TSTP Solution File: ALG340-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG340-1 : 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 16:43:00 EDT 2023
% Result : Unsatisfiable 44.52s 6.09s
% Output : Proof 44.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG340-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Aug 28 04:52:00 EDT 2023
% 0.11/0.31 % CPUTime :
% 44.52/6.09 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 44.52/6.09
% 44.52/6.09 % SZS status Unsatisfiable
% 44.52/6.09
% 44.52/6.10 % SZS output start Proof
% 44.52/6.10 Take the following subset of the input axioms:
% 44.52/6.10 fof(cls_add__less__cancel__right_1, axiom, ![T_a, V_a, V_b, V_c]: (~class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) | (c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a, V_c, T_a), c_HOL_Oplus__class_Oplus(V_b, V_c, T_a), T_a) | ~c_HOL_Oord__class_Oless(V_a, V_b, T_a)))).
% 44.52/6.10 fof(cls_class__semiring_Oadd__c_0, axiom, ![V_x, V_y, T_a2]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a2) | c_HOL_Oplus__class_Oplus(V_x, V_y, T_a2)=c_HOL_Oplus__class_Oplus(V_y, V_x, T_a2))).
% 44.52/6.10 fof(cls_class__semiring_Osemiring__rules_I5_J_0, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a2) | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a2), V_a2, T_a2)=V_a2)).
% 44.52/6.10 fof(cls_conjecture_1, negated_conjecture, ![V_xa]: (~c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(V_xa), tc_Complex_Ocomplex), tc_Complex_Ocomplex), V_xa, tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), V_xa, tc_RealDef_Oreal))).
% 44.52/6.10 fof(cls_less__le__not__le_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Opreorder(T_a2) | (~c_lessequals(V_y2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2)))).
% 44.52/6.10 fof(cls_linorder__antisym__conv2_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | (~c_lessequals(V_x2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2)))).
% 44.52/6.10 fof(cls_linorder__neq__iff_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Olinorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 44.52/6.10 fof(cls_linorder__not__le_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_lessequals(V_x2, V_y2, T_a2) | ~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2)))).
% 44.52/6.10 fof(cls_linorder__not__less_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2) | ~c_lessequals(V_y2, V_x2, T_a2)))).
% 44.52/6.10 fof(cls_norm__not__less__zero_0, axiom, ![T_a2, V_x2]: (~class_RealVector_Oreal__normed__vector(T_a2) | ~c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x2, T_a2), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal))).
% 44.52/6.10 fof(cls_norm__zero_0, axiom, ![T_a2]: (~class_RealVector_Oreal__normed__vector(T_a2) | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a2), T_a2)=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 44.52/6.10 fof(cls_not__less__iff__gr__or__eq_1, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Olinorder(T_a2) | (~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2) | ~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2)))).
% 44.52/6.10 fof(cls_not__square__less__zero_0, axiom, ![T_a2, V_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a2, V_a2, T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 44.52/6.10 fof(cls_not__sum__squares__lt__zero_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x2, V_x2, T_a2), c_HOL_Otimes__class_Otimes(V_y2, V_y2, T_a2), T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 44.52/6.10 fof(cls_order__less__asym_0, axiom, ![T_a2, V_x2, V_y2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_y2, V_x2, T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_y2, T_a2)))).
% 44.52/6.10 fof(cls_order__less__asym_H_0, axiom, ![T_a2, V_a2, V_b2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_b2, V_a2, T_a2) | ~c_HOL_Oord__class_Oless(V_a2, V_b2, T_a2)))).
% 44.52/6.10 fof(cls_order__less__irrefl_0, axiom, ![T_a2, V_x2]: (~class_Orderings_Opreorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 44.52/6.10 fof(cls_order__less__le_1, axiom, ![T_a2, V_x2]: (~class_Orderings_Oorder(T_a2) | ~c_HOL_Oord__class_Oless(V_x2, V_x2, T_a2))).
% 44.52/6.10 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))).
% 44.52/6.10 fof(cls_real__less__def_0, axiom, ![V_x2, V_y2]: (c_lessequals(V_x2, V_y2, tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(V_x2, V_y2, tc_RealDef_Oreal))).
% 44.52/6.10 fof(cls_real__less__def_1, axiom, ![V_x2]: ~c_HOL_Oord__class_Oless(V_x2, V_x2, tc_RealDef_Oreal)).
% 44.52/6.10 fof(cls_real__of__preal__zero__less_0, axiom, ![V_m]: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(V_m), tc_RealDef_Oreal)).
% 44.52/6.10 fof(cls_sum__squares__gt__zero__iff_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__ring__strict(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2), c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2), T_a2), T_a2))).
% 44.52/6.10 fof(cls_xt1_I9_J_0, axiom, ![T_a2, V_a2, V_b2]: (~class_Orderings_Oorder(T_a2) | (~c_HOL_Oord__class_Oless(V_a2, V_b2, T_a2) | ~c_HOL_Oord__class_Oless(V_b2, V_a2, T_a2)))).
% 44.52/6.10 fof(cls_zero__less__norm__iff_0, axiom, ![T_a2]: (~class_RealVector_Oreal__normed__vector(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a2), T_a2), tc_RealDef_Oreal))).
% 44.52/6.10 fof(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, axiom, class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)).
% 44.52/6.10 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, axiom, class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)).
% 44.52/6.10 fof(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le, axiom, class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)).
% 44.52/6.10 fof(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)).
% 44.52/6.10
% 44.52/6.10 Now clausify the problem and encode Horn clauses using encoding 3 of
% 44.52/6.10 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 44.52/6.10 We repeatedly replace C & s=t => u=v by the two clauses:
% 44.52/6.10 fresh(y, y, x1...xn) = u
% 44.52/6.10 C => fresh(s, t, x1...xn) = v
% 44.52/6.10 where fresh is a fresh function symbol and x1..xn are the free
% 44.52/6.10 variables of u and v.
% 44.52/6.10 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 44.52/6.10 input problem has no model of domain size 1).
% 44.52/6.10
% 44.52/6.10 The encoding turns the above axioms into the following unit equations and goals:
% 44.52/6.10
% 44.52/6.10 Axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) = true2.
% 44.52/6.10 Axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le): class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) = true2.
% 44.52/6.10 Axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Oidom): class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) = true2.
% 44.52/6.10 Axiom 4 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector): class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) = true2.
% 44.52/6.10 Axiom 5 (cls_norm__zero_0): fresh154(X, X, Y) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 44.52/6.10 Axiom 6 (cls_norm__zero_0): fresh154(class_RealVector_Oreal__normed__vector(X), true2, X) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X), X).
% 44.52/6.10 Axiom 7 (cls_order__root_1): fresh144(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 44.52/6.10 Axiom 8 (cls_real__less__def_0): fresh131(X, X, Y, Z) = true2.
% 44.52/6.10 Axiom 9 (cls_class__semiring_Osemiring__rules_I5_J_0): fresh33(X, X, Y, Z) = Z.
% 44.52/6.10 Axiom 10 (cls_real__of__preal__zero__less_0): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal) = true2.
% 44.52/6.10 Axiom 11 (cls_class__semiring_Oadd__c_0): fresh300(X, X, Y, Z, W) = c_HOL_Oplus__class_Oplus(W, Z, Y).
% 44.52/6.10 Axiom 12 (cls_order__root_1): fresh144(class_Ring__and__Field_Oidom(X), true2, X, Y) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X)), Y, X).
% 44.52/6.10 Axiom 13 (cls_class__semiring_Osemiring__rules_I5_J_0): fresh33(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X), Y, X).
% 44.52/6.10 Axiom 14 (cls_add__less__cancel__right_1): fresh322(X, X, Y, Z, W, V) = true2.
% 44.52/6.10 Axiom 15 (cls_class__semiring_Oadd__c_0): fresh300(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y, Z) = c_HOL_Oplus__class_Oplus(Y, Z, X).
% 44.52/6.10 Axiom 16 (cls_real__less__def_0): fresh131(c_HOL_Oord__class_Oless(X, Y, tc_RealDef_Oreal), true2, X, Y) = c_lessequals(X, Y, tc_RealDef_Oreal).
% 44.52/6.10 Axiom 17 (cls_add__less__cancel__right_1): fresh323(X, X, Y, Z, W, V) = c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(Z, W, Y), c_HOL_Oplus__class_Oplus(V, W, Y), Y).
% 44.52/6.10 Axiom 18 (cls_add__less__cancel__right_1): fresh323(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X), true2, X, Y, Z, W) = fresh322(c_HOL_Oord__class_Oless(Y, W, X), true2, X, Y, Z, W).
% 44.52/6.10
% 44.52/6.10 Lemma 19: c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), X, tc_RealDef_Oreal) = X.
% 44.52/6.10 Proof:
% 44.52/6.10 c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), X, tc_RealDef_Oreal)
% 44.52/6.10 = { by axiom 13 (cls_class__semiring_Osemiring__rules_I5_J_0) R->L }
% 44.52/6.10 fresh33(class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, X)
% 44.52/6.10 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) }
% 44.52/6.10 fresh33(true2, true2, tc_RealDef_Oreal, X)
% 44.52/6.10 = { by axiom 9 (cls_class__semiring_Osemiring__rules_I5_J_0) }
% 44.52/6.10 X
% 44.52/6.10
% 44.52/6.10 Goal 1 (cls_conjecture_1): tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), X, tc_RealDef_Oreal), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(X), tc_Complex_Ocomplex), tc_Complex_Ocomplex), X, tc_RealDef_Oreal)) = tuple2(true2, true2).
% 44.52/6.10 The goal is true when:
% 44.52/6.10 X = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)
% 44.52/6.10
% 44.52/6.10 Proof:
% 44.52/6.10 tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.10 = { by axiom 11 (cls_class__semiring_Oadd__c_0) R->L }
% 44.94/6.10 tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), fresh300(true2, true2, tc_RealDef_Oreal, c_RealDef_Oreal__of__preal(X), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)), tc_RealDef_Oreal), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.10 = { by axiom 1 (clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) R->L }
% 44.94/6.10 tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), fresh300(class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_RealDef_Oreal__of__preal(X), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)), tc_RealDef_Oreal), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.10 = { by axiom 15 (cls_class__semiring_Oadd__c_0) }
% 44.94/6.10 tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(c_RealDef_Oreal__of__preal(X), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.10 = { by lemma 19 R->L }
% 44.94/6.10 tuple2(c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(c_RealDef_Oreal__of__preal(X), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.10 = { by axiom 17 (cls_add__less__cancel__right_1) R->L }
% 44.94/6.10 tuple2(fresh323(true2, true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X)), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.10 = { by axiom 2 (clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) R->L }
% 44.94/6.10 tuple2(fresh323(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X)), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.10 = { by axiom 18 (cls_add__less__cancel__right_1) }
% 44.94/6.10 tuple2(fresh322(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X)), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.10 = { by axiom 10 (cls_real__of__preal__zero__less_0) }
% 44.94/6.10 tuple2(fresh322(true2, true2, tc_RealDef_Oreal, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X)), c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.10 = { by axiom 14 (cls_add__less__cancel__right_1) }
% 44.94/6.11 tuple2(true2, c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal)), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.11 = { by axiom 12 (cls_order__root_1) R->L }
% 44.94/6.11 tuple2(true2, c_lessequals(c_RealVector_Onorm__class_Onorm(fresh144(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal))), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.11 = { by axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) }
% 44.94/6.11 tuple2(true2, c_lessequals(c_RealVector_Onorm__class_Onorm(fresh144(true2, true2, tc_Complex_Ocomplex, v_x(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal))), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.11 = { by axiom 7 (cls_order__root_1) }
% 44.94/6.11 tuple2(true2, c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.11 = { by axiom 6 (cls_norm__zero_0) R->L }
% 44.94/6.11 tuple2(true2, c_lessequals(fresh154(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.11 = { by axiom 4 (clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) }
% 44.94/6.11 tuple2(true2, c_lessequals(fresh154(true2, true2, tc_Complex_Ocomplex), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.11 = { by axiom 5 (cls_norm__zero_0) }
% 44.94/6.11 tuple2(true2, c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), tc_RealDef_Oreal))
% 44.94/6.11 = { by lemma 19 }
% 44.94/6.11 tuple2(true2, c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal))
% 44.94/6.11 = { by axiom 16 (cls_real__less__def_0) R->L }
% 44.94/6.11 tuple2(true2, fresh131(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X), tc_RealDef_Oreal), true2, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X)))
% 44.94/6.11 = { by axiom 10 (cls_real__of__preal__zero__less_0) }
% 44.94/6.11 tuple2(true2, fresh131(true2, true2, c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal__of__preal(X)))
% 44.94/6.11 = { by axiom 8 (cls_real__less__def_0) }
% 44.94/6.11 tuple2(true2, true2)
% 44.94/6.11 % SZS output end Proof
% 44.94/6.11
% 44.94/6.11 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------