a____), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 4 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), fresh11(true2, true2, tc_Complex_Ocomplex, v_a____), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 8 (cls_monoid__add__class_Oadd__0__right_0) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), v_a____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 13 (cls_class__semiring_Omul__c_0) R->L }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), fresh747(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), v_a____), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), fresh747(true2, true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), v_a____), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 = { by axiom 9 (cls_class__semiring_Omul__c_0) }
% 100.09/13.16 c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(v_a____, c_Power_Opower__class_Opower(v_w____, v_k____, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 100.09/13.16 % SZS output end Proof
% 100.09/13.16
% 100.09/13.16 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------