%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWV621-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 03:06:36 PM UTC 2026
% Result : Unsatisfiable 2.45s 0.83s
% Output : CNFRefutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of clauses : 82 ( 38 unt; 8 nHn; 34 RR)
% Number of literals : 144 ( 71 equ; 63 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-4 aty)
% Number of variables : 112 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_class__semiring_Omul__1_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_zero__neq__one_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
cnf(cls_eq__divide__imp_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,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) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(cls_inverse__eq__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_divide__inverse_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),v_n),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_geometric__sum_0,axiom,
( ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Oone__class_Oone(X1)
| c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),tc_nat,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(X2,X1),X3),c_HOL_Oone__class_Oone(X1),X1),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_geometric__sum_0) ).
cnf(cls_inverse__inverse__eq_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(cls_power__one_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X1),X2) = c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
cnf(cls_right__minus__eq_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_eq__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
cnf(cls_power__one__over_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),hAPP(c_Power_Opower__class_Opower(X2,X1),X3),X1) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(cls_root__summation_0,axiom,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__summation_0) ).
cnf(cls_k_I1_J_0,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),v_k)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_k_I1_J_0) ).
cnf(cls_k_I2_J_0,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_k,tc_nat),v_n)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_k_I2_J_0) ).
cnf(c_0_24,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Omul__1_0]) ).
cnf(c_0_25,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I12_J_0]) ).
cnf(c_0_26,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
inference(fof_simplification,[status(thm)],[cls_zero__neq__one_0]) ).
cnf(c_0_27,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_eq__divide__imp_0]) ).
cnf(c_0_28,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2 ),
c_0_24 ).
cnf(c_0_29,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_30,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2 ),
c_0_25 ).
cnf(c_0_31,plain,
( c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ozero__neq__one(X1) ),
c_0_26 ).
cnf(c_0_32,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one ).
cnf(c_0_33,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_inverse__eq__divide_0]) ).
cnf(c_0_34,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
c_0_27 ).
cnf(c_0_35,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_37,plain,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_38,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
inference(fof_simplification,[status(thm)],[cls_class__semiring_Osemiring__rules_I7_J_0]) ).
cnf(c_0_40,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1) ),
c_0_33 ).
cnf(c_0_41,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_42,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_37]),c_0_36])]),c_0_38]) ).
cnf(c_0_43,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
c_0_39 ).
cnf(c_0_44,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_divide__inverse_0]) ).
cnf(c_0_45,negated_conjecture,
c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),v_n),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_46,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Oone__class_Oone(X1)
| c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),tc_nat,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(X2,X1),X3),c_HOL_Oone__class_Oone(X1),X1),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(X1),X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_geometric__sum_0]) ).
cnf(c_0_47,plain,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36])]) ).
cnf(c_0_48,plain,
c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_36])]) ).
cnf(c_0_49,plain,
c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_43,c_0_29]) ).
cnf(c_0_50,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
c_0_44 ).
cnf(c_0_51,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ),
inference(fof_simplification,[status(thm)],[cls_inverse__inverse__eq_0]) ).
cnf(c_0_52,plain,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X1),X2) = c_HOL_Oone__class_Oone(X1) ),
inference(fof_simplification,[status(thm)],[cls_power__one_0]) ).
cnf(c_0_53,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
inference(fof_simplification,[status(thm)],[cls_right__minus__eq_1]) ).
cnf(c_0_54,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(fof_simplification,[status(thm)],[cls_eq__divide__eq_2]) ).
cnf(c_0_55,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),hAPP(c_Power_Opower__class_Opower(X2,X1),X3),X1) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1),X3) ),
inference(fof_simplification,[status(thm)],[cls_power__one__over_0]) ).
cnf(c_0_56,negated_conjecture,
c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),v_n),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
c_0_45 ).
cnf(c_0_57,plain,
( ~ class_Ring__and__Field_Ofield(X1)
| X2 = c_HOL_Oone__class_Oone(X1)
| c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(X2,X1),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),tc_nat,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(X2,X1),X3),c_HOL_Oone__class_Oone(X1),X1),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oone__class_Oone(X1),X1),X1) ),
c_0_46 ).
cnf(c_0_58,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_40]),c_0_48]),c_0_36])]),c_0_38]) ).
cnf(c_0_59,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X2,X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_36])]) ).
cnf(c_0_60,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ),
c_0_51 ).
cnf(c_0_61,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_62,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_63,plain,
( ~ class_OrderedGroup_Omonoid__mult(X1)
| hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X1),X2) = c_HOL_Oone__class_Oone(X1) ),
c_0_52 ).
cnf(c_0_64,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult ).
cnf(c_0_65,plain,
( ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1) ),
c_0_53 ).
cnf(c_0_66,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_67,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
c_0_54 ).
cnf(c_0_68,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(fof_simplification,[status(thm)],[cls_root__summation_0]) ).
cnf(c_0_69,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),hAPP(c_Power_Opower__class_Opower(X2,X1),X3),X1) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1),X1),X3) ),
c_0_55 ).
cnf(c_0_70,negated_conjecture,
hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_36])]) ).
cnf(c_0_71,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oinverse__class_Oinverse(X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_62])]) ).
cnf(c_0_72,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),v_n),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat,tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_36])]) ).
cnf(c_0_73,plain,
hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_74,plain,
c_HOL_Ominus__class_Ominus(X1,X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_36]),c_0_62])]) ).
cnf(c_0_76,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
c_0_68 ).
cnf(c_0_77,negated_conjecture,
hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_42]),c_0_71]),c_0_37]),c_0_36]),c_0_62])]) ).
cnf(c_0_78,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),v_k)),
cls_k_I1_J_0 ).
cnf(c_0_79,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_k,tc_nat),v_n)),
cls_k_I2_J_0 ).
cnf(c_0_80,negated_conjecture,
c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_70]),c_0_73]),c_0_74]),c_0_74]),c_0_75]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_79])]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV621-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 09:14:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 2.45/0.83 % Version: 3.5.1
% 2.45/0.83 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.45/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.45/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.45/0.83 % Starting new_bool_3 with 300s (1) cores
% 2.45/0.83 % Starting new_bool_1 with 300s (1) cores
% 2.45/0.83 % Starting sh5l with 300s (1) cores
% 2.45/0.83 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1395836 completed with status 0
% 2.45/0.83 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.45/0.83 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.45/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.45/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.45/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.45/0.83 % No SInE strategy applied
% 2.45/0.83 % Search class: FGHSM-FSLM32-DFFFFFNN
% 2.45/0.83 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 2.45/0.83 % Starting SubtermCWHack with 151s (1) cores
% 2.45/0.83 % Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 125s (1) cores
% 2.45/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 125s (1) cores
% 2.45/0.83 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 125s (1) cores
% 2.45/0.83 % Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 125s (1) cores
% 2.45/0.83 % G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 1395845 completed with status 0
% 2.45/0.83 % Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 2.45/0.83 % Preprocessing class: FSLSSMSSSSSNFFN.
% 2.45/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.45/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.45/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.45/0.83 % No SInE strategy applied
% 2.45/0.83 % Search class: FGHSM-FSLM32-DFFFFFNN
% 2.45/0.83 % Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 2.45/0.83 % Starting SubtermCWHack with 151s (1) cores
% 2.45/0.83 % Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 125s (1) cores
% 2.45/0.83 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 125s (1) cores
% 2.45/0.83 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 125s (1) cores
% 2.45/0.83 % Preprocessing time : 0.014 s
% 2.45/0.83 % Presaturation interreduction done
% 2.45/0.83
% 2.45/0.83 % Proof found!
% 2.45/0.83 % SZS status Unsatisfiable
% 2.45/0.83 % SZS output start CNFRefutation
% See solution above
% 2.45/0.83 % Parsed axioms : 897
% 2.45/0.83 % Removed by relevancy pruning/SinE : 0
% 2.45/0.83 % Initial clauses : 897
% 2.45/0.83 % Removed in clause preprocessing : 0
% 2.45/0.83 % Initial clauses in saturation : 897
% 2.45/0.83 % Processed clauses : 3299
% 2.45/0.83 % ...of these trivial : 280
% 2.45/0.83 % ...subsumed : 1464
% 2.45/0.83 % ...remaining for further processing : 1555
% 2.45/0.83 % Other redundant clauses eliminated : 76
% 2.45/0.83 % Clauses deleted for lack of memory : 0
% 2.45/0.83 % Backward-subsumed : 53
% 2.45/0.83 % Backward-rewritten : 30
% 2.45/0.83 % Generated clauses : 12185
% 2.45/0.83 % ...of the previous two non-redundant : 7780
% 2.45/0.83 % ...aggressively subsumed : 0
% 2.45/0.83 % Contextual simplify-reflections : 0
% 2.45/0.83 % Paramodulations : 12085
% 2.45/0.83 % Factorizations : 15
% 2.45/0.83 % NegExts : 0
% 2.45/0.83 % Equation resolutions : 85
% 2.45/0.83 % Disequality decompositions : 0
% 2.45/0.83 % Total rewrite steps : 13649
% 2.45/0.83 % ...of those cached : 12596
% 2.45/0.83 % Propositional unsat checks : 0
% 2.45/0.83 % Propositional check models : 0
% 2.45/0.83 % Propositional check unsatisfiable : 0
% 2.45/0.83 % Propositional clauses : 0
% 2.45/0.83 % Propositional clauses after purity: 0
% 2.45/0.83 % Propositional unsat core size : 0
% 2.45/0.83 % Propositional preprocessing time : 0.000
% 2.45/0.83 % Propositional encoding time : 0.000
% 2.45/0.83 % Propositional solver time : 0.000
% 2.45/0.83 % Success case prop preproc time : 0.000
% 2.45/0.83 % Success case prop encoding time : 0.000
% 2.45/0.83 % Success case prop solver time : 0.000
% 2.45/0.83 % Current number of processed clauses : 805
% 2.45/0.83 % Positive orientable unit clauses : 372
% 2.45/0.83 % Positive unorientable unit clauses: 5
% 2.45/0.83 % Negative unit clauses : 47
% 2.45/0.83 % Non-unit-clauses : 381
% 2.45/0.83 % Current number of unprocessed clauses: 5986
% 2.45/0.83 % ...number of literals in the above : 13840
% 2.45/0.83 % Current number of archived formulas : 0
% 2.45/0.83 % Current number of archived clauses : 750
% 2.45/0.83 % Clause-clause subsumption calls (NU) : 118296
% 2.45/0.83 % Rec. Clause-clause subsumption calls : 56010
% 2.45/0.83 % Non-unit clause-clause subsumptions : 966
% 2.45/0.83 % Unit Clause-clause subsumption calls : 8794
% 2.45/0.83 % Rewrite failures with RHS unbound : 29
% 2.45/0.83 % BW rewrite match attempts : 778
% 2.45/0.83 % BW rewrite match successes : 65
% 2.45/0.83 % Condensation attempts : 0
% 2.45/0.83 % Condensation successes : 0
% 2.45/0.83 % Termbank termtop insertions : 211057
% 2.45/0.83 % Search garbage collected termcells : 2161
% 2.45/0.83
% 2.45/0.83 % -------------------------------------------------
% 2.45/0.83 % User time : 0.321 s
% 2.45/0.83 % System time : 0.022 s
% 2.45/0.83 % Total time : 0.343 s
% 2.45/0.83 % Maximum resident set size: 5360 pages
% 2.45/0.83
% 2.45/0.83 % -------------------------------------------------
% 2.45/0.83 % User time : 1.360 s
% 2.45/0.83 % System time : 0.070 s
% 2.45/0.83 % Total time : 1.430 s
% 2.45/0.83 % Maximum resident set size: 5632 pages
% 2.45/0.83 % E exiting
%------------------------------------------------------------------------------