TSTP Solution File: SWV706-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV706-1 : 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 : n017.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 23:05:58 EDT 2023
% Result : Unsatisfiable 210.85s 27.18s
% Output : Proof 211.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV706-1 : 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 : n017.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 : Tue Aug 29 03:42:13 EDT 2023
% 0.12/0.34 % CPUTime :
% 210.85/27.18 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 210.85/27.18
% 210.85/27.18 % SZS status Unsatisfiable
% 210.85/27.18
% 211.02/27.20 % SZS output start Proof
% 211.02/27.20 Take the following subset of the input axioms:
% 211.02/27.21 fof(cls_Suc_Ohyps_0, axiom, ![V_a, V_i]: (c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), V_a, V_i)=hAPP(c_FFT__Mirabelle_OFFT(v_ka____, V_a), V_i) | ~c_HOL_Oord__class_Oless(V_i, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))).
% 211.02/27.21 fof(cls_conjecture_1, negated_conjecture, c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)).
% 211.02/27.21 fof(cls_conjecture_2, negated_conjecture, c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), c_COMBB(v_a____, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_Complex_Ocomplex, tc_nat), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)), hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____)))), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), c_COMBB(v_a____, c_COMBB(c_Suc, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_nat, tc_nat), tc_nat, tc_Complex_Ocomplex, tc_nat), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), tc_Complex_Ocomplex)!=c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____, c_COMBB(v_a____, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_Complex_Ocomplex, tc_nat)), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)), hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____)))), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), hAPP(c_FFT__Mirabelle_OFFT(v_ka____, c_COMBB(v_a____, c_COMBB(c_Suc, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_nat, tc_nat), tc_nat, tc_Complex_Ocomplex, tc_nat)), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), tc_Complex_Ocomplex)).
% 211.02/27.21
% 211.02/27.21 Now clausify the problem and encode Horn clauses using encoding 3 of
% 211.02/27.21 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 211.02/27.21 We repeatedly replace C & s=t => u=v by the two clauses:
% 211.02/27.21 fresh(y, y, x1...xn) = u
% 211.02/27.21 C => fresh(s, t, x1...xn) = v
% 211.02/27.21 where fresh is a fresh function symbol and x1..xn are the free
% 211.02/27.21 variables of u and v.
% 211.02/27.21 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 211.02/27.21 input problem has no model of domain size 1).
% 211.02/27.21
% 211.02/27.21 The encoding turns the above axioms into the following unit equations and goals:
% 211.02/27.21
% 211.02/27.21 Axiom 1 (cls_Suc_Ohyps_0): fresh1141(X, X, Y, Z) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____, Y), Z).
% 211.02/27.21 Axiom 2 (cls_Suc_Ohyps_0): fresh1141(c_HOL_Oord__class_Oless(X, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat), true2, Y, X) = c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), Y, X).
% 211.02/27.21 Axiom 3 (cls_conjecture_1): c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat) = true2.
% 211.02/27.21
% 211.02/27.21 Lemma 4: c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), X, c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____, X), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)).
% 211.02/27.21 Proof:
% 211.02/27.21 c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), X, c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))
% 211.02/27.21 = { by axiom 2 (cls_Suc_Ohyps_0) R->L }
% 211.02/27.21 fresh1141(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat), true2, X, c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))
% 211.02/27.21 = { by axiom 3 (cls_conjecture_1) }
% 211.02/27.21 fresh1141(true2, true2, X, c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))
% 211.02/27.21 = { by axiom 1 (cls_Suc_Ohyps_0) }
% 211.02/27.21 hAPP(c_FFT__Mirabelle_OFFT(v_ka____, X), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))
% 211.02/27.21
% 211.02/27.21 Goal 1 (cls_conjecture_2): c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), c_COMBB(v_a____, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_Complex_Ocomplex, tc_nat), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)), hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____)))), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), c_COMBB(v_a____, c_COMBB(c_Suc, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_nat, tc_nat), tc_nat, tc_Complex_Ocomplex, tc_nat), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____, c_COMBB(v_a____, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_Complex_Ocomplex, tc_nat)), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)), hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____)))), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), hAPP(c_FFT__Mirabelle_OFFT(v_ka____, c_COMBB(v_a____, c_COMBB(c_Suc, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_nat, tc_nat), tc_nat, tc_Complex_Ocomplex, tc_nat)), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), tc_Complex_Ocomplex).
% 211.02/27.21 Proof:
% 211.02/27.21 c_HOL_Ominus__class_Ominus(c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), c_COMBB(v_a____, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_Complex_Ocomplex, tc_nat), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)), hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____)))), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), c_COMBB(v_a____, c_COMBB(c_Suc, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_nat, tc_nat), tc_nat, tc_Complex_Ocomplex, tc_nat), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), tc_Complex_Ocomplex)
% 211.02/27.21 = { by lemma 4 }
% 211.02/27.21 c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____, c_COMBB(v_a____, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_Complex_Ocomplex, tc_nat)), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)), hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____)))), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), c_COMBB(v_a____, c_COMBB(c_Suc, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_nat, tc_nat), tc_nat, tc_Complex_Ocomplex, tc_nat), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), tc_Complex_Ocomplex)
% 211.02/27.21 = { by lemma 4 }
% 211.02/27.21 c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_OFFT(v_ka____, c_COMBB(v_a____, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_Complex_Ocomplex, tc_nat)), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat)), hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____)))), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), hAPP(c_FFT__Mirabelle_OFFT(v_ka____, c_COMBB(v_a____, c_COMBB(c_Suc, hAPP(c_HOL_Otimes__class_Otimes(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), tc_nat, tc_nat, tc_nat), tc_nat, tc_Complex_Ocomplex, tc_nat)), c_HOL_Ominus__class_Ominus(v_i____, hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat), c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)), tc_nat)), v_ka____), tc_nat))), tc_Complex_Ocomplex)
% 211.02/27.21 % SZS output end Proof
% 211.02/27.21
% 211.02/27.21 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------