TSTP Solution File: SWV621-1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 19:55:01 EDT 2023
% Result : Unsatisfiable 2.23s 0.83s
% Output : CNFRefutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of clauses : 67 ( 37 unt; 6 nHn; 31 RR)
% Number of literals : 109 ( 54 equ; 43 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 : 80 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_class__semiring_Omul__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_class__semiring_Omul__1_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/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_zero__neq__one_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_zero__neq__one_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(cls_eq__divide__imp_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_eq__divide__imp_0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
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.LIi3Bqf4eS/E---3.1_23827.p',cls_inverse__eq__divide_0) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_divide__inverse_0,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.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/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.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/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_geometric__sum_0) ).
cnf(cls_inverse__inverse__eq_0,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_inverse__inverse__eq_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.LIi3Bqf4eS/E---3.1_23827.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.LIi3Bqf4eS/E---3.1_23827.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
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.LIi3Bqf4eS/E---3.1_23827.p',cls_power__one_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
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/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_right__minus__eq_1) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
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/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_eq__divide__eq_2) ).
cnf(cls_power__one__over_0,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_power__one__over_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)
| ~ 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/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.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/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.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/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p',cls_k_I2_J_0) ).
cnf(c_0_24,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__1_0 ).
cnf(c_0_25,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_26,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I12_J_0 ).
cnf(c_0_27,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
cls_zero__neq__one_0 ).
cnf(c_0_28,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one ).
cnf(c_0_29,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X2,X1),X2,X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_eq__divide__imp_0 ).
cnf(c_0_30,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_24,c_0_25]) ).
cnf(c_0_31,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield ).
cnf(c_0_32,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_26,c_0_25]) ).
cnf(c_0_33,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,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_35,plain,
( c_HOL_Oinverse__class_Odivide(X1,X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_36,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_29,c_0_32]),c_0_31])]),c_0_33]) ).
cnf(c_0_37,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I7_J_0 ).
cnf(c_0_38,plain,
( 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)
| X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_31])]) ).
cnf(c_0_39,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_34,c_0_36]),c_0_31])]) ).
cnf(c_0_40,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_37,c_0_25]) ).
cnf(c_0_41,axiom,
( c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_divide__inverse_0 ).
cnf(c_0_42,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_43,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_44,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_38,c_0_34]),c_0_39]),c_0_31])]),c_0_33]) ).
cnf(c_0_45,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_40,c_0_41]),c_0_31])]) ).
cnf(c_0_46,axiom,
( c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__inverse__eq_0 ).
cnf(c_0_47,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring ).
cnf(c_0_48,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero ).
cnf(c_0_49,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_50,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult ).
cnf(c_0_51,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_52,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_53,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_54,axiom,
( 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)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_power__one__over_0 ).
cnf(c_0_55,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_42,c_0_43]),c_0_44]),c_0_31])]) ).
cnf(c_0_56,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_45,c_0_46]),c_0_47]),c_0_48])]) ).
cnf(c_0_57,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_42,c_0_34]),c_0_31])]) ).
cnf(c_0_58,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_49,c_0_50]) ).
cnf(c_0_59,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_51,c_0_52]) ).
cnf(c_0_60,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_53,c_0_31]),c_0_48])]) ).
cnf(c_0_61,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_62,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_54,c_0_55]),c_0_36]),c_0_56]),c_0_32]),c_0_31]),c_0_48])]) ).
cnf(c_0_63,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_64,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_k,tc_nat),v_n)),
cls_k_I2_J_0 ).
cnf(c_0_65,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_57,c_0_55]),c_0_58]),c_0_59]),c_0_59]),c_0_60]) ).
cnf(c_0_66,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_61,c_0_62]),c_0_63]),c_0_64])]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.17/0.18 % Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% 0.17/0.19 % Command : run_E %s %d THM
% 0.18/0.37 % Computer : n023.cluster.edu
% 0.18/0.37 % Model : x86_64 x86_64
% 0.18/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.37 % Memory : 8042.1875MB
% 0.18/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.37 % CPULimit : 2400
% 0.18/0.37 % WCLimit : 300
% 0.18/0.37 % DateTime : Tue Oct 3 03:35:07 EDT 2023
% 0.18/0.37 % CPUTime :
% 0.22/0.52 Running first-order theorem proving
% 0.22/0.52 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.LIi3Bqf4eS/E---3.1_23827.p
% 2.23/0.83 # Version: 3.1pre001
% 2.23/0.83 # Preprocessing class: FSLSSMSSSSSNFFN.
% 2.23/0.83 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.23/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.23/0.83 # Starting new_bool_3 with 300s (1) cores
% 2.23/0.83 # Starting new_bool_1 with 300s (1) cores
% 2.23/0.83 # Starting sh5l with 300s (1) cores
% 2.23/0.83 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 23906 completed with status 0
% 2.23/0.83 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 2.23/0.83 # Preprocessing class: FSLSSMSSSSSNFFN.
% 2.23/0.83 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.23/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.23/0.83 # No SInE strategy applied
% 2.23/0.83 # Search class: FGHSM-FSLM32-DFFFFFNN
% 2.23/0.83 # Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 2.23/0.83 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 125s (1) cores
% 2.23/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 125s (1) cores
% 2.23/0.83 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 125s (1) cores
% 2.23/0.83 # Starting U----_206c_05_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 125s (1) cores
% 2.23/0.83 # Starting G-E--_208_B07_F1_AE_CS_SP_PS_S5PRR_S0Y with 125s (1) cores
% 2.23/0.83 # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 23912 completed with status 0
% 2.23/0.83 # Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 2.23/0.83 # Preprocessing class: FSLSSMSSSSSNFFN.
% 2.23/0.83 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.23/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 2.23/0.83 # No SInE strategy applied
% 2.23/0.83 # Search class: FGHSM-FSLM32-DFFFFFNN
% 2.23/0.83 # Scheduled 12 strats onto 5 cores with 1500 seconds (1500 total)
% 2.23/0.83 # Starting G-E--_301_C18_F1_URBAN_S5PRR_S0Y with 125s (1) cores
% 2.23/0.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 125s (1) cores
% 2.23/0.83 # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 125s (1) cores
% 2.23/0.83 # Preprocessing time : 0.012 s
% 2.23/0.83 # Presaturation interreduction done
% 2.23/0.83
% 2.23/0.83 # Proof found!
% 2.23/0.83 # SZS status Unsatisfiable
% 2.23/0.83 # SZS output start CNFRefutation
% See solution above
% 2.23/0.83 # Parsed axioms : 897
% 2.23/0.83 # Removed by relevancy pruning/SinE : 0
% 2.23/0.83 # Initial clauses : 897
% 2.23/0.83 # Removed in clause preprocessing : 0
% 2.23/0.83 # Initial clauses in saturation : 897
% 2.23/0.83 # Processed clauses : 3295
% 2.23/0.83 # ...of these trivial : 280
% 2.23/0.83 # ...subsumed : 1460
% 2.23/0.83 # ...remaining for further processing : 1555
% 2.23/0.83 # Other redundant clauses eliminated : 76
% 2.23/0.83 # Clauses deleted for lack of memory : 0
% 2.23/0.83 # Backward-subsumed : 53
% 2.23/0.83 # Backward-rewritten : 30
% 2.23/0.83 # Generated clauses : 12159
% 2.23/0.83 # ...of the previous two non-redundant : 7754
% 2.23/0.83 # ...aggressively subsumed : 0
% 2.23/0.83 # Contextual simplify-reflections : 0
% 2.23/0.83 # Paramodulations : 12059
% 2.23/0.83 # Factorizations : 15
% 2.23/0.83 # NegExts : 0
% 2.23/0.83 # Equation resolutions : 85
% 2.23/0.83 # Total rewrite steps : 13649
% 2.23/0.83 # Propositional unsat checks : 0
% 2.23/0.83 # Propositional check models : 0
% 2.23/0.83 # Propositional check unsatisfiable : 0
% 2.23/0.83 # Propositional clauses : 0
% 2.23/0.83 # Propositional clauses after purity: 0
% 2.23/0.83 # Propositional unsat core size : 0
% 2.23/0.83 # Propositional preprocessing time : 0.000
% 2.23/0.83 # Propositional encoding time : 0.000
% 2.23/0.83 # Propositional solver time : 0.000
% 2.23/0.83 # Success case prop preproc time : 0.000
% 2.23/0.83 # Success case prop encoding time : 0.000
% 2.23/0.83 # Success case prop solver time : 0.000
% 2.23/0.83 # Current number of processed clauses : 805
% 2.23/0.83 # Positive orientable unit clauses : 373
% 2.23/0.83 # Positive unorientable unit clauses: 5
% 2.23/0.83 # Negative unit clauses : 47
% 2.23/0.83 # Non-unit-clauses : 380
% 2.23/0.83 # Current number of unprocessed clauses: 5964
% 2.23/0.83 # ...number of literals in the above : 13805
% 2.23/0.83 # Current number of archived formulas : 0
% 2.23/0.83 # Current number of archived clauses : 750
% 2.23/0.83 # Clause-clause subsumption calls (NU) : 113437
% 2.23/0.83 # Rec. Clause-clause subsumption calls : 53396
% 2.23/0.83 # Non-unit clause-clause subsumptions : 965
% 2.23/0.83 # Unit Clause-clause subsumption calls : 8799
% 2.23/0.83 # Rewrite failures with RHS unbound : 29
% 2.23/0.83 # BW rewrite match attempts : 778
% 2.23/0.83 # BW rewrite match successes : 65
% 2.23/0.83 # Condensation attempts : 0
% 2.23/0.83 # Condensation successes : 0
% 2.23/0.83 # Termbank termtop insertions : 196101
% 2.23/0.83
% 2.23/0.83 # -------------------------------------------------
% 2.23/0.83 # User time : 0.258 s
% 2.23/0.83 # System time : 0.012 s
% 2.23/0.83 # Total time : 0.270 s
% 2.23/0.83 # Maximum resident set size: 3456 pages
% 2.23/0.83
% 2.23/0.83 # -------------------------------------------------
% 2.23/0.83 # User time : 1.294 s
% 2.23/0.83 # System time : 0.052 s
% 2.23/0.83 # Total time : 1.346 s
% 2.23/0.83 # Maximum resident set size: 2384 pages
% 2.23/0.83 % E---3.1 exiting
% 2.23/0.83 % E---3.1 exiting
%------------------------------------------------------------------------------