TSTP Solution File: ALG368-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG368-1 : 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 : n031.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 16:43:05 EDT 2023
% Result : Unsatisfiable 68.05s 9.07s
% Output : Proof 68.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG368-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 05:14:24 EDT 2023
% 0.12/0.34 % CPUTime :
% 68.05/9.07 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 68.05/9.07
% 68.05/9.07 % SZS status Unsatisfiable
% 68.05/9.07
% 68.05/9.07 % SZS output start Proof
% 68.05/9.07 Take the following subset of the input axioms:
% 68.05/9.08 fof(cls_abs__add__one__not__less__self_0, axiom, ![V_x]: ~c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_x, tc_RealDef_Oreal), c_HOL_Oone__class_Oone(tc_RealDef_Oreal), tc_RealDef_Oreal), V_x, tc_RealDef_Oreal)).
% 68.05/9.08 fof(cls_abs__not__less__zero_0, axiom, ![T_a, V_a]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a) | ~c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a, T_a), c_HOL_Ozero__class_Ozero(T_a), T_a))).
% 68.05/9.08 fof(cls_conjecture_2, negated_conjecture, ![V_xa]: (~c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(hAPP(v_x, V_xa), v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(v_z, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), V_xa, tc_RealDef_Oreal))).
% 68.05/9.08 fof(cls_diff__self_0, axiom, ![T_a2, V_a2]: (~class_OrderedGroup_Ogroup__add(T_a2) | c_HOL_Ominus__class_Ominus(V_a2, V_a2, T_a2)=c_HOL_Ozero__class_Ozero(T_a2))).
% 68.05/9.08 fof(cls_dist__complex__def_0, axiom, ![V_y, V_x2]: c_RealVector_Odist__class_Odist(V_x2, V_y, tc_Complex_Ocomplex)=c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_x2, V_y, tc_Complex_Ocomplex), tc_Complex_Ocomplex)).
% 68.05/9.08 fof(cls_dist__not__less__zero_0, axiom, ![T_a2, V_x2, V_y2]: (~class_RealVector_Ometric__space(T_a2) | ~c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(V_x2, V_y2, T_a2), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal))).
% 68.05/9.08 fof(cls_dist__self_0, axiom, ![T_a2, V_x2]: (~class_RealVector_Ometric__space(T_a2) | c_RealVector_Odist__class_Odist(V_x2, V_x2, T_a2)=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 68.05/9.08 fof(cls_ep_0, axiom, c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_e, tc_RealDef_Oreal)).
% 68.05/9.08 fof(cls_exp__gt__zero_0, axiom, ![V_x2]: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oexp(V_x2, tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 68.05/9.08 fof(cls_exp__not__eq__zero_0, axiom, ![T_a2, V_x2]: (~class_SEQ_Obanach(T_a2) | (~class_RealVector_Oreal__normed__field(T_a2) | c_Transcendental_Oexp(V_x2, T_a2)!=c_HOL_Ozero__class_Ozero(T_a2)))).
% 68.05/9.08 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)))).
% 68.05/9.08 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)))).
% 68.05/9.08 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))).
% 68.05/9.08 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)))).
% 68.05/9.08 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)))).
% 68.05/9.08 fof(cls_ln__less__self_0, axiom, ![V_x2]: (c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x2), V_x2, tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), V_x2, tc_RealDef_Oreal))).
% 68.05/9.08 fof(cls_ln__unique_0, axiom, ![V_y2]: c_Transcendental_Oln(c_Transcendental_Oexp(V_y2, tc_RealDef_Oreal))=V_y2).
% 68.05/9.08 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))).
% 68.05/9.08 fof(cls_not__exp__le__zero_0, axiom, ![V_x2]: ~c_lessequals(c_Transcendental_Oexp(V_x2, tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 68.05/9.08 fof(cls_not__exp__less__zero_0, axiom, ![V_x2]: ~c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x2, tc_RealDef_Oreal), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 68.05/9.08 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)))).
% 68.05/9.08 fof(cls_not__one__le__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_lessequals(c_HOL_Oone__class_Oone(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 68.05/9.08 fof(cls_not__one__less__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__semidom(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a2), c_HOL_Ozero__class_Ozero(T_a2), T_a2))).
% 68.05/9.08 fof(cls_not__pos__poly__0_0, axiom, ![T_a2]: (~class_Ring__and__Field_Oordered__idom(T_a2) | ~c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a2)), T_a2))).
% 68.05/9.08 fof(cls_not__real__of__nat__less__zero_0, axiom, ![V_n]: ~c_HOL_Oord__class_Oless(c_RealDef_Oreal(V_n, tc_nat), c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 68.05/9.08 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))).
% 68.05/9.08 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))).
% 68.05/9.08 fof(cls_one__neq__zero_0, axiom, ![T_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | c_HOL_Oone__class_Oone(T_a2)!=c_HOL_Ozero__class_Ozero(T_a2))).
% 68.05/9.08 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)))).
% 68.05/9.08 fof(cls_order__less__asym_H_0, axiom, ![V_b, T_a2, V_a2]: (~class_Orderings_Opreorder(T_a2) | (~c_HOL_Oord__class_Oless(V_b, V_a2, T_a2) | ~c_HOL_Oord__class_Oless(V_a2, V_b, T_a2)))).
% 68.05/9.08 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))).
% 68.05/9.08 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))).
% 68.05/9.08 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))).
% 68.05/9.08 fof(cls_real__less__def_1, axiom, ![V_x2]: ~c_HOL_Oord__class_Oless(V_x2, V_x2, tc_RealDef_Oreal)).
% 68.05/9.08 fof(cls_real__sqrt__not__eq__zero_0, axiom, ![V_x2]: (c_NthRoot_Osqrt(V_x2)!=c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), V_x2, tc_RealDef_Oreal))).
% 68.05/9.08 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))).
% 68.05/9.08 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)))).
% 68.05/9.08 fof(cls_zero__less__abs__iff_0, axiom, ![T_a2]: (~class_OrderedGroup_Opordered__ab__group__add__abs(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a2), c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a2), T_a2), T_a2))).
% 68.05/9.08 fof(cls_zero__less__dist__iff_0, axiom, ![T_a2, V_x2]: (~class_RealVector_Ometric__space(T_a2) | ~c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Odist__class_Odist(V_x2, V_x2, T_a2), tc_RealDef_Oreal))).
% 68.05/9.08 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))).
% 68.05/9.08 fof(cls_zero__neq__one_0, axiom, ![T_a2]: (~class_Ring__and__Field_Ozero__neq__one(T_a2) | c_HOL_Ozero__class_Ozero(T_a2)!=c_HOL_Oone__class_Oone(T_a2))).
% 68.05/9.08 fof(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, axiom, class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)).
% 68.05/9.08 fof(clsarity_Complex__Ocomplex__RealVector_Ometric__space, axiom, class_RealVector_Ometric__space(tc_Complex_Ocomplex)).
% 68.05/9.08 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, axiom, class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)).
% 68.05/9.08
% 68.05/9.08 Now clausify the problem and encode Horn clauses using encoding 3 of
% 68.05/9.08 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 68.05/9.08 We repeatedly replace C & s=t => u=v by the two clauses:
% 68.05/9.08 fresh(y, y, x1...xn) = u
% 68.05/9.08 C => fresh(s, t, x1...xn) = v
% 68.05/9.08 where fresh is a fresh function symbol and x1..xn are the free
% 68.05/9.08 variables of u and v.
% 68.05/9.08 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 68.05/9.08 input problem has no model of domain size 1).
% 68.05/9.08
% 68.05/9.08 The encoding turns the above axioms into the following unit equations and goals:
% 68.05/9.08
% 68.05/9.08 Axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Oidom): class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) = true2.
% 68.05/9.08 Axiom 2 (clsarity_Complex__Ocomplex__RealVector_Ometric__space): class_RealVector_Ometric__space(tc_Complex_Ocomplex) = true2.
% 68.05/9.08 Axiom 3 (clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add): class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) = true2.
% 68.05/9.08 Axiom 4 (cls_ln__unique_0): c_Transcendental_Oln(c_Transcendental_Oexp(X, tc_RealDef_Oreal)) = X.
% 68.05/9.08 Axiom 5 (cls_ln__less__self_0): fresh446(X, X, Y) = true2.
% 68.05/9.08 Axiom 6 (cls_ep_0): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_e, tc_RealDef_Oreal) = true2.
% 68.05/9.08 Axiom 7 (cls_dist__complex__def_0): c_RealVector_Odist__class_Odist(X, Y, tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X, Y, tc_Complex_Ocomplex), tc_Complex_Ocomplex).
% 68.05/9.08 Axiom 8 (cls_diff__self_0): fresh596(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 68.05/9.08 Axiom 9 (cls_dist__self_0): fresh592(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal).
% 68.05/9.08 Axiom 10 (cls_order__root_1): fresh317(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 68.05/9.08 Axiom 11 (cls_exp__gt__zero_0): c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oexp(X, tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 68.05/9.08 Axiom 12 (cls_diff__self_0): fresh596(class_OrderedGroup_Ogroup__add(X), true2, X, Y) = c_HOL_Ominus__class_Ominus(Y, Y, X).
% 68.05/9.08 Axiom 13 (cls_dist__self_0): fresh592(class_RealVector_Ometric__space(X), true2, X, Y) = c_RealVector_Odist__class_Odist(Y, Y, X).
% 68.05/9.08 Axiom 14 (cls_order__root_1): fresh317(class_Ring__and__Field_Oidom(X), true2, X, Y) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X)), Y, X).
% 68.05/9.08 Axiom 15 (cls_ln__less__self_0): fresh446(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), X, tc_RealDef_Oreal), true2, X) = c_HOL_Oord__class_Oless(c_Transcendental_Oln(X), X, tc_RealDef_Oreal).
% 68.05/9.08
% 68.05/9.08 Lemma 16: c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), X, tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(Y, Y, tc_Complex_Ocomplex).
% 68.05/9.08 Proof:
% 68.05/9.08 c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), X, tc_Complex_Ocomplex)
% 68.05/9.08 = { by axiom 14 (cls_order__root_1) R->L }
% 68.05/9.08 fresh317(class_Ring__and__Field_Oidom(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, X)
% 68.05/9.08 = { by axiom 1 (clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) }
% 68.05/9.08 fresh317(true2, true2, tc_Complex_Ocomplex, X)
% 68.05/9.08 = { by axiom 10 (cls_order__root_1) }
% 68.05/9.08 c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 68.05/9.08 = { by axiom 8 (cls_diff__self_0) R->L }
% 68.05/9.08 fresh596(true2, true2, tc_Complex_Ocomplex, Y)
% 68.05/9.08 = { by axiom 3 (clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) R->L }
% 68.05/9.08 fresh596(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, Y)
% 68.05/9.08 = { by axiom 12 (cls_diff__self_0) }
% 68.05/9.08 c_HOL_Ominus__class_Ominus(Y, Y, tc_Complex_Ocomplex)
% 68.05/9.08
% 68.05/9.08 Goal 1 (cls_conjecture_2): tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), X, tc_RealDef_Oreal), c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(hAPP(v_x, X), v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(v_z, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal)) = tuple2(true2, true2).
% 68.05/9.08 The goal is true when:
% 68.05/9.08 X = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)
% 68.05/9.08
% 68.05/9.08 Proof:
% 68.05/9.08 tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(hAPP(v_x, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(v_z, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal))
% 68.05/9.08 = { by axiom 7 (cls_dist__complex__def_0) R->L }
% 68.05/9.08 tuple2(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(hAPP(v_x, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(v_z, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal))
% 68.05/9.08 = { by axiom 4 (cls_ln__unique_0) R->L }
% 68.05/9.08 tuple2(c_HOL_Oord__class_Oless(c_Transcendental_Oln(c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(hAPP(v_x, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(v_z, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal))
% 68.05/9.08 = { by axiom 15 (cls_ln__less__self_0) R->L }
% 68.05/9.08 tuple2(fresh446(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal), true2, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(hAPP(v_x, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(v_z, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal))
% 68.05/9.08 = { by axiom 11 (cls_exp__gt__zero_0) }
% 68.05/9.08 tuple2(fresh446(true2, true2, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(hAPP(v_x, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(v_z, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal))
% 68.05/9.09 = { by axiom 5 (cls_ln__less__self_0) }
% 68.05/9.09 tuple2(true2, c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(hAPP(v_x, c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), tc_RealDef_Oreal)), v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(v_z, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal))
% 68.05/9.09 = { by lemma 16 }
% 68.05/9.09 tuple2(true2, c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(c_HOL_Ominus__class_Ominus(X, X, tc_Complex_Ocomplex), c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_HOL_Ominus__class_Ominus(v_z, v_z, tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal))
% 68.05/9.09 = { by lemma 16 }
% 68.05/9.09 tuple2(true2, c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(c_HOL_Ominus__class_Ominus(X, X, tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(X, X, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_e, tc_RealDef_Oreal))
% 68.05/9.09 = { by axiom 13 (cls_dist__self_0) R->L }
% 68.05/9.09 tuple2(true2, c_HOL_Oord__class_Oless(fresh592(class_RealVector_Ometric__space(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, c_HOL_Ominus__class_Ominus(X, X, tc_Complex_Ocomplex)), v_e, tc_RealDef_Oreal))
% 68.05/9.09 = { by axiom 2 (clsarity_Complex__Ocomplex__RealVector_Ometric__space) }
% 68.05/9.09 tuple2(true2, c_HOL_Oord__class_Oless(fresh592(true2, true2, tc_Complex_Ocomplex, c_HOL_Ominus__class_Ominus(X, X, tc_Complex_Ocomplex)), v_e, tc_RealDef_Oreal))
% 68.05/9.09 = { by axiom 9 (cls_dist__self_0) }
% 68.05/9.09 tuple2(true2, c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal), v_e, tc_RealDef_Oreal))
% 68.05/9.09 = { by axiom 6 (cls_ep_0) }
% 68.05/9.09 tuple2(true2, true2)
% 68.05/9.09 % SZS output end Proof
% 68.05/9.09
% 68.05/9.09 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------