%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV702-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:24:02 PM UTC 2026
% Result : Unsatisfiable 45.92s 7.33s
% Output : CNFRefutation 45.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 23 unt; 0 def)
% Number of atoms : 49 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-5 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f407,axiom,
c_HOL_Oone__class_Oone(tc_nat) = hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
fof(f408,plain,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
inference(reorient_equations,[],[f407]) ).
fof(f1148,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__2__eq__2_0) ).
fof(f1149,plain,
hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
inference(reorient_equations,[],[f1148]) ).
fof(f1229,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,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____),X0,X1) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc_Ohyps_0) ).
fof(f1232,axiom,
! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).
fof(f1241,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/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
fof(f1335,axiom,
! [X2,X0,X1] :
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f1370,negated_conjecture,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),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),v_i____)),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____)))),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____),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_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)),v_i____)),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____)))),v_i____)),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)),v_i____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1387,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1469,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
tcf(c_1237,negated_conjecture,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),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),v_i____)),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____)))),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____),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_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)),v_i____)),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____)))),v_i____)),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)),v_i____))),
inference(cnf_transformation,[],[f1370]) ).
tcf(c_1322,plain,
hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
inference(cnf_transformation,[],[f1149]) ).
tcf(c_1373,plain,
hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
inference(cnf_transformation,[],[f408]) ).
tcf(c_1441,plain,
! [X0: $i,X1: $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____),X1,X0) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X1),X0) )
| ~ c_HOL_Oord__class_Oless(X0,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(cnf_transformation,[],[f1229]) ).
tcf(c_1447,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1469]) ).
tcf(c_1453,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(cnf_transformation,[],[f1241]) ).
tcf(c_1671,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(cnf_transformation,[],[f1387]) ).
tcf(c_1679,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f1335]) ).
tcf(c_1698,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X2)) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f1232]) ).
tcf(c_2651,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X2)) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_1698]) ).
tcf(c_2679,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_1679]) ).
tcf(c_2917,plain,
! [X0: $i,X1: $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____),X1,X0) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X1),X0) )
| ~ c_HOL_Oord__class_Oless(X0,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(prop_impl_just,[status(thm)],[c_1441]) ).
tcf(c_6735,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),
inference(light_normalisation,[status(thm)],[c_1322,c_1373]) ).
tcf(c_6736,plain,
c_HOL_Oord__class_Oless(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat),
inference(demodulation,[status(thm)],[c_1453,c_6735]) ).
tcf(c_8772,plain,
! [X0: $i,X1: $i] :
( ( c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),X1,X0) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X1),X0) )
| ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
inference(light_normalisation,[status(thm)],[c_2917,c_6735]) ).
tcf(c_8975,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)))),v_i____)),c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(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_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____)))),v_i____)),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____))),
inference(light_normalisation,[status(thm)],[c_1237,c_6735]) ).
tcf(c_9901,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X2)) )
| ( X0 != tc_nat ) ),
inference(resolution_lifted,[status(thm)],[c_2651,c_1671]) ).
tcf(c_9902,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),X1)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),X0),hAPP(c_Suc,X1)),
inference(unflattening,[status(thm)],[c_9901]) ).
tcf(c_10159,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),X2) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X2),X1) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2679,c_1447]) ).
tcf(c_10160,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),X0),
inference(unflattening,[status(thm)],[c_10159]) ).
tcf(c_17206,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),v_i____)),c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(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_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),v_i____)),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____))),
inference(demodulation,[status(thm)],[c_8975,c_9902,c_10160]) ).
tcf(c_17661,plain,
! [X0: $i,X1: $i] :
( ( c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),X1,X0) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X1),X0) )
| ~ c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),tc_nat) ),
inference(prop_impl_just,[status(thm)],[c_8772]) ).
tcf(c_83463,plain,
! [X0: $i] : c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),X0,v_i____) = hAPP(c_FFT__Mirabelle_OFFT(v_ka____,X0),v_i____),
inference(superposition,[status(thm)],[c_6736,c_17661]) ).
tcf(c_83509,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),v_i____)),c_FFT__Mirabelle_ODFT(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),v_ka____),c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(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_OFFT(v_ka____,c_COMBB(v_a____,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(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_FFT__Mirabelle_Oroot(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),hAPP(c_Suc,v_ka____)))),v_i____)),hAPP(c_FFT__Mirabelle_OFFT(v_ka____,c_COMBB(v_a____,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat)),v_i____))),
inference(demodulation,[status(thm)],[c_17206,c_83463]) ).
tcf(c_84169,plain,
$false,
inference(ground_joinability,[status(thm)],[c_83509,c_83463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV702-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 20:58:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 45.92/7.33 % SZS status Started for theBenchmark.p
% 45.92/7.33 % SZS status Unsatisfiable for theBenchmark.p
% 45.92/7.33
% 45.92/7.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 45.92/7.33
% 45.92/7.33 % ------ iProver source info
% 45.92/7.33
% 45.92/7.33 % git: date: 2026-07-19 20:42:38 +0200
% 45.92/7.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 45.92/7.33 % git: non_committed_changes: false
% 45.92/7.33
% 45.92/7.33 % ------ Parsing...% successful
% 45.92/7.33
% 45.92/7.33
% 45.92/7.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 45.92/7.33
% 45.92/7.33 % ------ Preprocessing... sup_sim: 120 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 113 sf_s rm: 10 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e %
% 45.92/7.33
% 45.92/7.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 45.92/7.33
% 45.92/7.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 45.92/7.33 % ------ Proving...
% 45.92/7.33 % ------ Problem Properties
% 45.92/7.33
% 45.92/7.33 %
% 45.92/7.33 % clauses 534
% 45.92/7.33 % conjectures 0
% 45.92/7.33 % EPR 28
% 45.92/7.33 % Horn 435
% 45.92/7.33 % unary 254
% 45.92/7.33 % binary 160
% 45.92/7.33 % lits 954
% 45.92/7.33 % lits eq 449
% 45.92/7.33 % fd_pure 0
% 45.92/7.33 % fd_pseudo 0
% 45.92/7.33 % fd_cond 61
% 45.92/7.33 % fd_pseudo_cond 25
% 45.92/7.33 % AC symbols 0
% 45.92/7.33
% 45.92/7.33 % ------ Schedule dynamic 5 is on
% 45.92/7.33
% 45.92/7.33 % ------ no conjectures: strip conj schedule
% 45.92/7.33
% 45.92/7.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 45.92/7.33
% 45.92/7.33
% 45.92/7.33 % ------
% 45.92/7.33 % Current options:
% 45.92/7.33 % ------
% 45.92/7.33
% 45.92/7.33
% 45.92/7.33 %
% 45.92/7.33
% 45.92/7.33 % ------ Proving...
% 45.92/7.33 %
% 45.92/7.33
% 45.92/7.33 % SZS status Unsatisfiable for theBenchmark.p
% 45.92/7.33
% 45.92/7.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 45.92/7.33
% 45.92/7.33
%------------------------------------------------------------------------------