TSTP Solution File: SWV618-1 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWV618-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:55:00 EDT 2023
% Result : Unsatisfiable 33.05s 4.84s
% Output : CNFRefutation 33.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of clauses : 80 ( 49 unt; 6 nHn; 44 RR)
% Number of literals : 125 ( 55 equ; 52 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-4 aty)
% Number of variables : 109 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.p',cls_less__Suc__eq_2) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.Rukm396sw7/E---3.1_9232.p',clsarity_nat__Orderings_Oorder) ).
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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.p',cls_power__mult_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.p',cls_power__one_0) ).
cnf(cls_less__SucI_0,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.Rukm396sw7/E---3.1_9232.p',cls_less__SucI_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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.p',cls_root__unity_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_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.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/tmp/tmp.Rukm396sw7/E---3.1_9232.p',cls_k_I2_J_0) ).
cnf(c_0_30,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_31,axiom,
c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
cls_less__Suc__eq_2 ).
cnf(c_0_32,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder ).
cnf(c_0_33,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_34,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_35,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_36,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult ).
cnf(c_0_37,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_38,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_30,c_0_31]),c_0_32])]) ).
cnf(c_0_39,axiom,
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_less__SucI_0 ).
cnf(c_0_40,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_41,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_42,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_33,c_0_34]) ).
cnf(c_0_43,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_44,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_35,c_0_36]) ).
cnf(c_0_45,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_46,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_37,c_0_36]) ).
cnf(c_0_47,plain,
~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X1)),X1,tc_nat),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,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_49,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_40,c_0_41]),c_0_42]),c_0_42]),c_0_43])]) ).
cnf(c_0_50,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_44,c_0_45]),c_0_46]) ).
cnf(c_0_51,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_52,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_53,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_54,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add ).
cnf(c_0_55,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_56,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field ).
cnf(c_0_57,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_58,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_59,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_60,axiom,
c_FFT__Mirabelle_Oroot(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_root__nonzero_0 ).
cnf(c_0_61,plain,
~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X1))),X1,tc_nat),
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_62,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_63,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_48,c_0_49]) ).
cnf(c_0_64,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_65,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_50,c_0_51]) ).
cnf(c_0_66,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_52,c_0_34]) ).
cnf(c_0_67,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_53,c_0_54]) ).
cnf(c_0_68,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_55,c_0_56]) ).
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)
| ~ 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_57,c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_70,plain,
c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_Suc(c_Suc(X1)))),tc_nat),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,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_72,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_63,c_0_64]),c_0_49]),c_0_44]),c_0_65]),c_0_66]),c_0_67]),c_0_68]),c_0_34])]) ).
cnf(c_0_73,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_69,c_0_70]) ).
cnf(c_0_74,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_71,c_0_72]),c_0_34])]),c_0_73]) ).
cnf(c_0_75,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_76,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_77,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
cls_k_I2_J_0 ).
cnf(c_0_78,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_63,c_0_74]),c_0_66]) ).
cnf(c_0_79,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_75,c_0_74]),c_0_76]),c_0_77])]),c_0_78]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.18 % Problem : SWV618-1 : TPTP v8.1.2. Released v4.1.0.
% 0.09/0.19 % Command : run_E %s %d THM
% 0.18/0.39 % Computer : n004.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 2400
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Tue Oct 3 03:40:30 EDT 2023
% 0.18/0.40 % CPUTime :
% 0.24/0.58 Running first-order theorem proving
% 0.24/0.58 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/tmp/tmp.Rukm396sw7/E---3.1_9232.p
% 33.05/4.84 # Version: 3.1pre001
% 33.05/4.84 # Preprocessing class: FSLSSMSSSSSNFFN.
% 33.05/4.84 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.05/4.84 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 33.05/4.84 # Starting new_bool_3 with 300s (1) cores
% 33.05/4.84 # Starting new_bool_1 with 300s (1) cores
% 33.05/4.84 # Starting sh5l with 300s (1) cores
% 33.05/4.84 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 9324 completed with status 0
% 33.05/4.84 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 33.05/4.84 # Preprocessing class: FSLSSMSSSSSNFFN.
% 33.05/4.84 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.05/4.84 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 33.05/4.84 # No SInE strategy applied
% 33.05/4.84 # Search class: FGHSM-FSLM32-DFFFFFNN
% 33.05/4.84 # Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 33.05/4.84 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 125s (1) cores
% 33.05/4.84 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 125s (1) cores
% 33.05/4.84 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 125s (1) cores
% 33.05/4.84 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 125s (1) cores
% 33.05/4.84 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 125s (1) cores
% 33.05/4.84 # G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with pid 9335 completed with status 0
% 33.05/4.84 # Result found by G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y
% 33.05/4.84 # Preprocessing class: FSLSSMSSSSSNFFN.
% 33.05/4.84 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.05/4.84 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 33.05/4.84 # No SInE strategy applied
% 33.05/4.84 # Search class: FGHSM-FSLM32-DFFFFFNN
% 33.05/4.84 # Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 33.05/4.84 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 125s (1) cores
% 33.05/4.84 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 125s (1) cores
% 33.05/4.84 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 125s (1) cores
% 33.05/4.84 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 125s (1) cores
% 33.05/4.84 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 125s (1) cores
% 33.05/4.84 # Preprocessing time : 0.010 s
% 33.05/4.84 # Presaturation interreduction done
% 33.05/4.84
% 33.05/4.84 # Proof found!
% 33.05/4.84 # SZS status Unsatisfiable
% 33.05/4.84 # SZS output start CNFRefutation
% See solution above
% 33.05/4.84 # Parsed axioms : 833
% 33.05/4.84 # Removed by relevancy pruning/SinE : 0
% 33.05/4.84 # Initial clauses : 833
% 33.05/4.84 # Removed in clause preprocessing : 0
% 33.05/4.84 # Initial clauses in saturation : 833
% 33.05/4.84 # Processed clauses : 31595
% 33.05/4.84 # ...of these trivial : 496
% 33.05/4.84 # ...subsumed : 26810
% 33.05/4.84 # ...remaining for further processing : 4288
% 33.05/4.84 # Other redundant clauses eliminated : 1726
% 33.05/4.84 # Clauses deleted for lack of memory : 0
% 33.05/4.84 # Backward-subsumed : 365
% 33.05/4.84 # Backward-rewritten : 99
% 33.05/4.84 # Generated clauses : 180874
% 33.05/4.84 # ...of the previous two non-redundant : 150052
% 33.05/4.84 # ...aggressively subsumed : 0
% 33.05/4.84 # Contextual simplify-reflections : 31
% 33.05/4.84 # Paramodulations : 178884
% 33.05/4.84 # Factorizations : 30
% 33.05/4.84 # NegExts : 0
% 33.05/4.84 # Equation resolutions : 1959
% 33.05/4.84 # Total rewrite steps : 70813
% 33.05/4.84 # Propositional unsat checks : 0
% 33.05/4.84 # Propositional check models : 0
% 33.05/4.84 # Propositional check unsatisfiable : 0
% 33.05/4.84 # Propositional clauses : 0
% 33.05/4.84 # Propositional clauses after purity: 0
% 33.05/4.84 # Propositional unsat core size : 0
% 33.05/4.84 # Propositional preprocessing time : 0.000
% 33.05/4.84 # Propositional encoding time : 0.000
% 33.05/4.84 # Propositional solver time : 0.000
% 33.05/4.84 # Success case prop preproc time : 0.000
% 33.05/4.84 # Success case prop encoding time : 0.000
% 33.05/4.84 # Success case prop solver time : 0.000
% 33.05/4.84 # Current number of processed clauses : 3205
% 33.05/4.84 # Positive orientable unit clauses : 319
% 33.05/4.84 # Positive unorientable unit clauses: 24
% 33.05/4.84 # Negative unit clauses : 331
% 33.05/4.84 # Non-unit-clauses : 2531
% 33.05/4.84 # Current number of unprocessed clauses: 118626
% 33.05/4.84 # ...number of literals in the above : 461571
% 33.05/4.84 # Current number of archived formulas : 0
% 33.05/4.84 # Current number of archived clauses : 1083
% 33.05/4.84 # Clause-clause subsumption calls (NU) : 968806
% 33.05/4.84 # Rec. Clause-clause subsumption calls : 605983
% 33.05/4.84 # Non-unit clause-clause subsumptions : 11156
% 33.05/4.84 # Unit Clause-clause subsumption calls : 29772
% 33.05/4.84 # Rewrite failures with RHS unbound : 94
% 33.05/4.84 # BW rewrite match attempts : 1381
% 33.05/4.84 # BW rewrite match successes : 412
% 33.05/4.84 # Condensation attempts : 0
% 33.05/4.84 # Condensation successes : 0
% 33.05/4.84 # Termbank termtop insertions : 2792801
% 33.05/4.84
% 33.05/4.84 # -------------------------------------------------
% 33.05/4.84 # User time : 4.004 s
% 33.05/4.84 # System time : 0.088 s
% 33.05/4.84 # Total time : 4.093 s
% 33.05/4.84 # Maximum resident set size: 3256 pages
% 33.05/4.84
% 33.05/4.84 # -------------------------------------------------
% 33.05/4.84 # User time : 19.823 s
% 33.05/4.84 # System time : 0.548 s
% 33.05/4.84 # Total time : 20.372 s
% 33.05/4.84 # Maximum resident set size: 2292 pages
% 33.05/4.84 % E---3.1 exiting
% 33.05/4.84 % E---3.1 exiting
%------------------------------------------------------------------------------