%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWV716-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 : Thu Sep 24 03:06:45 PM UTC 2026
% Result : Unsatisfiable 9.61s 7.25s
% Output : CNFRefutation 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 15 ( 11 unt; 0 nHn; 10 RR)
% Number of literals : 19 ( 11 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-5 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Suc_Ohyps_0,axiom,
( ~ c_HOL_Oord__class_Oless(X2,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____),X1,X2) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc_Ohyps_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_HOL_Ominus__class_Ominus(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),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),c_FFT__Mirabelle_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),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_numeral__2__eq__2_0,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/sandbox/benchmark/theBenchmark.p',cls_numeral__2__eq__2_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_4,plain,
( ~ c_HOL_Oord__class_Oless(X2,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____),X1,X2) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X1),X2) ),
inference(fof_simplification,[status(thm)],[cls_Suc_Ohyps_0]) ).
cnf(c_0_5,negated_conjecture,
c_HOL_Ominus__class_Ominus(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),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),c_FFT__Mirabelle_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),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_6,plain,
( ~ c_HOL_Oord__class_Oless(X2,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____),X1,X2) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X1),X2) ),
c_0_4 ).
cnf(c_0_7,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))),
cls_numeral__2__eq__2_0 ).
cnf(c_0_8,negated_conjecture,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat),
cls_conjecture_1 ).
cnf(c_0_9,negated_conjecture,
c_HOL_Ominus__class_Ominus(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),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),c_FFT__Mirabelle_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),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(hAPP(c_FFT__Mirabelle_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),hAPP(c_FFT__Mirabelle_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)),c_HOL_Ominus__class_Ominus(v_i____,hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_ka____),tc_nat))),tc_Complex_Ocomplex),
c_0_5 ).
cnf(c_0_10,plain,
( ~ c_HOL_Oord__class_Oless(X2,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____),X1,X2) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7]) ).
cnf(c_0_11,negated_conjecture,
c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(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),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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_7]),c_0_7]) ).
cnf(c_0_12,negated_conjecture,
c_HOL_Ominus__class_Ominus(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),c_HOL_Ominus__class_Ominus(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)),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)),c_HOL_Ominus__class_Ominus(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),c_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex) != c_HOL_Ominus__class_Ominus(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)),c_HOL_Ominus__class_Ominus(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)),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)),c_HOL_Ominus__class_Ominus(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))),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)),c_HOL_Ominus__class_Ominus(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))),tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]) ).
cnf(c_0_13,negated_conjecture,
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____),X1,c_HOL_Ominus__class_Ominus(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)) = hAPP(c_FFT__Mirabelle_OIFFT(v_ka____,X1),c_HOL_Ominus__class_Ominus(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(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV716-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/5.46 % Computer : n006.cluster.edu
% 0.20/5.46 % Model : x86_64 x86_64
% 0.20/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.46 % Memory : 8046.5625MB
% 0.20/5.46 % OS : Linux 6.8.0-71-generic
% 0.20/5.46 % CPULimit : 300
% 0.20/5.46 % WCLimit : 300
% 0.20/5.46 % DateTime : Mon Sep 21 09:21:20 UTC 2026
% 0.20/5.46 % CPUTime :
% 0.20/5.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/5.52 Running first-order theorem proving
% 0.24/5.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.61/7.25 % Version: 3.5.1
% 9.61/7.25 % Preprocessing class: FMLMSMSMSSSNFFN.
% 9.61/7.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.61/7.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.61/7.25 % Starting new_bool_3 with 300s (1) cores
% 9.61/7.25 % Starting new_bool_1 with 300s (1) cores
% 9.61/7.25 % Starting sh5l with 300s (1) cores
% 9.61/7.25 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2509111 completed with status 0
% 9.61/7.25 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 9.61/7.25 % Preprocessing class: FMLMSMSMSSSNFFN.
% 9.61/7.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.61/7.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.61/7.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.61/7.25 % No SInE strategy applied
% 9.61/7.25 % Search class: FGHSM-SMLM32-DFFFFFNN
% 9.61/7.25 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 9.61/7.25 % Starting SubtermCWHack with 136s (1) cores
% 9.61/7.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 9.61/7.25 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 9.61/7.25 % Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 113s (1) cores
% 9.61/7.25 % Starting G-E--_208_B07CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 113s (1) cores
% 9.61/7.25 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 2509120 completed with status 0
% 9.61/7.25 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 9.61/7.25 % Preprocessing class: FMLMSMSMSSSNFFN.
% 9.61/7.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.61/7.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.61/7.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.61/7.25 % No SInE strategy applied
% 9.61/7.25 % Search class: FGHSM-SMLM32-DFFFFFNN
% 9.61/7.25 % Scheduled 13 strats onto 5 cores with 1500 seconds (1500 total)
% 9.61/7.25 % Starting SubtermCWHack with 136s (1) cores
% 9.61/7.25 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 9.61/7.25 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 113s (1) cores
% 9.61/7.25 % Preprocessing time : 0.030 s
% 9.61/7.25
% 9.61/7.25 % Proof found!
% 9.61/7.25 % SZS status Unsatisfiable
% 9.61/7.25 % SZS output start CNFRefutation
% See solution above
% 9.61/7.25 % Parsed axioms : 1575
% 9.61/7.25 % Removed by relevancy pruning/SinE : 0
% 9.61/7.25 % Initial clauses : 1575
% 9.61/7.25 % Removed in clause preprocessing : 1
% 9.61/7.25 % Initial clauses in saturation : 1574
% 9.61/7.25 % Processed clauses : 3982
% 9.61/7.25 % ...of these trivial : 121
% 9.61/7.25 % ...subsumed : 1538
% 9.61/7.25 % ...remaining for further processing : 2323
% 9.61/7.25 % Other redundant clauses eliminated : 105
% 9.61/7.25 % Clauses deleted for lack of memory : 0
% 9.61/7.25 % Backward-subsumed : 5
% 9.61/7.25 % Backward-rewritten : 15
% 9.61/7.25 % Generated clauses : 34021
% 9.61/7.25 % ...of the previous two non-redundant : 28004
% 9.61/7.25 % ...aggressively subsumed : 0
% 9.61/7.25 % Contextual simplify-reflections : 3
% 9.61/7.25 % Paramodulations : 33870
% 9.61/7.25 % Factorizations : 14
% 9.61/7.25 % NegExts : 0
% 9.61/7.25 % Equation resolutions : 137
% 9.61/7.25 % Disequality decompositions : 0
% 9.61/7.25 % Total rewrite steps : 26711
% 9.61/7.25 % ...of those cached : 24621
% 9.61/7.25 % Propositional unsat checks : 0
% 9.61/7.25 % Propositional check models : 0
% 9.61/7.25 % Propositional check unsatisfiable : 0
% 9.61/7.25 % Propositional clauses : 0
% 9.61/7.25 % Propositional clauses after purity: 0
% 9.61/7.25 % Propositional unsat core size : 0
% 9.61/7.25 % Propositional preprocessing time : 0.000
% 9.61/7.25 % Propositional encoding time : 0.000
% 9.61/7.25 % Propositional solver time : 0.000
% 9.61/7.25 % Success case prop preproc time : 0.000
% 9.61/7.25 % Success case prop encoding time : 0.000
% 9.61/7.25 % Success case prop solver time : 0.000
% 9.61/7.25 % Current number of processed clauses : 2303
% 9.61/7.25 % Positive orientable unit clauses : 600
% 9.61/7.25 % Positive unorientable unit clauses: 8
% 9.61/7.25 % Negative unit clauses : 650
% 9.61/7.25 % Non-unit-clauses : 1045
% 9.61/7.25 % Current number of unprocessed clauses: 25566
% 9.61/7.25 % ...number of literals in the above : 63946
% 9.61/7.25 % Current number of archived formulas : 0
% 9.61/7.25 % Current number of archived clauses : 21
% 9.61/7.25 % Clause-clause subsumption calls (NU) : 215452
% 9.61/7.25 % Rec. Clause-clause subsumption calls : 93362
% 9.61/7.25 % Non-unit clause-clause subsumptions : 343
% 9.61/7.25 % Unit Clause-clause subsumption calls : 205061
% 9.61/7.25 % Rewrite failures with RHS unbound : 6
% 9.61/7.25 % BW rewrite match attempts : 5874
% 9.61/7.25 % BW rewrite match successes : 73
% 9.61/7.25 % Condensation attempts : 0
% 9.61/7.25 % Condensation successes : 0
% 9.61/7.25 % Termbank termtop insertions : 820296
% 9.61/7.25 % Search garbage collected termcells : 3158
% 9.61/7.25
% 9.61/7.25 % -------------------------------------------------
% 9.61/7.25 % User time : 1.526 s
% 9.61/7.25 % System time : 0.066 s
% 9.61/7.25 % Total time : 1.592 s
% 9.61/7.25 % Maximum resident set size: 6808 pages
% 9.61/7.25
% 9.61/7.25 % -------------------------------------------------
% 9.61/7.25 % User time : 7.544 s
% 9.61/7.25 % System time : 0.295 s
% 9.61/7.25 % Total time : 7.839 s
% 9.61/7.25 % Maximum resident set size: 5888 pages
% 9.61/7.25 % E exiting
%------------------------------------------------------------------------------