TSTP Solution File: ALG432-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG432-1 : TPTP v8.1.2. 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 : n025.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 Aug 22 10:32:43 EDT 2023
% Result : Unsatisfiable 65.88s 44.08s
% Output : CNFRefutation 66.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 139
% Syntax : Number of formulae : 179 ( 32 unt; 119 typ; 0 def)
% Number of atoms : 98 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 162 ( 112 >; 50 *; 0 +; 0 <<)
% Number of predicates : 81 ( 79 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 7 con; 0-3 aty)
% Number of variables : 86 (; 86 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Ring__and__Field_Odvd__class_Odvd > c_HOL_Oord__class_Oless > c_HOL_Oeq__class_Oeq > c_Polynomial_Opos__poly > c_Int_Oiszero > class_SEQ_Obanach > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osgn__if > 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__ring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > 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_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odvd > class_Ring__and__Field_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > 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_Ring__and__Field_Oabs__if > class_RealVector_Oreal__vector > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__field > class_RealVector_Oreal__algebra > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > 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__group__add__abs > 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__meet > class_OrderedGroup_Olordered__ab__group__add__join > class_OrderedGroup_Olordered__ab__group__add__abs > 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_Lattices_Oupper__semilattice > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Odistrib__lattice > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > class_HOL_Ozero > class_HOL_Oeq > class_Divides_Osemiring__div > class_Divides_Oring__div > c_RealVector_OscaleR__class_OscaleR > c_Power_Opower__class_Opower > c_Polynomial_Osynthetic__div > c_Polynomial_Osmult > c_Polynomial_Opoly > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_Polynomial_Oorder > c_Polynomial_Omonom > c_Lattices_Oupper__semilattice__class_Osup > c_Lattices_Olower__semilattice__class_Oinf > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_HOL_Oinverse__class_Odivide > c_Divides_Odiv__class_Omod > c_Divides_Odiv__class_Odiv > c_Transcendental_Oexp > c_OrderedGroup_Olordered__ab__group__add__class_Opprt > c_OrderedGroup_Olordered__ab__group__add__class_Onprt > c_HOL_Ouminus__class_Ouminus > c_HOL_Osgn__class_Osgn > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > c_Fun_Oid > #nlpp > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1 > tc_Polynomial_Opoly > c_Suc > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > c_Complex_Ocnj > v_x > v_p > tc_nat > tc_RealDef_Oreal > tc_Complex_Ocomplex > t_a > c_Complex_Oii
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_HOL_Ozero,type,
class_HOL_Ozero: $i > $o ).
tff(v_x,type,
v_x: $i ).
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(class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $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(c_OrderedGroup_Olordered__ab__group__add__class_Opprt,type,
c_OrderedGroup_Olordered__ab__group__add__class_Opprt: ( $i * $i ) > $i ).
tff(c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(class_RealVector_Oreal__vector,type,
class_RealVector_Oreal__vector: $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(c_RealVector_OscaleR__class_OscaleR,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
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_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add__abs,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $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(class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1: $i > $i ).
tff(c_Polynomial_Osynthetic__div,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(c_Polynomial_Omonom,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(t_a,type,
t_a: $i ).
tff(class_OrderedGroup_Olordered__ab__group__add__meet,type,
class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).
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(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add__join,type,
class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).
tff(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(c_HOL_Oinverse__class_Odivide,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $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_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $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(c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(c_Complex_Oii,type,
c_Complex_Oii: $i ).
tff(class_SEQ_Obanach,type,
class_SEQ_Obanach: $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(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
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(class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_OrderedGroup_Olordered__ab__group__add__class_Onprt,type,
c_OrderedGroup_Olordered__ab__group__add__class_Onprt: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_Divides_Oring__div,type,
class_Divides_Oring__div: $i > $o ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_Polynomial_Osmult,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(class_RealVector_Oreal__normed__div__algebra,type,
class_RealVector_Oreal__normed__div__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(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(c_Polynomial_Opos__poly,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_Ring__and__Field_Oabs__if,type,
class_Ring__and__Field_Oabs__if: $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_RealVector_Oreal__algebra,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff(class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(c_Ring__and__Field_Odvd__class_Odvd,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Polynomial_Opoly,type,
c_Polynomial_Opoly: ( $i * $i * $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(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2: $i > $i ).
tff(c_Transcendental_Oexp,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(c_Polynomial_OpCons,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(c_HOL_Osgn__class_Osgn,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_Fun_Oid,type,
c_Fun_Oid: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Olordered__ab__group__add__abs,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(class_Ring__and__Field_Osgn__if,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
tff(class_Ring__and__Field_Odvd,type,
class_Ring__and__Field_Odvd: $i > $o ).
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(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff(c_Polynomial_Opcompose,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_Complex_Ocnj,type,
c_Complex_Ocnj: $i > $i ).
tff(class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(v_p,type,
v_p: $i ).
tff(c_HOL_Oeq__class_Oeq,type,
c_HOL_Oeq__class_Oeq: ( $i * $i * $i ) > $o ).
tff(class_RealVector_Oreal__field,type,
class_RealVector_Oreal__field: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
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(class_HOL_Oeq,type,
class_HOL_Oeq: $i > $o ).
tff(c_Int_Oiszero,type,
c_Int_Oiszero: ( $i * $i ) > $o ).
tff(class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(f_5603,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_5617,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_5625,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_5143,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_5612,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_2884,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
file(unknown,unknown) ).
tff(f_3921,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Ogroup__add(T_a)
| ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ),
file(unknown,unknown) ).
tff(f_2506,axiom,
! [T_a,V_xa,V_y,V_x] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) )
| ( V_xa = V_y ) ),
file(unknown,unknown) ).
tff(f_5629,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_5602,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_4949,axiom,
! [T_a,V_a] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_2334,axiom,
! [T_a,V_a,V_b] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ),
file(unknown,unknown) ).
tff(f_5630,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_5632,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_3377,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_5162,axiom,
! [T_a,V_x,V_a] :
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a) )
| ( V_a = c_HOL_Ozero__class_Ozero(T_a) ) ),
file(unknown,unknown) ).
tff(f_1196,axiom,
! [T_a,V_a,V_b] :
( ~ class_Ring__and__Field_Oring(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) ) ),
file(unknown,unknown) ).
tff(f_5479,axiom,
c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(f_5384,axiom,
! [T_a,V_a,V_p,V_x] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_5481,axiom,
c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file(unknown,unknown) ).
tff(c_1710,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5603]) ).
tff(c_1738,plain,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5617]) ).
tff(c_1754,plain,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5625]) ).
tff(c_2098,plain,
! [V_a_2349,T_a_2350] :
( ( c_HOL_Ominus__class_Ominus(V_a_2349,V_a_2349,T_a_2350) = c_HOL_Ozero__class_Ozero(T_a_2350) )
| ~ class_OrderedGroup_Ogroup__add(T_a_2350) ),
inference(cnfTransformation,[status(thm)],[f_5143]) ).
tff(c_2107,plain,
! [V_a_2349] : ( c_HOL_Ominus__class_Ominus(V_a_2349,V_a_2349,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1754,c_2098]) ).
tff(c_1728,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5612]) ).
tff(c_3962,plain,
! [V_b_2506,V_a_2507,T_a_2508] :
( ( c_HOL_Oplus__class_Oplus(V_b_2506,V_a_2507,T_a_2508) = c_HOL_Oplus__class_Oplus(V_a_2507,V_b_2506,T_a_2508) )
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a_2508) ),
inference(cnfTransformation,[status(thm)],[f_2884]) ).
tff(c_3973,plain,
! [V_b_2506,V_a_2507] : ( c_HOL_Oplus__class_Oplus(V_b_2506,V_a_2507,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(V_a_2507,V_b_2506,tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1728,c_3962]) ).
tff(c_5245,plain,
! [V_a_2542,V_b_2543,T_a_2544] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a_2542,V_b_2543,T_a_2544),V_b_2543,T_a_2544) = V_a_2542 )
| ~ class_OrderedGroup_Ogroup__add(T_a_2544) ),
inference(cnfTransformation,[status(thm)],[f_3921]) ).
tff(c_5268,plain,
! [V_b_2506,V_a_2507] :
( ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_b_2506,V_a_2507,tc_Complex_Ocomplex),V_b_2506,tc_Complex_Ocomplex) = V_a_2507 )
| ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_3973,c_5245]) ).
tff(c_5322,plain,
! [V_b_2506,V_a_2507] : ( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_b_2506,V_a_2507,tc_Complex_Ocomplex),V_b_2506,tc_Complex_Ocomplex) = V_a_2507 ),
inference(demodulation,[status(thm),theory(equality)],[c_1754,c_5268]) ).
tff(c_17912,plain,
! [V_y_2829,V_xa_2830,T_a_2831,V_x_2832] :
( ( V_y_2829 = V_xa_2830 )
| ( c_HOL_Ominus__class_Ominus(V_xa_2830,V_y_2829,T_a_2831) != c_HOL_Ominus__class_Ominus(V_x_2832,V_x_2832,T_a_2831) )
| ~ class_OrderedGroup_Oab__group__add(T_a_2831) ),
inference(cnfTransformation,[status(thm)],[f_2506]) ).
tff(c_17914,plain,
! [V_b_2506,V_a_2507,V_x_2832] :
( ( c_HOL_Oplus__class_Oplus(V_b_2506,V_a_2507,tc_Complex_Ocomplex) = V_b_2506 )
| ( c_HOL_Ominus__class_Ominus(V_x_2832,V_x_2832,tc_Complex_Ocomplex) != V_a_2507 )
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_5322,c_17912]) ).
tff(c_19785,plain,
! [V_b_2506] : ( c_HOL_Oplus__class_Oplus(V_b_2506,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = V_b_2506 ),
inference(demodulation,[status(thm),theory(equality)],[c_1738,c_2107,c_17914]) ).
tff(c_1762,plain,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5629]) ).
tff(c_1708,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5602]) ).
tff(c_1302,plain,
! [V_a_2031,T_a_2030] :
( ( c_HOL_Otimes__class_Otimes(V_a_2031,c_HOL_Ozero__class_Ozero(T_a_2030),T_a_2030) = c_HOL_Ozero__class_Ozero(T_a_2030) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a_2030) ),
inference(cnfTransformation,[status(thm)],[f_4949]) ).
tff(c_5220,plain,
! [V_b_2536,V_a_2537,T_a_2538] :
( ( c_HOL_Otimes__class_Otimes(V_b_2536,V_a_2537,T_a_2538) = c_HOL_Otimes__class_Otimes(V_a_2537,V_b_2536,T_a_2538) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a_2538) ),
inference(cnfTransformation,[status(thm)],[f_2334]) ).
tff(c_6760,plain,
! [V_b_2588,V_a_2589] : ( c_HOL_Otimes__class_Otimes(V_b_2588,V_a_2589,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_a_2589,V_b_2588,tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1708,c_5220]) ).
tff(c_6958,plain,
! [V_a_2031] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),V_a_2031,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1302,c_6760]) ).
tff(c_7108,plain,
! [V_a_2031] : ( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),V_a_2031,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1708,c_6958]) ).
tff(c_5231,plain,
! [V_b_2536,V_a_2537] : ( c_HOL_Otimes__class_Otimes(V_b_2536,V_a_2537,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_a_2537,V_b_2536,tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1708,c_5220]) ).
tff(c_1764,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5630]) ).
tff(c_1768,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5632]) ).
tff(c_4713,plain,
! [V_b_2532,V_a_2533] : ( c_HOL_Oplus__class_Oplus(V_b_2532,V_a_2533,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(V_a_2533,V_b_2532,tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_1728,c_3962]) ).
tff(c_884,plain,
! [V_a_1426,T_a_1425] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a_1426,T_a_1425),V_a_1426,T_a_1425) = c_HOL_Ozero__class_Ozero(T_a_1425) )
| ~ class_OrderedGroup_Oab__group__add(T_a_1425) ),
inference(cnfTransformation,[status(thm)],[f_3377]) ).
tff(c_4729,plain,
! [V_b_2532] :
( ( c_HOL_Oplus__class_Oplus(V_b_2532,c_HOL_Ouminus__class_Ouminus(V_b_2532,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_4713,c_884]) ).
tff(c_4871,plain,
! [V_b_2532] : ( c_HOL_Oplus__class_Oplus(V_b_2532,c_HOL_Ouminus__class_Ouminus(V_b_2532,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1738,c_4729]) ).
tff(c_16820,plain,
! [T_a_2805,V_a_2806,V_x_2807] :
( ( c_HOL_Ozero__class_Ozero(T_a_2805) = V_a_2806 )
| ( c_HOL_Oplus__class_Oplus(V_x_2807,V_a_2806,T_a_2805) != V_x_2807 )
| ~ class_Int_Onumber__ring(T_a_2805)
| ~ class_Ring__and__Field_Oidom(T_a_2805) ),
inference(cnfTransformation,[status(thm)],[f_5162]) ).
tff(c_16824,plain,
! [V_b_2532] :
( ( c_HOL_Ouminus__class_Ouminus(V_b_2532,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_b_2532 )
| ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_4871,c_16820]) ).
tff(c_16888,plain,
! [V_b_2532] :
( ( c_HOL_Ouminus__class_Ouminus(V_b_2532,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_b_2532 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1764,c_1768,c_16824]) ).
tff(c_39938,plain,
! [V_a_3195,T_a_3196,V_b_3197] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a_3195,T_a_3196),c_HOL_Ouminus__class_Ouminus(V_b_3197,T_a_3196),T_a_3196) = c_HOL_Otimes__class_Otimes(V_a_3195,V_b_3197,T_a_3196) )
| ~ class_Ring__and__Field_Oring(T_a_3196) ),
inference(cnfTransformation,[status(thm)],[f_1196]) ).
tff(c_40089,plain,
! [V_a_3195,V_b_2532] :
( ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a_3195,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_a_3195,V_b_2532,tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != V_b_2532 ) ),
inference(superposition,[status(thm),theory(equality)],[c_16888,c_39938]) ).
tff(c_79065,plain,
! [V_a_3195] : ( c_HOL_Otimes__class_Otimes(V_a_3195,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_1762,c_7108,c_5231,c_40089]) ).
tff(c_1472,plain,
c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5479]) ).
tff(c_183960,plain,
! [V_a_4380,V_x_4381,V_p_4382,T_a_4383] :
( ( c_HOL_Oplus__class_Oplus(V_a_4380,c_HOL_Otimes__class_Otimes(V_x_4381,c_Polynomial_Opoly(V_p_4382,V_x_4381,T_a_4383),T_a_4383),T_a_4383) = c_Polynomial_Opoly(c_Polynomial_OpCons(V_a_4380,V_p_4382,T_a_4383),V_x_4381,T_a_4383) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_a_4383) ),
inference(cnfTransformation,[status(thm)],[f_5384]) ).
tff(c_184771,plain,
! [V_a_4380] :
( ( c_HOL_Oplus__class_Oplus(V_a_4380,c_HOL_Otimes__class_Otimes(v_x,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(V_a_4380,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[status(thm),theory(equality)],[c_1472,c_183960]) ).
tff(c_184961,plain,
! [V_a_4380] : ( c_Polynomial_Opoly(c_Polynomial_OpCons(V_a_4380,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = V_a_4380 ),
inference(demodulation,[status(thm),theory(equality)],[c_1710,c_19785,c_79065,c_184771]) ).
tff(c_1474,plain,
c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5481]) ).
tff(c_184964,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_184961,c_1474]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG432-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 20:28:05 EDT 2023
% 0.14/0.36 % CPUTime :
% 65.88/44.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.88/44.09
% 65.88/44.09 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 66.02/44.13
% 66.02/44.13 Inference rules
% 66.02/44.13 ----------------------
% 66.02/44.13 #Ref : 42
% 66.02/44.13 #Sup : 40462
% 66.02/44.13 #Fact : 4
% 66.02/44.13 #Define : 0
% 66.02/44.13 #Split : 29
% 66.02/44.13 #Chain : 0
% 66.02/44.13 #Close : 0
% 66.02/44.13
% 66.02/44.13 Ordering : KBO
% 66.02/44.13
% 66.02/44.13 Simplification rules
% 66.02/44.13 ----------------------
% 66.02/44.13 #Subsume : 5353
% 66.02/44.13 #Demod : 30850
% 66.02/44.13 #Tautology : 10943
% 66.02/44.13 #SimpNegUnit : 513
% 66.02/44.13 #BackRed : 9
% 66.02/44.13
% 66.02/44.13 #Partial instantiations: 0
% 66.02/44.13 #Strategies tried : 1
% 66.02/44.13
% 66.02/44.13 Timing (in seconds)
% 66.02/44.13 ----------------------
% 66.02/44.13 Preprocessing : 1.66
% 66.02/44.13 Parsing : 0.93
% 66.02/44.13 CNF conversion : 0.15
% 66.02/44.13 Main loop : 41.40
% 66.02/44.13 Inferencing : 5.12
% 66.02/44.13 Reduction : 21.25
% 66.02/44.13 Demodulation : 17.65
% 66.02/44.13 BG Simplification : 0.58
% 66.02/44.13 Subsumption : 12.43
% 66.02/44.13 Abstraction : 0.56
% 66.02/44.13 MUC search : 0.00
% 66.02/44.13 Cooper : 0.00
% 66.02/44.13 Total : 43.12
% 66.02/44.13 Index Insertion : 0.00
% 66.02/44.13 Index Deletion : 0.00
% 66.02/44.13 Index Matching : 0.00
% 66.02/44.13 BG Taut test : 0.00
%------------------------------------------------------------------------------