TSTP Solution File: SWV627-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV627-1 : 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 : n018.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 : Thu Aug 31 23:05:40 EDT 2023
% Result : Unsatisfiable 60.09s 8.03s
% Output : Proof 60.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV627-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 07:53:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 60.09/8.03 Command-line arguments: --no-flatten-goal
% 60.09/8.03
% 60.09/8.03 % SZS status Unsatisfiable
% 60.09/8.03
% 60.09/8.04 % SZS output start Proof
% 60.09/8.04 Take the following subset of the input axioms:
% 60.09/8.04 fof(cls_class__fieldgb_Oinverse__divide_0, axiom, ![T_a, V_x]: (~class_Ring__and__Field_Ofield(T_a) | (~class_Int_Onumber__ring(T_a) | c_HOL_Oinverse__class_Oinverse(V_x, T_a)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a), V_x, T_a)))).
% 60.09/8.04 fof(cls_conjecture_0, negated_conjecture, c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 60.09/8.04 fof(cls_diff__divide__distrib_0, axiom, ![V_a, V_b, V_c, T_a2]: (~class_Ring__and__Field_Ofield(T_a2) | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a, V_b, T_a2), V_c, T_a2)=c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_a, V_c, T_a2), c_HOL_Oinverse__class_Odivide(V_b, V_c, T_a2), T_a2))).
% 60.09/8.04 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))).
% 60.09/8.04 fof(cls_inverse__1_0, axiom, ![T_a2]: (~class_Ring__and__Field_Odivision__ring(T_a2) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a2), T_a2)=c_HOL_Oone__class_Oone(T_a2))).
% 60.09/8.04 fof(cls_power__inverse_0, axiom, ![V_n, T_a2, V_a2]: (~class_Ring__and__Field_Odivision__ring(T_a2) | (~class_Ring__and__Field_Odivision__by__zero(T_a2) | c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a2, V_n, T_a2), T_a2)=c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a2, T_a2), V_n, T_a2)))).
% 60.09/8.04 fof(cls_power__one_0, axiom, ![V_n2, T_a2]: (~class_OrderedGroup_Omonoid__mult(T_a2) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a2), V_n2, T_a2)=c_HOL_Oone__class_Oone(T_a2))).
% 60.09/8.04 fof(cls_root__unity_0, axiom, ![V_n2]: c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n2), V_n2, tc_Complex_Ocomplex)=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)).
% 60.09/8.04 fof(clsarity_Complex__Ocomplex__Int_Onumber__ring, axiom, class_Int_Onumber__ring(tc_Complex_Ocomplex)).
% 60.09/8.04 fof(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, axiom, class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)).
% 60.09/8.04 fof(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, axiom, class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)).
% 60.09/8.04 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, axiom, class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)).
% 60.09/8.04 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring, axiom, class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)).
% 60.09/8.04 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, axiom, class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)).
% 60.09/8.04
% 60.09/8.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 60.09/8.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 60.09/8.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 60.09/8.04 fresh(y, y, x1...xn) = u
% 60.09/8.04 C => fresh(s, t, x1...xn) = v
% 60.09/8.04 where fresh is a fresh function symbol and x1..xn are the free
% 60.09/8.04 variables of u and v.
% 60.09/8.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 60.09/8.04 input problem has no model of domain size 1).
% 60.09/8.04
% 60.09/8.04 The encoding turns the above axioms into the following unit equations and goals:
% 60.09/8.04
% 60.09/8.04 Axiom 1 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult): class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) = true2.
% 60.09/8.04 Axiom 2 (clsarity_Complex__Ocomplex__Int_Onumber__ring): class_Int_Onumber__ring(tc_Complex_Ocomplex) = true2.
% 60.09/8.04 Axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring): class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) = true2.
% 60.09/8.04 Axiom 4 (clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add): class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) = true2.
% 60.09/8.04 Axiom 5 (clsarity_Complex__Ocomplex__Ring__and__Field_Ofield): class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) = true2.
% 60.09/8.04 Axiom 6 (clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero): class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) = true2.
% 60.09/8.04 Axiom 7 (cls_inverse__1_0): fresh332(X, X, Y) = c_HOL_Oone__class_Oone(Y).
% 60.09/8.04 Axiom 8 (cls_class__fieldgb_Oinverse__divide_0): fresh456(X, X, Y, Z) = c_HOL_Oinverse__class_Oinverse(Z, Y).
% 60.09/8.04 Axiom 9 (cls_diff__self_0): fresh436(X, X, Y, Z) = c_HOL_Ozero__class_Ozero(Y).
% 60.09/8.04 Axiom 10 (cls_inverse__1_0): fresh332(class_Ring__and__Field_Odivision__ring(X), true2, X) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X), X).
% 60.09/8.04 Axiom 11 (cls_power__one_0): fresh85(X, X, Y, Z) = c_HOL_Oone__class_Oone(Y).
% 60.09/8.04 Axiom 12 (cls_root__unity_0): c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X), X, tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 60.09/8.04 Axiom 13 (cls_class__fieldgb_Oinverse__divide_0): fresh457(X, X, Y, Z) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(Y), Z, Y).
% 60.09/8.04 Axiom 14 (cls_class__fieldgb_Oinverse__divide_0): fresh457(class_Ring__and__Field_Ofield(X), true2, X, Y) = fresh456(class_Int_Onumber__ring(X), true2, X, Y).
% 60.09/8.04 Axiom 15 (cls_diff__self_0): fresh436(class_OrderedGroup_Ogroup__add(X), true2, X, Y) = c_HOL_Ominus__class_Ominus(Y, Y, X).
% 60.09/8.04 Axiom 16 (cls_power__one_0): fresh85(class_OrderedGroup_Omonoid__mult(X), true2, X, Y) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X), Y, X).
% 60.09/8.04 Axiom 17 (cls_power__inverse_0): fresh94(X, X, Y, Z, W) = c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(Z, W, Y), Y).
% 60.09/8.04 Axiom 18 (cls_power__inverse_0): fresh93(X, X, Y, Z, W) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(Z, Y), W, Y).
% 60.09/8.04 Axiom 19 (cls_power__inverse_0): fresh94(class_Ring__and__Field_Odivision__ring(X), true2, X, Y, Z) = fresh93(class_Ring__and__Field_Odivision__by__zero(X), true2, X, Y, Z).
% 60.09/8.04 Axiom 20 (cls_diff__divide__distrib_0): fresh437(X, X, Y, Z, W, V) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(Z, W, Y), V, Y).
% 60.09/8.04 Axiom 21 (cls_diff__divide__distrib_0): fresh437(class_Ring__and__Field_Ofield(X), true2, X, Y, Z, W) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(Y, W, X), c_HOL_Oinverse__class_Odivide(Z, W, X), X).
% 60.09/8.04
% 60.09/8.04 Lemma 22: fresh457(X, X, tc_Complex_Ocomplex, Y) = c_HOL_Oinverse__class_Oinverse(Y, tc_Complex_Ocomplex).
% 60.09/8.04 Proof:
% 60.09/8.04 fresh457(X, X, tc_Complex_Ocomplex, Y)
% 60.09/8.04 = { by axiom 13 (cls_class__fieldgb_Oinverse__divide_0) }
% 60.09/8.04 c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), Y, tc_Complex_Ocomplex)
% 60.09/8.04 = { by axiom 13 (cls_class__fieldgb_Oinverse__divide_0) R->L }
% 60.09/8.04 fresh457(true2, true2, tc_Complex_Ocomplex, Y)
% 60.09/8.04 = { by axiom 5 (clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) R->L }
% 60.09/8.04 fresh457(class_Ring__and__Field_Ofield(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, Y)
% 60.09/8.04 = { by axiom 14 (cls_class__fieldgb_Oinverse__divide_0) }
% 60.09/8.04 fresh456(class_Int_Onumber__ring(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, Y)
% 60.09/8.04 = { by axiom 2 (clsarity_Complex__Ocomplex__Int_Onumber__ring) }
% 60.09/8.04 fresh456(true2, true2, tc_Complex_Ocomplex, Y)
% 60.09/8.04 = { by axiom 8 (cls_class__fieldgb_Oinverse__divide_0) }
% 60.09/8.05 c_HOL_Oinverse__class_Oinverse(Y, tc_Complex_Ocomplex)
% 60.09/8.05
% 60.09/8.05 Lemma 23: fresh93(X, X, tc_Complex_Ocomplex, Y, Z) = fresh94(W, W, tc_Complex_Ocomplex, Y, Z).
% 60.09/8.05 Proof:
% 60.09/8.05 fresh93(X, X, tc_Complex_Ocomplex, Y, Z)
% 60.09/8.05 = { by axiom 18 (cls_power__inverse_0) }
% 60.09/8.05 c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(Y, tc_Complex_Ocomplex), Z, tc_Complex_Ocomplex)
% 60.09/8.05 = { by axiom 18 (cls_power__inverse_0) R->L }
% 60.09/8.05 fresh93(true2, true2, tc_Complex_Ocomplex, Y, Z)
% 60.09/8.05 = { by axiom 6 (clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) R->L }
% 60.09/8.05 fresh93(class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, Y, Z)
% 60.09/8.05 = { by axiom 19 (cls_power__inverse_0) R->L }
% 60.09/8.05 fresh94(class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, Y, Z)
% 60.09/8.05 = { by axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) }
% 60.09/8.05 fresh94(true2, true2, tc_Complex_Ocomplex, Y, Z)
% 60.09/8.05 = { by axiom 17 (cls_power__inverse_0) }
% 60.09/8.05 c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(Y, Z, tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 60.09/8.05 = { by axiom 17 (cls_power__inverse_0) R->L }
% 60.09/8.05 fresh94(W, W, tc_Complex_Ocomplex, Y, Z)
% 60.09/8.05
% 60.09/8.05 Goal 1 (cls_conjecture_0): c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 60.09/8.05 Proof:
% 60.09/8.05 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 60.09/8.05 = { by axiom 13 (cls_class__fieldgb_Oinverse__divide_0) R->L }
% 60.09/8.05 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(fresh457(X, X, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n)), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 60.09/8.05 = { by axiom 13 (cls_class__fieldgb_Oinverse__divide_0) R->L }
% 60.09/8.05 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(fresh457(X, X, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n)), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(fresh457(Y, Y, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n)), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 60.09/8.05 = { by lemma 22 }
% 60.09/8.05 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(fresh457(Y, Y, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n)), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 60.09/8.05 = { by lemma 22 }
% 60.09/8.05 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 60.09/8.05 = { by axiom 18 (cls_power__inverse_0) R->L }
% 60.09/8.05 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(fresh93(Z, Z, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 60.09/8.05 = { by axiom 18 (cls_power__inverse_0) R->L }
% 60.09/8.05 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(fresh93(Z, Z, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh93(W, W, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 60.09/8.05 = { by axiom 20 (cls_diff__divide__distrib_0) R->L }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(fresh93(Z, Z, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh93(W, W, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by lemma 23 }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(fresh94(V, V, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh93(W, W, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by lemma 23 }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(fresh94(V, V, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_n), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 17 (cls_power__inverse_0) }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n), v_n, tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 12 (cls_root__unity_0) }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 10 (cls_inverse__1_0) R->L }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(fresh332(class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(fresh332(true2, true2, tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 7 (cls_inverse__1_0) }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), v_k, tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 16 (cls_power__one_0) R->L }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, fresh85(class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 1 (clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, fresh85(true2, true2, tc_Complex_Ocomplex, v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 11 (cls_power__one_0) }
% 60.09/8.05 fresh437(true2, true2, tc_Complex_Ocomplex, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 5 (clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) R->L }
% 60.09/8.05 fresh437(class_Ring__and__Field_Ofield(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 21 (cls_diff__divide__distrib_0) }
% 60.09/8.05 c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex)
% 60.09/8.05 = { by axiom 15 (cls_diff__self_0) R->L }
% 60.09/8.05 fresh436(class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 4 (clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) }
% 60.09/8.05 fresh436(true2, true2, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh94(U, U, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 60.09/8.05 = { by axiom 9 (cls_diff__self_0) }
% 60.09/8.05 c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
% 60.09/8.05 % SZS output end Proof
% 60.09/8.05
% 60.09/8.05 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------