TSTP Solution File: SWV712-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV712-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 Sep 29 15:24:09 EDT 2022
% Result : Unsatisfiable 0.55s 0.67s
% Output : Proof 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 37
% Syntax : Number of formulae : 59 ( 17 unt; 22 typ; 0 def)
% Number of atoms : 97 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 108 ( 51 ~; 44 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 15 >; 13 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-5 aty)
% Number of variables : 50 ( 44 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_i_____type,type,
v_i____: $i ).
tff(c_FFT__Mirabelle_OIFFT_type,type,
c_FFT__Mirabelle_OIFFT: ( $i * $i ) > $i ).
tff(c_COMBB_type,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Suc_type,type,
c_Suc: $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
tff(v_a_____type,type,
v_a____: $i ).
tff(v_ka_____type,type,
v_ka____: $i ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(c_FFT__Mirabelle_Oroot_type,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(c_FFT__Mirabelle_OIDFT_type,type,
c_FFT__Mirabelle_OIDFT: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
tff(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
tff(c_Int_OPls_type,type,
c_Int_OPls: $i ).
tff(1,plain,
( 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)
<=> c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( 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)
<=> 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) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
tff(4,plain,
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),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [V_i: $i,V_a: $i] :
refl(
( ( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
<=> ( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
<=> ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [V_i: $i,V_a: $i] :
rewrite(
( ( ~ 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)
| ( c_FFT__Mirabelle_OIDFT(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_OIFFT(v_ka____,V_a),V_i) ) )
<=> ( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [V_i: $i,V_a: $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)
| ( c_FFT__Mirabelle_OIDFT(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_OIFFT(v_ka____,V_a),V_i) ) )
<=> ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [V_i: $i,V_a: $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)
| ( c_FFT__Mirabelle_OIDFT(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_OIFFT(v_ka____,V_a),V_i) ) )
<=> ! [V_i: $i,V_a: $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)
| ( c_FFT__Mirabelle_OIDFT(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_OIFFT(v_ka____,V_a),V_i) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
^ [V_i: $i,V_a: $i] :
rewrite(
( ( ( c_FFT__Mirabelle_OIDFT(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_OIFFT(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) )
<=> ( ~ 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)
| ( c_FFT__Mirabelle_OIDFT(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_OIFFT(v_ka____,V_a),V_i) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [V_i: $i,V_a: $i] :
( ( c_FFT__Mirabelle_OIDFT(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_OIFFT(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) )
<=> ! [V_i: $i,V_a: $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)
| ( c_FFT__Mirabelle_OIDFT(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_OIFFT(v_ka____,V_a),V_i) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [V_i: $i,V_a: $i] :
( ( c_FFT__Mirabelle_OIDFT(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_OIFFT(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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc_Ohyps_0) ).
tff(14,plain,
! [V_i: $i,V_a: $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)
| ( c_FFT__Mirabelle_OIDFT(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_OIFFT(v_ka____,V_a),V_i) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V_i: $i,V_a: $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)
| ( c_FFT__Mirabelle_OIDFT(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_OIFFT(v_ka____,V_a),V_i) ) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) ),
inference(modus_ponens,[status(thm)],[15,9]) ).
tff(17,plain,
! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,plain,
( ( ~ ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
| ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____) ) )
<=> ( ~ ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
| ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ~ ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
| ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
( ~ ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
| ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),
inference(unit_resolution,[status(thm)],[21,18,5]) ).
tff(23,plain,
hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( ~ ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
| ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____) ) )
<=> ( ~ ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
| ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ~ ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
| ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_i: $i,V_a: $i] :
( ~ c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),V_a,V_i) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,V_a),V_i) ) )
| ~ c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),tc_nat)
| ( c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____),
inference(unit_resolution,[status(thm)],[26,18,5]) ).
tff(28,plain,
hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____) = c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)) = hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)) = hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____))),
inference(monotonicity,[status(thm)],[30,23]) ).
tff(32,plain,
( ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(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),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(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),v_i____))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____))) )
<=> ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(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),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(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),v_i____))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____))) )
<=> ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(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),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(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),v_i____))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(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),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(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),v_i____))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(35,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(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),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(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),v_i____))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(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____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(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)),v_i____))),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____))),tc_Complex_Ocomplex)),v_i____)),c_FFT__Mirabelle_OIDFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),v_i____))) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),v_ka____))),tc_Complex_Ocomplex)),v_i____)),hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____))),
inference(modus_ponens,[status(thm)],[35,32]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV712-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 07:31:06 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.55/0.67 % SZS status Unsatisfiable
% 0.55/0.67 % SZS output start Proof
% See solution above
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