TSTP Solution File: SWV626-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV626-1 : 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 : n015.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 107.39s 17.54s
% Output : Proof 107.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV626-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.19/0.35 % Computer : n015.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Tue Aug 29 08:38:40 EDT 2023
% 0.19/0.35 % CPUTime :
% 107.39/17.54 Command-line arguments: --no-flatten-goal
% 107.39/17.54
% 107.39/17.54 % SZS status Unsatisfiable
% 107.39/17.54
% 107.39/17.55 % SZS output start Proof
% 107.39/17.55 Take the following subset of the input axioms:
% 107.97/17.55 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)))).
% 107.97/17.55 fof(cls_class__semiring_Opwr__pwr_0, axiom, ![V_q, V_p, T_a2, V_x2]: (~class_Ring__and__Field_Ocomm__semiring__1(T_a2) | c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_x2, V_p, T_a2), V_q, T_a2)=c_Power_Opower__class_Opower(V_x2, c_HOL_Otimes__class_Otimes(V_p, V_q, tc_nat), T_a2))).
% 107.97/17.55 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_k, tc_Complex_Ocomplex), v_n, 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_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)).
% 107.97/17.55 fof(cls_nat__mult__commute_0, axiom, ![V_m, V_n]: c_HOL_Otimes__class_Otimes(V_m, V_n, tc_nat)=c_HOL_Otimes__class_Otimes(V_n, V_m, tc_nat)).
% 107.97/17.55 fof(clsarity_Complex__Ocomplex__Int_Onumber__ring, axiom, class_Int_Onumber__ring(tc_Complex_Ocomplex)).
% 107.97/17.55 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, axiom, class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)).
% 107.97/17.55 fof(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, axiom, class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)).
% 107.97/17.55
% 107.97/17.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 107.97/17.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 107.97/17.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 107.97/17.55 fresh(y, y, x1...xn) = u
% 107.97/17.55 C => fresh(s, t, x1...xn) = v
% 107.97/17.55 where fresh is a fresh function symbol and x1..xn are the free
% 107.97/17.55 variables of u and v.
% 107.97/17.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 107.97/17.55 input problem has no model of domain size 1).
% 107.97/17.55
% 107.97/17.55 The encoding turns the above axioms into the following unit equations and goals:
% 107.97/17.55
% 107.97/17.55 Axiom 1 (clsarity_Complex__Ocomplex__Int_Onumber__ring): class_Int_Onumber__ring(tc_Complex_Ocomplex) = true2.
% 107.97/17.55 Axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ofield): class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) = true2.
% 107.97/17.55 Axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1): class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true2.
% 107.97/17.55 Axiom 4 (cls_nat__mult__commute_0): c_HOL_Otimes__class_Otimes(X, Y, tc_nat) = c_HOL_Otimes__class_Otimes(Y, X, tc_nat).
% 107.97/17.55 Axiom 5 (cls_class__fieldgb_Oinverse__divide_0): fresh734(X, X, Y, Z) = c_HOL_Oinverse__class_Oinverse(Z, Y).
% 107.97/17.55 Axiom 6 (cls_class__fieldgb_Oinverse__divide_0): fresh733(X, X, Y, Z) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(Y), Z, Y).
% 107.97/17.55 Axiom 7 (cls_class__fieldgb_Oinverse__divide_0): fresh733(class_Ring__and__Field_Ofield(X), true2, X, Y) = fresh734(class_Int_Onumber__ring(X), true2, X, Y).
% 107.97/17.55 Axiom 8 (cls_class__semiring_Opwr__pwr_0): fresh719(X, X, Y, Z, W, V) = c_Power_Opower__class_Opower(Z, c_HOL_Otimes__class_Otimes(W, V, tc_nat), Y).
% 107.97/17.55 Axiom 9 (cls_power__mult_0): fresh170(X, X, Y, Z, W, V) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(Z, W, Y), V, Y).
% 107.97/17.55 Axiom 10 (cls_power__divide_0): fresh853(X, X, Y, Z, W, V) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(Z, W, Y), V, Y).
% 107.97/17.55 Axiom 11 (cls_diff__divide__distrib_0): fresh691(X, X, Y, Z, W, V) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(Z, W, Y), V, Y).
% 107.97/17.55 Axiom 12 (cls_class__semiring_Opwr__pwr_0): fresh719(class_Ring__and__Field_Ocomm__semiring__1(X), true2, X, Y, Z, W) = c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(Y, Z, X), W, X).
% 107.97/17.55 Axiom 13 (cls_power__one__over_0): fresh851(X, X, Y, Z, W) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(Y), Z, Y), W, Y).
% 107.97/17.55
% 107.97/17.55 Lemma 14: fresh733(X, X, tc_Complex_Ocomplex, Y) = c_HOL_Oinverse__class_Oinverse(Y, tc_Complex_Ocomplex).
% 107.97/17.55 Proof:
% 107.97/17.55 fresh733(X, X, tc_Complex_Ocomplex, Y)
% 107.97/17.55 = { by axiom 6 (cls_class__fieldgb_Oinverse__divide_0) }
% 107.97/17.55 c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), Y, tc_Complex_Ocomplex)
% 107.97/17.55 = { by axiom 6 (cls_class__fieldgb_Oinverse__divide_0) R->L }
% 107.97/17.55 fresh733(true2, true2, tc_Complex_Ocomplex, Y)
% 107.97/17.55 = { by axiom 2 (clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) R->L }
% 107.97/17.55 fresh733(class_Ring__and__Field_Ofield(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, Y)
% 107.97/17.55 = { by axiom 7 (cls_class__fieldgb_Oinverse__divide_0) }
% 107.97/17.55 fresh734(class_Int_Onumber__ring(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, Y)
% 107.97/17.55 = { by axiom 1 (clsarity_Complex__Ocomplex__Int_Onumber__ring) }
% 107.97/17.55 fresh734(true2, true2, tc_Complex_Ocomplex, Y)
% 107.97/17.55 = { by axiom 5 (cls_class__fieldgb_Oinverse__divide_0) }
% 107.97/17.55 c_HOL_Oinverse__class_Oinverse(Y, tc_Complex_Ocomplex)
% 107.97/17.55
% 107.97/17.55 Lemma 15: fresh170(X, X, tc_Complex_Ocomplex, Y, Z, W) = fresh719(V, V, tc_Complex_Ocomplex, Y, Z, W).
% 107.97/17.55 Proof:
% 107.97/17.55 fresh170(X, X, tc_Complex_Ocomplex, Y, Z, W)
% 107.97/17.55 = { by axiom 9 (cls_power__mult_0) }
% 107.97/17.55 c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(Y, Z, tc_Complex_Ocomplex), W, tc_Complex_Ocomplex)
% 107.97/17.55 = { by axiom 12 (cls_class__semiring_Opwr__pwr_0) R->L }
% 107.97/17.55 fresh719(class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex), true2, tc_Complex_Ocomplex, Y, Z, W)
% 107.97/17.55 = { by axiom 3 (clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) }
% 107.97/17.55 fresh719(true2, true2, tc_Complex_Ocomplex, Y, Z, W)
% 107.97/17.55 = { by axiom 8 (cls_class__semiring_Opwr__pwr_0) }
% 107.97/17.55 c_Power_Opower__class_Opower(Y, c_HOL_Otimes__class_Otimes(Z, W, tc_nat), tc_Complex_Ocomplex)
% 107.97/17.55 = { by axiom 8 (cls_class__semiring_Opwr__pwr_0) R->L }
% 107.97/17.55 fresh719(V, V, tc_Complex_Ocomplex, Y, Z, W)
% 107.97/17.55
% 107.97/17.55 Lemma 16: fresh853(X, X, Y, c_HOL_Oone__class_Oone(Y), Z, W) = fresh851(V, V, Y, Z, W).
% 107.97/17.55 Proof:
% 107.97/17.55 fresh853(X, X, Y, c_HOL_Oone__class_Oone(Y), Z, W)
% 107.97/17.55 = { by axiom 10 (cls_power__divide_0) }
% 107.97/17.55 c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(Y), Z, Y), W, Y)
% 107.97/17.55 = { by axiom 13 (cls_power__one__over_0) R->L }
% 107.97/17.56 fresh851(V, V, Y, Z, W)
% 107.97/17.56
% 107.97/17.56 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_k, tc_Complex_Ocomplex), v_n, 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_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).
% 107.97/17.56 Proof:
% 107.97/17.56 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_k, tc_Complex_Ocomplex), v_n, 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)
% 107.97/17.56 = { by axiom 9 (cls_power__mult_0) R->L }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(X, X, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, v_n), 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)
% 107.97/17.56 = { by axiom 10 (cls_power__divide_0) R->L }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(X, X, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, v_n), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh853(Y, Y, tc_Complex_Ocomplex, c_HOL_Oone__class_Oone(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)
% 107.97/17.56 = { by lemma 16 }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(X, X, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, v_n), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, 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)
% 107.97/17.56 = { by axiom 6 (cls_class__fieldgb_Oinverse__divide_0) R->L }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(X, X, tc_Complex_Ocomplex, fresh733(W, W, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n)), v_k, v_n), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, 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)
% 107.97/17.56 = { by lemma 14 }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(X, X, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, v_n), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, 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)
% 107.97/17.56 = { by axiom 11 (cls_diff__divide__distrib_0) R->L }
% 107.97/17.56 fresh691(V, V, tc_Complex_Ocomplex, fresh170(X, X, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, v_n), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 107.97/17.56 = { by lemma 15 }
% 107.97/17.56 fresh691(V, V, tc_Complex_Ocomplex, fresh719(U, U, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_k, v_n), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 107.97/17.56 = { by axiom 8 (cls_class__semiring_Opwr__pwr_0) }
% 107.97/17.56 fresh691(V, V, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(v_k, v_n, tc_nat), tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 107.97/17.56 = { by axiom 4 (cls_nat__mult__commute_0) R->L }
% 107.97/17.56 fresh691(V, V, tc_Complex_Ocomplex, c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), c_HOL_Otimes__class_Otimes(v_n, v_k, tc_nat), tc_Complex_Ocomplex), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 107.97/17.56 = { by axiom 8 (cls_class__semiring_Opwr__pwr_0) R->L }
% 107.97/17.56 fresh691(V, V, tc_Complex_Ocomplex, fresh719(T, T, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 107.97/17.56 = { by lemma 15 R->L }
% 107.97/17.56 fresh691(V, V, tc_Complex_Ocomplex, fresh170(S, S, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n), v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex))
% 107.97/17.56 = { by axiom 11 (cls_diff__divide__distrib_0) }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(S, S, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, 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)
% 107.97/17.56 = { by lemma 14 R->L }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(S, S, tc_Complex_Ocomplex, fresh733(X2, X2, tc_Complex_Ocomplex, c_FFT__Mirabelle_Oroot(v_n)), v_n, v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, 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)
% 107.97/17.56 = { by axiom 6 (cls_class__fieldgb_Oinverse__divide_0) }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(S, S, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh851(Z, Z, 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)
% 107.97/17.56 = { by lemma 16 R->L }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(S, S, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, v_k), c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), tc_Complex_Ocomplex), c_HOL_Ominus__class_Ominus(fresh853(Y2, Y2, tc_Complex_Ocomplex, c_HOL_Oone__class_Oone(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)
% 107.97/17.56 = { by axiom 10 (cls_power__divide_0) }
% 107.97/17.56 c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(fresh170(S, S, tc_Complex_Ocomplex, c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(v_n), tc_Complex_Ocomplex), v_n, v_k), 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)
% 107.97/17.56 = { by axiom 9 (cls_power__mult_0) }
% 107.97/17.56 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)
% 107.97/17.56 % SZS output end Proof
% 107.97/17.56
% 107.97/17.56 RESULT: Unsatisfiable (the axioms are contradictory).
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