TSTP Solution File: SWV621-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 21:47:32 EDT 2023
% Result : Unsatisfiable 0.57s 1.15s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 105
% Syntax : Number of formulae : 135 ( 27 unt; 87 typ; 0 def)
% Number of atoms : 81 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 36 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 121 ( 81 >; 40 *; 0 +; 0 <<)
% Number of predicates : 59 ( 57 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 6 con; 0-6 aty)
% Number of variables : 55 ( 3 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_nat: $i ).
tff(decl_23,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_24,type,
c_HOL_Oord__class_Oless: ( $i * $i ) > $i ).
tff(decl_25,type,
c_Suc: $i > $i ).
tff(decl_26,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_27,type,
hBOOL: $i > $o ).
tff(decl_28,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_29,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_30,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_31,type,
c_lessequals: ( $i * $i ) > $i ).
tff(decl_32,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_34,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_35,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_36,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_37,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_39,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_40,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_41,type,
class_Int_Onumber: $i > $o ).
tff(decl_42,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_44,type,
c_Power_Opower__class_Opower: ( $i * $i ) > $i ).
tff(decl_45,type,
class_Power_Opower: $i > $o ).
tff(decl_46,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_47,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_48,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_49,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_50,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_51,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_52,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_53,type,
class_Orderings_Obot: $i > $o ).
tff(decl_54,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_55,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_56,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
tc_bool: $i ).
tff(decl_58,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_59,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_60,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_61,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_62,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_63,type,
c_SetInterval_Oord__class_OlessThan: ( $i * $i ) > $i ).
tff(decl_64,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_66,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_67,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_68,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_69,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_70,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_71,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_72,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_73,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_74,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_75,type,
class_SEQ_Obanach: $i > $o ).
tff(decl_76,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_77,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(decl_78,type,
v_n: $i ).
tff(decl_79,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_80,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_81,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_82,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_83,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_84,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_85,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_86,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_87,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_88,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_89,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_90,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_91,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_92,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_93,type,
class_HOL_Oord: $i > $o ).
tff(decl_94,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_95,type,
c_Finite__Set_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_97,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_98,type,
c_Series_Osums: ( $i * $i * $i ) > $o ).
tff(decl_99,type,
c_Series_Osko__Series__Xseries__zero__1__1: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
tff(decl_101,type,
tc_Complex_Ocomplex: $i ).
tff(decl_102,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_103,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_104,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
v_k: $i ).
tff(decl_106,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_107,type,
tc_Int_Oint: $i ).
tff(decl_108,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_inverse__eq__iff__eq_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oinverse__class_Oinverse(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_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(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,
( 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)
| X2 = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_geometric__sum_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_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
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_inverse__1_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
cnf(cls_class__semiring_Opwr__pwr_0,axiom,
( hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(X2,X1),X3),X1),X4) = hAPP(c_Power_Opower__class_Opower(X2,X1),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_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(cls_nat__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
cnf(cls_power__inverse_0,axiom,
( c_HOL_Oinverse__class_Oinverse(hAPP(c_Power_Opower__class_Opower(X2,X1),X3),X1) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X1),X1),X3)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
cnf(cls_inverse__eq__divide_0,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
cnf(cls_eq__divide__eq_2,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
cnf(cls_root__summation_0,axiom,
( 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)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2)) ),
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_18,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(X2,X1) != c_HOL_Oinverse__class_Oinverse(X3,X1) ),
cls_inverse__eq__iff__eq_0 ).
cnf(c_0_19,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_20,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_21,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),
cls_conjecture_0 ).
cnf(c_0_22,axiom,
( 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)
| X2 = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_geometric__sum_0 ).
cnf(c_0_23,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_24,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus__eq_1 ).
cnf(c_0_25,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_26,plain,
( X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,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_18,c_0_19]),c_0_20])]) ).
cnf(c_0_27,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_inverse__1_0 ).
cnf(c_0_28,axiom,
( hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(X2,X1),X3),X1),X4) = hAPP(c_Power_Opower__class_Opower(X2,X1),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__pwr_0 ).
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,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
cls_nat__mult__commute_0 ).
cnf(c_0_31,negated_conjecture,
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),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_32,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_24,c_0_25]) ).
cnf(c_0_33,plain,
( X1 = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(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_26,c_0_27]),c_0_19])]) ).
cnf(c_0_34,axiom,
( c_HOL_Oinverse__class_Oinverse(hAPP(c_Power_Opower__class_Opower(X2,X1),X3),X1) = hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X2,X1),X1),X3)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_power__inverse_0 ).
cnf(c_0_35,axiom,
( c_HOL_Oinverse__class_Oinverse(X2,X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_inverse__eq__divide_0 ).
cnf(c_0_36,negated_conjecture,
c_HOL_Oinverse__class_Odivide(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),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != 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),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_28]),c_0_29])]),c_0_30]),c_0_31]),c_0_32]),c_0_31]) ).
cnf(c_0_37,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_eq__divide__eq_2 ).
cnf(c_0_38,plain,
( hAPP(c_Power_Opower__class_Opower(X1,tc_Complex_Ocomplex),X2) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) != 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_33,c_0_34]),c_0_19]),c_0_20])]) ).
cnf(c_0_39,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(spm,[status(thm)],[c_0_31,c_0_35]),c_0_23])]) ).
cnf(c_0_40,negated_conjecture,
c_HOL_Oinverse__class_Odivide(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),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != 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),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_35]),c_0_23])]) ).
cnf(c_0_41,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_37,c_0_23]),c_0_20])]) ).
cnf(c_0_42,axiom,
( 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)
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(X2,tc_nat),X1))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X2)) ),
cls_root__summation_0 ).
cnf(c_0_43,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(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,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_45,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_k,tc_nat),v_n)),
cls_k_I2_J_0 ).
cnf(c_0_46,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)],[c_0_40,c_0_41]) ).
cnf(c_0_47,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_42,c_0_43]),c_0_44]),c_0_45])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 03:59:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 start to proof: theBenchmark
% 0.57/1.15 % Version : CSE_E---1.5
% 0.57/1.15 % Problem : theBenchmark.p
% 0.57/1.15 % Proof found
% 0.57/1.15 % SZS status Theorem for theBenchmark.p
% 0.57/1.15 % SZS output start Proof
% See solution above
% 0.57/1.16 % Total time : 0.513000 s
% 0.57/1.16 % SZS output end Proof
% 0.57/1.16 % Total time : 0.544000 s
%------------------------------------------------------------------------------