TSTP Solution File: ALG387-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG387-1 : 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 : n031.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 10:32:39 EDT 2023
% Result : Unsatisfiable 140.48s 111.16s
% Output : CNFRefutation 140.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 116
% Syntax : Number of formulae : 128 ( 8 unt; 110 typ; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 143 ( 102 >; 41 *; 0 +; 0 <<)
% Number of predicates : 72 ( 71 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 8 con; 0-3 aty)
% Number of variables : 20 (; 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > c_HOL_Oeq__class_Oeq > c_Polynomial_Opos__poly > class_SEQ_Obanach > class_Ring__and__Field_Ozero__neq__one > 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 > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring__abs > 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_Olordered__ring > 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_Ring__and__Field_Oabs__if > 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_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Orderings_Obot > 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__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__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_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Obounded__lattice > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > class_HOL_Ozero > class_HOL_Oeq > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1 > c_Power_Opower__class_Opower > c_Polynomial_Osynthetic__div > c_Polynomial_Osmult > c_Polynomial_Opoly > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_Orderings_Oord__class_Omin > c_Orderings_Oord__class_Omax > c_Lattices_Olower__semilattice__class_Oinf > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 > hAPP > c_Transcendental_Oexp > c_RealVector_Onorm__class_Onorm > c_HOL_Ouminus__class_Ouminus > c_HOL_Oabs__class_Oabs > c_Fun_Oid > #nlpp > v_sko__local__XpCons__Xhyps__1 > v_sko__local__XpCons__1 > tc_Polynomial_Opoly > c_Transcendental_Oarctan > c_Orderings_Obot__class_Obot > c_NthRoot_Osqrt > c_HOL_Ozero__class_Ozero > c_Complex_Ocnj > c_Complex_ORe > c_Complex_OIm > v_x > v_v____ > v_r____ > v_cs____ > v_c____ > tc_RealDef_Oreal > tc_Complex_Ocomplex > t_a
%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_Ring__and__Field_Opordered__ring__abs,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
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(c_Complex_OIm,type,
c_Complex_OIm: $i > $i ).
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_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1: ( $i * $i * $i ) > $i ).
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_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $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(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(c_Polynomial_Osynthetic__div,type,
c_Polynomial_Osynthetic__div: ( $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(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: ( $i * $i ) > $i ).
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(c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(class_SEQ_Obanach,type,
class_SEQ_Obanach: $i > $o ).
tff(v_cs____,type,
v_cs____: $i ).
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_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: ( $i * $i * $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_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(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(c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(c_NthRoot_Osqrt,type,
c_NthRoot_Osqrt: $i > $i ).
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(v_sko__local__XpCons__Xhyps__1,type,
v_sko__local__XpCons__Xhyps__1: $i > $i ).
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(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(v_v____,type,
v_v____: $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $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(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(c_Transcendental_Oexp,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
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_Fun_Oid,type,
c_Fun_Oid: ( $i * $i ) > $i ).
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_OrderedGroup_Olordered__ab__group__add__abs,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(v_sko__local__XpCons__1,type,
v_sko__local__XpCons__1: $i > $i ).
tff(class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $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(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_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(c_HOL_Oeq__class_Oeq,type,
c_HOL_Oeq__class_Oeq: ( $i * $i * $i ) > $o ).
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_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1,type,
v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1: ( $i * $i ) > $i ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_Transcendental_Oarctan,type,
c_Transcendental_Oarctan: $i > $i ).
tff(class_HOL_Oeq,type,
class_HOL_Oeq: $i > $o ).
tff(v_r____,type,
v_r____: $i ).
tff(c_Complex_ORe,type,
c_Complex_ORe: $i > $i ).
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_5280,axiom,
! [V_z] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_5283,axiom,
! [V_xa] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_xa,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_5357,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file(unknown,unknown) ).
tff(f_5167,axiom,
! [T_a,V_y,V_x] :
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_4986,axiom,
! [V_x,V_r] :
( c_lessequals(V_x,V_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(f_5275,axiom,
! [V_w] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file(unknown,unknown) ).
tff(c_336801,plain,
! [V_z_5148] :
( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(V_z_5148,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_z_5148,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_5280]) ).
tff(c_1472,plain,
! [V_xa_2176] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_xa_2176,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,V_xa_2176),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5283]) ).
tff(c_336875,plain,
~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_336801,c_1472]) ).
tff(c_1596,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5357]) ).
tff(c_1440,plain,
! [V_x_2135,V_y_2134,T_a_2133] :
( c_lessequals(V_x_2135,V_y_2134,T_a_2133)
| c_lessequals(V_y_2134,V_x_2135,T_a_2133)
| ~ class_Orderings_Olinorder(T_a_2133) ),
inference(cnfTransformation,[status(thm)],[f_5167]) ).
tff(c_9313,plain,
! [V_x_2622,V_r_2623] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x_2622,tc_RealDef_Oreal),V_r_2623,tc_RealDef_Oreal)
| c_lessequals(V_x_2622,V_r_2623,tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_4986]) ).
tff(c_9328,plain,
! [V_x_2622,V_x_2135] :
( c_lessequals(V_x_2622,V_x_2135,tc_RealDef_Oreal)
| c_lessequals(V_x_2135,c_HOL_Oabs__class_Oabs(V_x_2622,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_1440,c_9313]) ).
tff(c_9422,plain,
! [V_x_2622,V_x_2135] :
( c_lessequals(V_x_2622,V_x_2135,tc_RealDef_Oreal)
| c_lessequals(V_x_2135,c_HOL_Oabs__class_Oabs(V_x_2622,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(demodulation,[status(thm),theory(equality)],[c_1596,c_9328]) ).
tff(c_339995,plain,
! [V_w_5160] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w_5160,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_w_5160,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(cnfTransformation,[status(thm)],[f_5275]) ).
tff(c_340069,plain,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_339995,c_1472]) ).
tff(c_342358,plain,
c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[c_9422,c_340069]) ).
tff(c_342438,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_336875,c_342358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : ALG387-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.14 % 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
% 0.14/0.36 % Computer : n031.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 20:45:15 EDT 2023
% 0.14/0.36 % CPUTime :
% 140.48/111.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 140.48/111.16
% 140.48/111.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 140.48/111.19
% 140.48/111.19 Inference rules
% 140.48/111.19 ----------------------
% 140.48/111.19 #Ref : 52
% 140.48/111.19 #Sup : 76000
% 140.48/111.19 #Fact : 28
% 140.48/111.19 #Define : 0
% 140.48/111.19 #Split : 6
% 140.48/111.19 #Chain : 0
% 140.48/111.19 #Close : 0
% 140.48/111.19
% 140.48/111.19 Ordering : KBO
% 140.48/111.19
% 140.48/111.19 Simplification rules
% 140.48/111.19 ----------------------
% 140.48/111.19 #Subsume : 11025
% 140.48/111.19 #Demod : 60009
% 140.48/111.19 #Tautology : 15760
% 140.48/111.19 #SimpNegUnit : 734
% 140.48/111.19 #BackRed : 8
% 140.48/111.19
% 140.48/111.19 #Partial instantiations: 0
% 140.48/111.19 #Strategies tried : 1
% 140.48/111.19
% 140.48/111.19 Timing (in seconds)
% 140.48/111.19 ----------------------
% 140.48/111.20 Preprocessing : 1.70
% 140.48/111.20 Parsing : 0.96
% 140.48/111.20 CNF conversion : 0.14
% 140.48/111.20 Main loop : 108.37
% 140.48/111.20 Inferencing : 9.24
% 140.48/111.20 Reduction : 58.07
% 140.48/111.20 Demodulation : 49.30
% 140.48/111.20 BG Simplification : 0.96
% 140.48/111.20 Subsumption : 33.64
% 140.48/111.20 Abstraction : 1.17
% 140.48/111.20 MUC search : 0.00
% 140.48/111.20 Cooper : 0.00
% 140.48/111.20 Total : 110.12
% 140.48/111.20 Index Insertion : 0.00
% 140.48/111.20 Index Deletion : 0.00
% 140.48/111.20 Index Matching : 0.00
% 140.48/111.20 BG Taut test : 0.00
%------------------------------------------------------------------------------