%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV712-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 : Tue Sep 29 01:19:19 PM UTC 2026
% Result : Unsatisfiable 4.44s 1.37s
% Output : Refutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 19 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 13 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 14 ( 3 avg)
% 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 : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f722,axiom,
! [X0,X1] :
( 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____),X0,X1) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc_Ohyps_0) ).
fof(f782,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(f872,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),hAPP(c_Suc,X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
fof(f873,plain,
! [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) ),
inference(reorient_equations,[],[f872]) ).
fof(f912,negated_conjecture,
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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f925,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(f1027,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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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____)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(superposition,[],[f912,f873]) ).
fof(f1030,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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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(forward_subsumption_resolution,[],[f1027,f925]) ).
fof(f1035,plain,
( 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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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____)))
| ~ 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(superposition,[],[f1030,f722]) ).
fof(f1036,plain,
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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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(forward_subsumption_resolution,[],[f1035,f782]) ).
fof(f1038,plain,
( 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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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),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_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Suc,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____)))
| ~ 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(superposition,[],[f1036,f722]) ).
fof(f1039,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(trivial_inequality_removal,[],[f1038]) ).
fof(f1040,plain,
$false,
inference(forward_subsumption_resolution,[],[f1039,f782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV712-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 12:20:49 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.44/1.37 % (128151)Input is clausal, will run a generic CNF schedule.
% 4.44/1.37 % (128158)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3998157660:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.44/1.37 % (128162)dis-21_1_sil=8000:lcm=predicate:random_seed=1945059931:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.44/1.37 % (128159)lrs+10_1_sil=8000:sp=occurrence:random_seed=2105415261:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.44/1.37 % (128157)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2830180637:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.44/1.37 % (128161)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=502644045:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.44/1.37 % (128156)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=807490617:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.44/1.37 % (128160)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3187295246:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.44/1.37 % (128162)Instruction limit reached!
% 4.44/1.37 % (128162)------------------------------
% 4.44/1.37 % (128162)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.37 % (128162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.37 % (128162)CaDiCaL version: 2.1.3
% 4.44/1.37 % (128162)Termination reason: Instruction limit
% 4.44/1.37 % (128162)Termination phase: Saturation
% 4.44/1.37 % (128162)Time elapsed: 0.066 s
% 4.44/1.37 % (128162)Peak memory usage: 89 MB
% 4.44/1.37 % (128162)Instructions burned: 118 (million)
% 4.44/1.37 % (128160)Instruction limit reached!
% 4.44/1.37 % (128160)------------------------------
% 4.44/1.37 % (128160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.37 % (128160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.37 % (128160)CaDiCaL version: 2.1.3
% 4.44/1.37 % (128160)Termination reason: Instruction limit
% 4.44/1.37 % (128160)Termination phase: Saturation
% 4.44/1.37 % (128160)Time elapsed: 0.068 s
% 4.44/1.37 % (128160)Peak memory usage: 89 MB
% 4.44/1.37 % (128160)Instructions burned: 115 (million)
% 4.44/1.37 % (128159)Instruction limit reached!
% 4.44/1.37 % (128159)------------------------------
% 4.44/1.37 % (128159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.37 % (128159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.37 % (128159)CaDiCaL version: 2.1.3
% 4.44/1.37 % (128159)Termination reason: Instruction limit
% 4.44/1.37 % (128159)Termination phase: Saturation
% 4.44/1.37 % (128159)Time elapsed: 0.068 s
% 4.44/1.37 % (128159)Peak memory usage: 89 MB
% 4.44/1.37 % (128159)Instructions burned: 108 (million)
% 4.44/1.37 % (128161)Instruction limit reached!
% 4.44/1.37 % (128161)------------------------------
% 4.44/1.37 % (128161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.37 % (128161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.37 % (128161)CaDiCaL version: 2.1.3
% 4.44/1.37 % (128161)Termination reason: Instruction limit
% 4.44/1.37 % (128161)Termination phase: Saturation
% 4.44/1.37 % (128161)Time elapsed: 0.116 s
% 4.44/1.37 % (128161)Peak memory usage: 90 MB
% 4.44/1.37 % (128161)Instructions burned: 180 (million)
% 4.44/1.37 % (128171)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=260367849:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.44/1.37 % (128172)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3850346822:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.44/1.37 % (128170)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=773323013:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.44/1.37 % (128170)First to succeed.
% 4.44/1.37 % (128170)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-128151"
% 4.44/1.37 % (128173)lrs+10_64_to=lpo:sil=8000:random_seed=3684052281:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 4.44/1.37 % (128171)Instruction limit reached!
% 4.44/1.37 % (128171)------------------------------
% 4.44/1.37 % (128171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.37 % (128171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.37 % (128171)CaDiCaL version: 2.1.3
% 4.44/1.37 % (128171)Termination reason: Instruction limit
% 4.44/1.37 % (128171)Termination phase: Saturation
% 4.44/1.37 % (128171)Time elapsed: 0.095 s
% 4.44/1.37 % (128171)Peak memory usage: 91 MB
% 4.44/1.37 % (128171)Instructions burned: 191 (million)
% 4.44/1.37 % (128172)Instruction limit reached!
% 4.44/1.37 % (128172)------------------------------
% 4.44/1.37 % (128172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.37 % (128172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.37 % (128172)CaDiCaL version: 2.1.3
% 4.44/1.37 % (128172)Termination reason: Instruction limit
% 4.44/1.37 % (128172)Termination phase: Saturation
% 4.44/1.37 % (128172)Time elapsed: 0.105 s
% 4.44/1.37 % (128172)Peak memory usage: 90 MB
% 4.44/1.37 % (128172)Instructions burned: 221 (million)
% 4.44/1.37 % (128173)Instruction limit reached!
% 4.44/1.37 % (128173)------------------------------
% 4.44/1.37 % (128173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.37 % (128173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.37 % (128173)CaDiCaL version: 2.1.3
% 4.44/1.37 % (128173)Termination reason: Instruction limit
% 4.44/1.37 % (128173)Termination phase: Saturation
% 4.44/1.37 % (128173)Time elapsed: 0.078 s
% 4.44/1.37 % (128173)Peak memory usage: 90 MB
% 4.44/1.37 % (128173)Instructions burned: 127 (million)
% 4.44/1.37 % (128158)Also succeeded, but the first one will report.
% 4.44/1.37 % (128178)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1260250861:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 4.44/1.37 % (128179)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=445908342:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 4.44/1.37 % (128170)Refutation found. Thanks to Tanya!
% 4.44/1.37 % SZS status Unsatisfiable for theBenchmark
% 4.44/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 5.36/1.58 % (128170)------------------------------
% 5.36/1.58 % (128170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.36/1.58 % (128170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.36/1.58 % (128170)CaDiCaL version: 2.1.3
% 5.36/1.58 % (128170)Termination reason: Refutation
% 5.36/1.58 % (128170)Time elapsed: 0.015 s
% 5.36/1.58 % (128170)Peak memory usage: 89 MB
% 5.36/1.58 % (128170)Instructions burned: 25 (million)
% 5.36/1.58 % (128170)------------------------------
% 5.36/1.58 % (128170)------------------------------
% 5.36/1.58 % (128151)Success in time 0.701 s
% 5.36/1.58 % Vampire exiting
%------------------------------------------------------------------------------