TSTP Solution File: SWV618-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV618-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 21:47:31 EDT 2023
% Result : Unsatisfiable 102.79s 102.90s
% Output : CNFRefutation 102.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 115
% Syntax : Number of formulae : 162 ( 47 unt; 86 typ; 0 def)
% Number of atoms : 119 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 48 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 121 ( 80 >; 41 *; 0 +; 0 <<)
% Number of predicates : 60 ( 58 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 6 con; 0-6 aty)
% Number of variables : 103 ( 17 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Power_Opower: $i > $o ).
tff(decl_23,type,
c_Power_Opower__class_Opower: ( $i * $i ) > $i ).
tff(decl_24,type,
c_Suc: $i > $i ).
tff(decl_25,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_26,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_28,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_29,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_30,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_31,type,
class_Int_Onumber: $i > $o ).
tff(decl_32,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_33,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_36,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_37,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_38,type,
tc_nat: $i ).
tff(decl_39,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_40,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_41,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_42,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_44,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_45,type,
class_Orderings_Obot: $i > $o ).
tff(decl_46,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_47,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_48,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_49,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_51,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_52,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_54,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_55,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_56,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_57,type,
c_SetInterval_Oord__class_OlessThan: ( $i * $i ) > $i ).
tff(decl_58,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_59,type,
tc_bool: $i ).
tff(decl_60,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_61,type,
c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_63,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_64,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_65,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_66,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_67,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_68,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_69,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_70,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_71,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_72,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_73,type,
hBOOL: $i > $o ).
tff(decl_74,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_75,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_76,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_77,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_79,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_80,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_81,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_82,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_83,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_84,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_85,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_86,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_87,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_88,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_89,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_90,type,
class_HOL_Oord: $i > $o ).
tff(decl_91,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_92,type,
c_Finite__Set_Osetsum: ( $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
c_List_Osko__SetInterval__Xsetsum__ivl__cong__1__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(decl_95,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_96,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
tff(decl_97,type,
tc_Complex_Ocomplex: $i ).
tff(decl_98,type,
c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_100,type,
c_Series_Osko__Series__Xseries__zero__1__1: ( $i * $i * $i ) > $i ).
tff(decl_101,type,
c_Series_Osums: ( $i * $i * $i ) > $o ).
tff(decl_102,type,
v_k: $i ).
tff(decl_103,type,
v_n: $i ).
tff(decl_104,type,
c_Complex_Oexpi: $i > $i ).
tff(decl_105,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_106,type,
tc_Int_Oint: $i ).
tff(decl_107,type,
c_fequal: ( $i * $i * $i ) > $o ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(cls_power__mult_0,axiom,
( hAPP(c_Power_Opower__class_Opower(X2,X1),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(X2,X1),X3),X1),X4)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(cls_power__one_0,axiom,
( hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X1),X2) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_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/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(cls_root__unity_0,axiom,
hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),tc_Complex_Ocomplex),X1) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__unity_0) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_less__Suc__eq_2,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
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_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
cnf(cls_divide__1_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
cnf(cls_divide_Ozero_0,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
cnf(cls_field__power__not__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| hAPP(c_Power_Opower__class_Opower(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
cnf(cls_root__cancel_0,axiom,
( hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X2),tc_Complex_Ocomplex),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(cls_root__nonzero_0,axiom,
c_FFT__Mirabelle_Oroot(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__nonzero_0) ).
cnf(cls_not__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_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/sandbox/benchmark/theBenchmark.p',cls_geometric__sum_0) ).
cnf(cls_right__inverse__eq_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
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)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__summation_0) ).
cnf(cls_k_I1_J_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),v_k,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_k_I1_J_0) ).
cnf(cls_k_I2_J_0,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_k_I2_J_0) ).
cnf(c_0_29,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_30,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_31,axiom,
( hAPP(c_Power_Opower__class_Opower(X2,X1),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat)) = hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(X2,X1),X3),X1),X4)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__mult_0 ).
cnf(c_0_32,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult ).
cnf(c_0_33,axiom,
( hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X1),X2) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__one_0 ).
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,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_36,plain,
c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_38,plain,
hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex),X3) = hAPP(c_Power_Opower__class_Opower(X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,axiom,
hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),tc_Complex_Ocomplex),X1) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_root__unity_0 ).
cnf(c_0_40,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_33,c_0_32]) ).
cnf(c_0_41,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_xt1_I9_J_0 ).
cnf(c_0_42,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_less__Suc__eq_2 ).
cnf(c_0_43,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder ).
cnf(c_0_44,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_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_conjecture_0 ).
cnf(c_0_45,plain,
hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_36]),c_0_37])]) ).
cnf(c_0_46,plain,
hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_47,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_48,axiom,
( c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__1_0 ).
cnf(c_0_49,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_eq__iff__diff__eq__0_0 ).
cnf(c_0_50,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add ).
cnf(c_0_51,axiom,
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_divide_Ozero_0 ).
cnf(c_0_52,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field ).
cnf(c_0_53,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| hAPP(c_Power_Opower__class_Opower(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_field__power__not__zero_0 ).
cnf(c_0_54,axiom,
( hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat)) = hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X2),tc_Complex_Ocomplex),X3)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_root__cancel_0 ).
cnf(c_0_55,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors ).
cnf(c_0_56,axiom,
c_FFT__Mirabelle_Oroot(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_root__nonzero_0 ).
cnf(c_0_57,plain,
~ c_HOL_Oord__class_Oless(c_Suc(X1),X1,tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_58,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
cls_not__less__eq_0 ).
cnf(c_0_59,negated_conjecture,
c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k),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(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_60,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_61,plain,
hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_62,plain,
c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_30]) ).
cnf(c_0_63,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_49,c_0_50]) ).
cnf(c_0_64,plain,
c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_65,plain,
( hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),tc_Complex_Ocomplex),X2) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),c_0_56]) ).
cnf(c_0_66,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(X1)),tc_nat),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X3
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) != c_HOL_Oone__class_Oone(X1) ),
cls_right__inverse__eq_0 ).
cnf(c_0_68,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_45]),c_0_38]),c_0_61]),c_0_62]),c_0_63]),c_0_64]),c_0_30])]) ).
cnf(c_0_69,plain,
hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),tc_Complex_Ocomplex),X2) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_30])]),c_0_69]) ).
cnf(c_0_71,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)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat) ),
cls_root__summation_0 ).
cnf(c_0_72,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),v_k,tc_nat),
cls_k_I1_J_0 ).
cnf(c_0_73,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
cls_k_I2_J_0 ).
cnf(c_0_74,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(spm,[status(thm)],[c_0_59,c_0_70]),c_0_62]) ).
cnf(c_0_75,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_71,c_0_70]),c_0_72]),c_0_73])]),c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV618-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n013.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 06:08:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 102.79/102.90 % Version : CSE_E---1.5
% 102.79/102.90 % Problem : theBenchmark.p
% 102.79/102.90 % Proof found
% 102.79/102.90 % SZS status Theorem for theBenchmark.p
% 102.79/102.90 % SZS output start Proof
% See solution above
% 102.93/102.91 % Total time : 102.303000 s
% 102.93/102.91 % SZS output end Proof
% 102.93/102.91 % Total time : 102.335000 s
%------------------------------------------------------------------------------