TSTP Solution File: SWW265+1 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SWW265+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 00:47:10 EDT 2022
% Result : Theorem 50.87s 50.13s
% Output : Proof 50.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW265+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : leancop_casc.sh %s %d
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 4 22:11:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 50.87/50.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 50.95/50.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 50.95/50.14
% 50.95/50.14 %-----------------------------------------------------
% 50.95/50.14 fof(conj_2, conjecture, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), v_m____)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', conj_2)).
% 50.95/50.14 fof(fact_m_I2_J, axiom, ! [_585104] : (c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _585104), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)) => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), _585104)), v_m____)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_m_I2_J)).
% 50.95/50.14 fof(fact_tw, axiom, c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_tw)).
% 50.95/50.14 fof(fact_zero__le__power, axiom, ! [_585479, _585482, _585485] : (class_Rings_Olinordered__semidom(_585485) => c_Orderings_Oord__class_Oless__eq(_585485, c_Groups_Ozero__class_Ozero(_585485), _585482) => c_Orderings_Oord__class_Oless__eq(_585485, c_Groups_Ozero__class_Ozero(_585485), hAPP(hAPP(c_Power_Opower__class_Opower(_585485), _585482), _585479))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_zero__le__power)).
% 50.95/50.14 fof(fact_norm__ge__zero, axiom, ! [_585747, _585750] : (class_RealVector_Oreal__normed__vector(_585750) => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_585750, _585747))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_norm__ge__zero)).
% 50.95/50.14 fof(fact_mult__nonneg__nonneg, axiom, ! [_585991, _585994, _585997] : (class_Rings_Oordered__cancel__semiring(_585997) => c_Orderings_Oord__class_Oless__eq(_585997, c_Groups_Ozero__class_Ozero(_585997), _585994) => c_Orderings_Oord__class_Oless__eq(_585997, c_Groups_Ozero__class_Ozero(_585997), _585991) => c_Orderings_Oord__class_Oless__eq(_585997, c_Groups_Ozero__class_Ozero(_585997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585997), _585994), _585991))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__nonneg__nonneg)).
% 50.95/50.14 fof(fact_mult__left__mono, axiom, ! [_586291, _586294, _586297, _586300] : (class_Rings_Oordered__semiring(_586300) => c_Orderings_Oord__class_Oless__eq(_586300, _586297, _586294) => c_Orderings_Oord__class_Oless__eq(_586300, c_Groups_Ozero__class_Ozero(_586300), _586291) => c_Orderings_Oord__class_Oless__eq(_586300, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586300), _586291), _586297), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586300), _586291), _586294))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', fact_mult__left__mono)).
% 50.95/50.14 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring, axiom, class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oordered__cancel__semiring)).
% 50.95/50.14 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom, axiom, class_Rings_Olinordered__semidom(tc_RealDef_Oreal), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Olinordered__semidom)).
% 50.95/50.14 fof(arity_RealDef__Oreal__Rings_Oordered__semiring, axiom, class_Rings_Oordered__semiring(tc_RealDef_Oreal), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_RealDef__Oreal__Rings_Oordered__semiring)).
% 50.95/50.14 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', arity_Complex__Ocomplex__RealVector_Oreal__normed__vector)).
% 50.95/50.14
% 50.95/50.14 cnf(1, plain, [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), v_m____))], clausify(conj_2)).
% 50.95/50.14 cnf(2, plain, [-(_63390 = _63390)], theory(equality)).
% 50.95/50.14 cnf(3, plain, [-(c_Orderings_Oord__class_Oless__eq(_63615, _63617, _63619)), c_Orderings_Oord__class_Oless__eq(_63614, _63616, _63618), _63614 = _63615, _63616 = _63617, _63618 = _63619], theory(equality)).
% 50.95/50.14 cnf(4, plain, [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _68174), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), _68174)), v_m____))], clausify(fact_m_I2_J)).
% 50.95/50.14 cnf(5, plain, [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)))], clausify(fact_tw)).
% 50.95/50.14 cnf(6, plain, [class_Rings_Olinordered__semidom(_71092), c_Orderings_Oord__class_Oless__eq(_71092, c_Groups_Ozero__class_Ozero(_71092), _71091), -(c_Orderings_Oord__class_Oless__eq(_71092, c_Groups_Ozero__class_Ozero(_71092), hAPP(hAPP(c_Power_Opower__class_Opower(_71092), _71091), _71090)))], clausify(fact_zero__le__power)).
% 50.95/50.14 cnf(7, plain, [class_RealVector_Oreal__normed__vector(_72250), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_72250, _72249)))], clausify(fact_norm__ge__zero)).
% 50.95/50.14 cnf(8, plain, [class_Rings_Oordered__cancel__semiring(_77307), c_Orderings_Oord__class_Oless__eq(_77307, c_Groups_Ozero__class_Ozero(_77307), _77306), c_Orderings_Oord__class_Oless__eq(_77307, c_Groups_Ozero__class_Ozero(_77307), _77305), -(c_Orderings_Oord__class_Oless__eq(_77307, c_Groups_Ozero__class_Ozero(_77307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_77307), _77306), _77305)))], clausify(fact_mult__nonneg__nonneg)).
% 50.95/50.14 cnf(9, plain, [class_Rings_Oordered__semiring(_77744), c_Orderings_Oord__class_Oless__eq(_77744, _77743, _77742), c_Orderings_Oord__class_Oless__eq(_77744, c_Groups_Ozero__class_Ozero(_77744), _77741), -(c_Orderings_Oord__class_Oless__eq(_77744, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_77744), _77741), _77743), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_77744), _77741), _77742)))], clausify(fact_mult__left__mono)).
% 50.95/50.14 cnf(10, plain, [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], clausify(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring)).
% 50.95/50.14 cnf(11, plain, [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], clausify(arity_RealDef__Oreal__Rings_Olinordered__semidom)).
% 50.95/50.14 cnf(12, plain, [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], clausify(arity_RealDef__Oreal__Rings_Oordered__semiring)).
% 50.95/50.14 cnf(13, plain, [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], clausify(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector)).
% 50.95/50.14
% 50.95/50.14 cnf('1',plain,[c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), v_m____))],start(1)).
% 50.95/50.14 cnf('1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____)))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), v_m____))), class_Rings_Oordered__semiring(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____))), v_m____), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____)))],extension(9,bind([[_77743, _77742, _77744, _77741], [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____))), v_m____, tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))]]))).
% 50.95/50.14 cnf('1.1.1',plain,[-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))],extension(12)).
% 50.95/50.14 cnf('1.1.2',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____))), v_m____)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____))), v_m____), tc_RealDef_Oreal = tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____))), v_m____ = v_m____],extension(3,bind([[_63614, _63615, _63616, _63617, _63618, _63619], [tc_RealDef_Oreal, tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____))), v_m____, v_m____]]))).
% 50.95/50.14 cnf('1.1.2.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____))), v_m____)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____))],extension(4,bind([[_68174], [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)]]))).
% 50.95/50.14 cnf('1.1.2.1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)))],extension(5)).
% 50.95/50.14 cnf('1.1.2.2',plain,[-(tc_RealDef_Oreal = tc_RealDef_Oreal)],extension(2,bind([[_63390], [tc_RealDef_Oreal]]))).
% 50.95/50.14 cnf('1.1.2.3',plain,[-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____))))],extension(2,bind([[_63390], [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 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____)))]]))).
% 50.95/50.14 cnf('1.1.2.4',plain,[-(v_m____ = v_m____)],extension(2,bind([[_63390], [v_m____]]))).
% 50.95/50.14 cnf('1.1.3',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____)))), class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))],extension(8,bind([[_77306, _77307, _77305], [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____), tc_RealDef_Oreal, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____)]]))).
% 50.95/50.14 cnf('1.1.3.1',plain,[-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))],extension(10)).
% 50.95/50.14 cnf('1.1.3.2',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____))), class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)],extension(7,bind([[_72249, _72250], [v_w____, tc_Complex_Ocomplex]]))).
% 50.95/50.14 cnf('1.1.3.2.1',plain,[-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))],extension(13)).
% 50.95/50.14 cnf('1.1.3.3',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), class_Rings_Olinordered__semidom(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____))],extension(6,bind([[_71090, _71092, _71091], [v_k____, tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)]]))).
% 50.95/50.14 cnf('1.1.3.3.1',plain,[-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))],extension(11)).
% 50.95/50.14 cnf('1.1.3.3.2',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)))],lemmata('1.1.3')).
% 50.95/50.14 %-----------------------------------------------------
% 50.95/50.15
% 50.95/50.15 % SZS output end Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
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