%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG397-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n017.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 : Wed Apr 9 05:25:09 PM UTC 2025
% Result : Unsatisfiable 8.54s 2.91s
% Output : CNFRefutation 8.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 2
% Syntax : Number of formulae : 5 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 65 ( 64 usr; 1 prp; 0-3 aty)
% Number of functors : 43 ( 43 usr; 10 con; 0-5 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_OrderedGroup_Omonoid__add__axioms > c_OrderedGroup_Ocomm__monoid__add__axioms > c_HOL_Oord__class_Oless > c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant > hBOOL > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring__0 > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring__1__no__zero__divisors > class_Ring__and__Field_Oring__1 > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring__0 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Ocomm__ring__1 > class_Ring__and__Field_Ocomm__ring > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__algebra > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Osemigroup__add > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__comm__monoid__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Lattices_Oboolean__algebra > class_Int_Oring__char__0 > class_Int_Onumber__ring > class_HOL_Ozero > c_Polynomial_Opoly__rec > c_List_Ofoldl > c_HOL_OIf > c_fequal > c_Power_Opower_Opower > c_Polynomial_Osmult > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_Polynomial_Oorder > c_Polynomial_Omonom > c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1 > tc_fun > hAPP > c_RealVector_Onorm__class_Onorm > c_Polynomial_Opoly > c_Polynomial_Odegree > c_Polynomial_Ocoeff > c_Nat_Osemiring__1__class_Oof__nat > c_HOL_Ouminus__class_Ouminus > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > #nlpp > v_sko__unknown__thm__rrS__1 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1 > tc_Polynomial_Opoly > c_Suc > c_Power_Opower__class_Opower > c_HOL_Ozero__class_Ozero > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Oone__class_Oone > v_q____ > v_pa____ > v_p > v_n____ > v_c____ > tc_nat > tc_RealDef_Oreal > tc_Complex_Ocomplex > t_b > t_a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_HOL_Ozero,type,
class_HOL_Ozero: $i > $o ).
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(class_OrderedGroup_Ocancel__comm__monoid__add,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__0,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(v_sko__unknown__thm__rrS__1,type,
v_sko__unknown__thm__rrS__1: $i > $i ).
tff(class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3: $i > $i ).
tff(c_HOL_OIf,type,
c_HOL_OIf: ( $i * $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $i > $i ).
tff(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(c_fequal,type,
c_fequal: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(c_Polynomial_Omonom,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(t_a,type,
t_a: $i ).
tff(class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(c_List_Ofoldl,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(c_Power_Opower_Opower,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2: $i > $i ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(v_n____,type,
v_n____: $i ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Polynomial_Osmult,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_OrderedGroup_Omonoid__add__axioms,type,
c_OrderedGroup_Omonoid__add__axioms: ( $i * $i * $i ) > $o ).
tff(class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__mult,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1: $i > $i ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(class_Ring__and__Field_Ocomm__ring,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(c_Polynomial_Opoly,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: $i > $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff(class_OrderedGroup_Osemigroup__add,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(c_Polynomial_OpCons,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(v_c____,type,
v_c____: $i ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(c_Polynomial_Ocoeff,type,
c_Polynomial_Ocoeff: ( $i * $i ) > $i ).
tff(c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(c_Polynomial_Odegree,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(c_Polynomial_Opcompose,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(v_p,type,
v_p: $i ).
tff(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(v_q____,type,
v_q____: $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(t_b,type,
t_b: $i ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1: ( $i * $i ) > $i ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2: $i > $i ).
tff(c_Polynomial_Oorder,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Opoly__rec,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(c_OrderedGroup_Ocomm__monoid__add__axioms,type,
c_OrderedGroup_Ocomm__monoid__add__axioms: ( $i * $i * $i ) > $o ).
tff(v_pa____,type,
v_pa____: $i ).
tff(f_3867,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_3866,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(c_1054,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_3867]) ).
tff(c_1052,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_3866]) ).
tff(c_1428,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1054,c_1052]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG397-1 : TPTP v9.0.0. Released v4.1.0.
% 0.04/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 14:41:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 8.54/2.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.54/2.91
% 8.54/2.91 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------