%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV616-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.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 : Tue May 5 05:27:06 PM UTC 2026
% Result : Unsatisfiable 254.59s 185.63s
% Output : CNFRefutation 255.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of clauses : 88 ( 50 unt; 2 nHn; 45 RR)
% Number of literals : 132 ( 69 equ; 53 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 127 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
cnf(cls_min__max_Oinf__le2_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
cnf(cls_min__max_Oinf__le1_0,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
cnf(cls_gr0I_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
cnf(cls_min__max_Osup__absorb1_0,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),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_root__unity_0,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__unity_0) ).
cnf(cls_power__one_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(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_cnj_Odiff_0,axiom,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X1),c_Complex_Ocnj(X2),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Odiff_0) ).
cnf(cls_complex__cnj__one_0,axiom,
c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__one_0) ).
cnf(cls_complex__cnj__cancel__iff_0,axiom,
( X1 = X2
| c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
cnf(cls_max__less__iff__conj_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
cnf(cls_complex__cnj__zero__iff_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Complex_Ocnj(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
cnf(cls_complex__cnj__power_0,axiom,
c_Complex_Ocnj(c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex)) = c_Power_Opower__class_Opower(c_Complex_Ocnj(X1),X2,tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__power_0) ).
cnf(cls_class__semiring_Opwr__pwr_0,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1)
| ~ 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_complex__cnj__cnj_0,axiom,
c_Complex_Ocnj(c_Complex_Ocnj(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
cnf(cls_k_I2_J_0,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_k_I2_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
cnf(cls_root__cancel_0,axiom,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X2),X3,tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_root__cancel_0) ).
cnf(cls_nat__mult__1__right_0,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
cnf(c_0_28,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_linorder__not__le_1 ).
cnf(c_0_29,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder ).
cnf(c_0_30,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__le2_0 ).
cnf(c_0_31,plain,
( ~ c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,tc_nat),X2,tc_nat),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_33,axiom,
( c_lessequals(c_Orderings_Oord__class_Omin(X2,X3,X1),X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_min__max_Oinf__le1_0 ).
cnf(c_0_34,plain,
~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X2,X1,tc_nat),tc_nat),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| X1 = c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_gr0I_0 ).
cnf(c_0_36,axiom,
( c_Orderings_Oord__class_Omax(X2,X3,X1) = X2
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_min__max_Osup__absorb1_0 ).
cnf(c_0_37,plain,
c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,tc_nat),X1,tc_nat),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_38,plain,
c_Orderings_Oord__class_Omin(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
cls_conjecture_0 ).
cnf(c_0_40,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_root__unity_0 ).
cnf(c_0_41,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X1),X2,X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_power__one_0 ).
cnf(c_0_42,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult ).
cnf(c_0_43,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_44,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add ).
cnf(c_0_45,axiom,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X1),c_Complex_Ocnj(X2),tc_Complex_Ocomplex),
cls_cnj_Odiff_0 ).
cnf(c_0_46,axiom,
c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
cls_complex__cnj__one_0 ).
cnf(c_0_47,axiom,
( X1 = X2
| c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2) ),
cls_complex__cnj__cancel__iff_0 ).
cnf(c_0_48,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X4,X2,X1),X3,X1) ),
cls_max__less__iff__conj_1 ).
cnf(c_0_49,plain,
( c_Orderings_Oord__class_Omax(X1,X2,tc_nat) = X1
| ~ c_lessequals(X2,X1,tc_nat) ),
inference(spm,[status(thm)],[c_0_36,c_0_29]) ).
cnf(c_0_50,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_51,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_52,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_53,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_43,c_0_44]) ).
cnf(c_0_54,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_55,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field ).
cnf(c_0_56,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Complex_Ocnj(X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
cls_complex__cnj__zero__iff_0 ).
cnf(c_0_57,plain,
c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X1),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,plain,
( X1 = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Complex_Ocnj(X1) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_47,c_0_46]) ).
cnf(c_0_59,axiom,
c_Complex_Ocnj(c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex)) = c_Power_Opower__class_Opower(c_Complex_Ocnj(X1),X2,tc_Complex_Ocomplex),
cls_complex__cnj__power_0 ).
cnf(c_0_60,plain,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,tc_nat),X2,tc_nat) ),
inference(spm,[status(thm)],[c_0_48,c_0_29]) ).
cnf(c_0_61,plain,
c_Orderings_Oord__class_Omax(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_63,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_54,c_0_55]) ).
cnf(c_0_64,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__pwr_0 ).
cnf(c_0_65,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_66,plain,
( c_HOL_Ominus__class_Ominus(X1,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(X1),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_67,plain,
( c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(c_Complex_Ocnj(X1),X2,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,axiom,
c_Complex_Ocnj(c_Complex_Ocnj(X1)) = X1,
cls_complex__cnj__cnj_0 ).
cnf(c_0_69,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,axiom,
c_HOL_Oord__class_Oless(v_k,v_n,tc_nat),
cls_k_I2_J_0 ).
cnf(c_0_71,axiom,
( c_Power_Opower__class_Opower(X2,c_HOL_Oone__class_Oone(tc_nat),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I33_J_0 ).
cnf(c_0_72,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_73,plain,
c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,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_75,plain,
( c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Complex_Ocnj(X1),X2,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_66,c_0_59]) ).
cnf(c_0_76,plain,
( c_Power_Opower__class_Opower(c_Complex_Ocnj(X1),X2,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,axiom,
( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat)),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X2),X3,tc_Complex_Ocomplex)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
cls_root__cancel_0 ).
cnf(c_0_78,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_79,plain,
c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = X1,
inference(spm,[status(thm)],[c_0_71,c_0_65]) ).
cnf(c_0_80,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_81,plain,
( c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_Power_Opower__class_Opower(X1,X2,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_75,c_0_76]),c_0_53])]) ).
cnf(c_0_82,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_n,X1,tc_nat)),c_HOL_Otimes__class_Otimes(v_n,X2,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(X1),X2,tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,axiom,
c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X1,
cls_nat__mult__1__right_0 ).
cnf(c_0_84,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_40,c_0_79]) ).
cnf(c_0_85,negated_conjecture,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,v_k,tc_nat),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_80,c_0_81]),c_0_63])]) ).
cnf(c_0_86,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),c_HOL_Otimes__class_Otimes(v_n,X1,tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_52]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV616-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n020.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 05:42:20 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 254.59/185.63 % Version : CSE_E---1.7
% 254.59/185.63 % Problem : theBenchmark.p
% 254.59/185.63 % SZS status Unsatisfiable for theBenchmark.p
% 254.59/185.63 % SZS output start CNFRefutation
% See solution above
% 255.39/186.40 % Total time : 153.154s
%------------------------------------------------------------------------------