%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWW204+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n016.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 09:52:19 PM UTC 2025
% Result : Theorem 136.03s 101.08s
% Output : CNFRefutation 136.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 51 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 20 ~; 17 |; 1 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 74 ( 72 usr; 1 prp; 0-2 aty)
% Number of functors : 129 ( 129 usr; 21 con; 0-5 aty)
% Number of variables : 46 ( 46 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_SEQ_Omonoseq > c_SEQ_Oincseq > c_SEQ_Odecseq > c_SEQ_OBseq > hBOOL > class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct > class_Rings_Ozero__neq__one > class_Rings_Osemiring__0 > class_Rings_Osemiring > class_Rings_Oring__no__zero__divisors > class_Rings_Oring__1__no__zero__divisors > class_Rings_Oring__1 > class_Rings_Oring > class_Rings_Oordered__semiring > class_Rings_Oordered__ring__abs > class_Rings_Oordered__ring > class_Rings_Oordered__comm__semiring > class_Rings_Oordered__cancel__semiring > class_Rings_Ono__zero__divisors > class_Rings_Omult__zero > class_Rings_Olinordered__semiring__strict > class_Rings_Olinordered__semiring__1__strict > class_Rings_Olinordered__semiring__1 > class_Rings_Olinordered__semiring > class_Rings_Olinordered__semidom > class_Rings_Olinordered__ring__strict > class_Rings_Olinordered__ring > class_Rings_Olinordered__idom > class_Rings_Olinordered__comm__semiring__strict > class_Rings_Oidom > class_Rings_Odivision__ring > class_Rings_Ocomm__semiring__1 > class_Rings_Ocomm__semiring__0 > class_Rings_Ocomm__semiring > class_Rings_Ocomm__ring__1 > class_Rings_Ocomm__ring > 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_Oord > class_Orderings_Olinorder > class_Lattices_Oab__semigroup__idem__mult > class_Groups_Ozero > class_Groups_Oordered__comm__monoid__add > class_Groups_Oordered__cancel__ab__semigroup__add > class_Groups_Oordered__ab__semigroup__add__imp__le > class_Groups_Oordered__ab__semigroup__add > class_Groups_Oordered__ab__group__add__abs > class_Groups_Oordered__ab__group__add > class_Groups_Oone > class_Groups_Omonoid__mult > class_Groups_Omonoid__add > class_Groups_Ominus > class_Groups_Olinordered__ab__group__add > class_Groups_Ogroup__add > class_Groups_Ocomm__monoid__mult > class_Groups_Ocomm__monoid__add > class_Groups_Ocancel__semigroup__add > class_Groups_Ocancel__comm__monoid__add > class_Groups_Ocancel__ab__semigroup__add > class_Groups_Oab__semigroup__mult > class_Groups_Oab__semigroup__add > class_Groups_Oab__group__add > class_Fields_Ofield__inverse__zero > class_Fields_Ofield > class_Divides_Osemiring__div > c_SEQ_Osubseq > c_Fun_Ocomp > c_COMBC > c_COMBB > c_Rings_Oinverse__class_Odivide > c_Power_Opower_Opower > c_Groups_Ominus__class_Ominus > c_Divides_Odiv__class_Odiv > c_Complex_Ocomplex_Ocomplex__rec > c_Complex_Ocomplex_Ocomplex__case > c_COMBK > tc_fun > hAPP > c_RealVector_Onorm__class_Onorm > c_RealDef_Oreal > c_Orderings_Oord__class_Oless__eq > c_Orderings_Oord__class_Oless > c_NthRoot_Oroot > c_Nat__Transfer_Otsub > c_Nat_Osize__class_Osize > c_Groups_Oabs__class_Oabs > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > c_Complex_Orcis > c_Complex_Ocomplex_OComplex > #nlpp > tc_Polynomial_Opoly > c_Transcendental_Osin > c_Transcendental_Oln > c_Transcendental_Ocos > c_RComplete_Onatfloor > c_RComplete_Onatceiling > c_Power_Opower__class_Opower > c_Nat_OSuc > c_Groups_Ozero__class_Ozero > c_Groups_Otimes__class_Otimes > c_Groups_Oplus__class_Oplus > c_Groups_Oone__class_Oone > c_Complex_Oexpi > c_Complex_Ocomplex_Ocomplex__size > c_Complex_Ocis > c_Complex_Oarg > v_s > v_r > v_ga____ > v_f____ > tc_RealDef_Oreal > tc_Nat_Onat > tc_Int_Oint > tc_HOL_Obool > tc_Complex_Ocomplex > c_Complex_Oii > c_Complex_ORe > c_Complex_OIm > #skF_33 > #skF_5 > #skF_69 > #skF_62 > #skF_35 > #skF_57 > #skF_11 > #skF_38 > #skF_21 > #skF_41 > #skF_6 > #skF_44 > #skF_31 > #skF_53 > #skF_17 > #skF_20 > #skF_56 > #skF_48 > #skF_45 > #skF_63 > #skF_22 > #skF_71 > #skF_72 > #skF_64 > #skF_60 > #skF_65 > #skF_36 > #skF_78 > #skF_3 > #skF_13 > #skF_52 > #skF_47 > #skF_77 > #skF_14 > #skF_58 > #skF_37 > #skF_74 > #skF_12 > #skF_18 > #skF_68 > #skF_19 > #skF_10 > #skF_2 > #skF_66 > #skF_67 > #skF_8 > #skF_51 > #skF_32 > #skF_26 > #skF_24 > #skF_40 > #skF_30 > #skF_50 > #skF_46 > #skF_59 > #skF_54 > #skF_25 > #skF_29 > #skF_55 > #skF_76 > #skF_23 > #skF_75 > #skF_43 > #skF_7 > #skF_49 > #skF_27 > #skF_61 > #skF_1 > #skF_16 > #skF_9 > #skF_28 > #skF_15 > #skF_73 > #skF_70 > #skF_4 > #skF_42 > #skF_34 > #skF_39
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_ga____,type,
v_ga____: $i ).
tff(class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(c_Transcendental_Oln,type,
c_Transcendental_Oln: $i > $i ).
tff(c_Transcendental_Osin,type,
c_Transcendental_Osin: $i > $i ).
tff(class_Rings_Ocomm__semiring__1,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff('#skF_33',type,
'#skF_33': $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_Groups_Omonoid__add,type,
class_Groups_Omonoid__add: $i > $o ).
tff(class_Rings_Oordered__ring,type,
class_Rings_Oordered__ring: $i > $o ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff('#skF_69',type,
'#skF_69': ( $i * $i * $i ) > $i ).
tff('#skF_62',type,
'#skF_62': ( $i * $i ) > $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i ) > $i ).
tff('#skF_57',type,
'#skF_57': $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__semiring__strict,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(c_COMBK,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff('#skF_38',type,
'#skF_38': ( $i * $i * $i ) > $i ).
tff(c_RealDef_Oreal,type,
c_RealDef_Oreal: ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': $i > $i ).
tff('#skF_41',type,
'#skF_41': ( $i * $i ) > $i ).
tff(class_Rings_Osemiring,type,
class_Rings_Osemiring: $i > $o ).
tff(c_Nat__Transfer_Otsub,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(c_Complex_Ocomplex_Ocomplex__rec,type,
c_Complex_Ocomplex_Ocomplex__rec: ( $i * $i * $i ) > $i ).
tff(tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff(c_COMBC,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(class_Rings_Ocomm__ring__1,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff('#skF_44',type,
'#skF_44': ( $i * $i * $i ) > $i ).
tff(class_Groups_Oordered__ab__semigroup__add__imp__le,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(class_Groups_Ogroup__add,type,
class_Groups_Ogroup__add: $i > $o ).
tff(tc_Nat_Onat,type,
tc_Nat_Onat: $i ).
tff(class_Groups_Oone,type,
class_Groups_Oone: $i > $o ).
tff(class_Rings_Olinordered__semiring,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(v_s,type,
v_s: $i ).
tff(class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(class_Groups_Ocancel__comm__monoid__add,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i ) > $i ).
tff(c_Complex_Ocomplex_Ocomplex__case,type,
c_Complex_Ocomplex_Ocomplex__case: ( $i * $i * $i ) > $i ).
tff(c_Fun_Ocomp,type,
c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff('#skF_31',type,
'#skF_31': $i ).
tff(c_SEQ_Odecseq,type,
c_SEQ_Odecseq: ( $i * $i ) > $o ).
tff(c_Groups_Otimes__class_Otimes,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(class_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(class_Groups_Omonoid__mult,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $i > $i ).
tff(c_Complex_Ocomplex_OComplex,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(class_Rings_Ocomm__ring,type,
class_Rings_Ocomm__ring: $i > $o ).
tff('#skF_53',type,
'#skF_53': ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__comm__semiring__strict,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(class_Groups_Oordered__ab__group__add,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff('#skF_56',type,
'#skF_56': ( $i * $i * $i ) > $i ).
tff('#skF_48',type,
'#skF_48': ( $i * $i ) > $i ).
tff('#skF_45',type,
'#skF_45': ( $i * $i ) > $i ).
tff(c_Groups_Oone__class_Oone,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff('#skF_63',type,
'#skF_63': ( $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': $i > $i ).
tff(tc_Int_Oint,type,
tc_Int_Oint: $i ).
tff('#skF_71',type,
'#skF_71': ( $i * $i * $i * $i ) > $i ).
tff('#skF_72',type,
'#skF_72': ( $i * $i * $i ) > $i ).
tff(class_Fields_Ofield__inverse__zero,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff('#skF_64',type,
'#skF_64': ( $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_COMBB,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Rings_Olinordered__ring,type,
class_Rings_Olinordered__ring: $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_Rings_Ocomm__semiring__0,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff('#skF_60',type,
'#skF_60': ( $i * $i ) > $i ).
tff(class_Groups_Ocomm__monoid__mult,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(c_NthRoot_Oroot,type,
c_NthRoot_Oroot: ( $i * $i ) > $i ).
tff('#skF_65',type,
'#skF_65': ( $i * $i ) > $i ).
tff(c_RComplete_Onatfloor,type,
c_RComplete_Onatfloor: $i > $i ).
tff(c_Complex_OIm,type,
c_Complex_OIm: $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i * $i ) > $i ).
tff(class_Rings_Oordered__comm__semiring,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff('#skF_78',type,
'#skF_78': ( $i * $i * $i ) > $i ).
tff(class_Rings_Olinordered__semidom,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff(c_Complex_Oii,type,
c_Complex_Oii: $i ).
tff(c_SEQ_Omonoseq,type,
c_SEQ_Omonoseq: ( $i * $i ) > $o ).
tff(c_Groups_Oplus__class_Oplus,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
tff(class_Rings_Odivision__ring,type,
class_Rings_Odivision__ring: $i > $o ).
tff('#skF_52',type,
'#skF_52': $i > $i ).
tff(c_Complex_Oexpi,type,
c_Complex_Oexpi: $i > $i ).
tff(c_SEQ_Oincseq,type,
c_SEQ_Oincseq: ( $i * $i ) > $o ).
tff(c_Complex_Oarg,type,
c_Complex_Oarg: $i > $i ).
tff('#skF_47',type,
'#skF_47': $i ).
tff('#skF_77',type,
'#skF_77': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff('#skF_58',type,
'#skF_58': $i > $i ).
tff(class_Rings_Ocomm__semiring,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff('#skF_37',type,
'#skF_37': ( $i * $i * $i * $i ) > $i ).
tff(class_Groups_Oordered__ab__group__add__abs,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(class_Groups_Ocancel__semigroup__add,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff('#skF_74',type,
'#skF_74': ( $i * $i * $i ) > $i ).
tff(class_Rings_Oordered__cancel__semiring,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(c_Rings_Oinverse__class_Odivide,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(class_Groups_Ominus,type,
class_Groups_Ominus: $i > $o ).
tff('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff(c_Complex_Ocomplex_Ocomplex__size,type,
c_Complex_Ocomplex_Ocomplex__size: $i > $i ).
tff('#skF_68',type,
'#skF_68': ( $i * $i * $i ) > $i ).
tff(class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__semiring__1,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i * $i ) > $i ).
tff(class_Rings_Oordered__ring__abs,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(class_Groups_Oordered__comm__monoid__add,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Groups_Ozero__class_Ozero,type,
c_Groups_Ozero__class_Ozero: $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(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(class_Rings_Oring__1,type,
class_Rings_Oring__1: $i > $o ).
tff('#skF_66',type,
'#skF_66': ( $i * $i ) > $i ).
tff(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff('#skF_67',type,
'#skF_67': ( $i * $i ) > $i ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(c_Complex_Orcis,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: ( $i * $i ) > $i ).
tff(class_Rings_Osemiring__0,type,
class_Rings_Osemiring__0: $i > $o ).
tff(class_Rings_Omult__zero,type,
class_Rings_Omult__zero: $i > $o ).
tff(class_Orderings_Oord,type,
class_Orderings_Oord: $i > $o ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(class_Groups_Oab__semigroup__add,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff('#skF_51',type,
'#skF_51': ( $i * $i ) > $i ).
tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(c_RComplete_Onatceiling,type,
c_RComplete_Onatceiling: $i > $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(c_Groups_Oabs__class_Oabs,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(c_SEQ_Osubseq,type,
c_SEQ_Osubseq: $i > $o ).
tff(v_r,type,
v_r: $i ).
tff(tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
tff(c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(class_Groups_Ocancel__ab__semigroup__add,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Rings_Oidom,type,
class_Rings_Oidom: $i > $o ).
tff(class_Groups_Ozero,type,
class_Groups_Ozero: $i > $o ).
tff('#skF_26',type,
'#skF_26': $i > $i ).
tff(class_Lattices_Oab__semigroup__idem__mult,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff('#skF_24',type,
'#skF_24': ( $i * $i ) > $i ).
tff(class_Rings_Oring__no__zero__divisors,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(class_Rings_Oring,type,
class_Rings_Oring: $i > $o ).
tff('#skF_40',type,
'#skF_40': ( $i * $i * $i ) > $i ).
tff(class_Rings_Olinordered__semiring__1__strict,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff('#skF_30',type,
'#skF_30': $i ).
tff(c_Nat_OSuc,type,
c_Nat_OSuc: $i > $i ).
tff(c_RealVector_Onorm__class_Onorm,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(c_SEQ_OBseq,type,
c_SEQ_OBseq: ( $i * $i ) > $o ).
tff('#skF_50',type,
'#skF_50': ( $i * $i ) > $i ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff('#skF_46',type,
'#skF_46': ( $i * $i ) > $i ).
tff(class_Groups_Oab__semigroup__mult,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(class_Groups_Oordered__cancel__ab__semigroup__add,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff('#skF_59',type,
'#skF_59': ( $i * $i ) > $i ).
tff(class_Rings_Ozero__neq__one,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(class_Rings_Ono__zero__divisors,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff('#skF_54',type,
'#skF_54': ( $i * $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff('#skF_55',type,
'#skF_55': ( $i * $i ) > $i ).
tff('#skF_76',type,
'#skF_76': ( $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_Complex_ORe,type,
c_Complex_ORe: $i ).
tff(class_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(class_Rings_Olinordered__idom,type,
class_Rings_Olinordered__idom: $i > $o ).
tff('#skF_75',type,
'#skF_75': ( $i * $i * $i ) > $i ).
tff(class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
tff('#skF_43',type,
'#skF_43': ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_49',type,
'#skF_49': $i > $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i ) > $i ).
tff(c_Transcendental_Ocos,type,
c_Transcendental_Ocos: $i > $i ).
tff(v_f____,type,
v_f____: $i ).
tff(class_Rings_Olinordered__ring__strict,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(class_Rings_Oring__1__no__zero__divisors,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff('#skF_61',type,
'#skF_61': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i ) > $i ).
tff(class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i ) > $i ).
tff('#skF_73',type,
'#skF_73': ( $i * $i * $i ) > $i ).
tff('#skF_70',type,
'#skF_70': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': ( $i * $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i ) > $i ).
tff(c_Complex_Ocis,type,
c_Complex_Ocis: $i > $i ).
tff(f_1238,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ( V_x_2 = V_y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
tff(f_47,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
tff(f_5787,negated_conjecture,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_5247,axiom,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_i__def) ).
tff(f_5279,axiom,
! [V_real2,V_real1] : ( c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex_Osize_I1_J) ).
tff(f_311,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
tff(f_5003,axiom,
! [V_x] : ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
tff(f_3895,axiom,
! [V_a] : ( c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rcis__zero__mod) ).
tff(f_5075,axiom,
! [V_a,V_r] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__rcis) ).
tff(f_5532,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
tff(f_39,axiom,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms) ).
tff(f_53,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
tff(f_184,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
<=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
tff(f_5508,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
tff(f_1075,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
tff(c_592,plain,
! [V_y_2_584] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2_584),V_y_2_584)),
inference(cnfTransformation,[status(thm)],[f_1238]) ).
tff(c_20060,plain,
! [V_w_3520,V_z_3521] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w_3520),V_z_3521))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z_3521),V_w_3520)) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_3445,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(cnfTransformation,[status(thm)],[f_5787]) ).
tff(c_20099,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(resolution,[status(thm)],[c_20060,c_3445]) ).
tff(c_37933,plain,
! [V_y_2_3836,V_x_2_3837] :
( ( V_y_2_3836 = V_x_2_3837 )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2_3837),V_y_2_3836))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2_3837),V_y_2_3836)) ),
inference(cnfTransformation,[status(thm)],[f_1238]) ).
tff(c_38094,plain,
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(resolution,[status(thm)],[c_20099,c_37933]) ).
tff(c_38149,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(splitLeft,[status(thm)],[c_38094]) ).
tff(c_2849,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Complex_Oii,
inference(cnfTransformation,[status(thm)],[f_5247]) ).
tff(c_2877,plain,
! [V_real1_2762,V_real2_2761] : ( c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1_2762,V_real2_2761)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(cnfTransformation,[status(thm)],[f_5279]) ).
tff(c_3891,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Complex_Ocomplex_Ocomplex__size(c_Complex_Oii),
inference(superposition,[status(thm),theory(equality)],[c_2849,c_2877]) ).
tff(c_151,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_311]) ).
tff(c_4001,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Complex_Ocomplex_Ocomplex__size(c_Complex_Oii)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_3891,c_151]) ).
tff(c_4466,plain,
! [V_x_3006] : ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x_3006)) = c_RealDef_Oreal(tc_Nat_Onat,V_x_3006) ),
inference(cnfTransformation,[status(thm)],[f_5003]) ).
tff(c_4475,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Complex_Ocomplex_Ocomplex__size(c_Complex_Oii)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(superposition,[status(thm),theory(equality)],[c_4001,c_4466]) ).
tff(c_4481,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_4001,c_4475]) ).
tff(c_1998,plain,
! [V_a_1995] : ( c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a_1995) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(cnfTransformation,[status(thm)],[f_3895]) ).
tff(c_5405,plain,
! [V_r_3060,V_a_3061] : ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r_3060,V_a_3061)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r_3060) ),
inference(cnfTransformation,[status(thm)],[f_5075]) ).
tff(c_5417,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(superposition,[status(thm),theory(equality)],[c_1998,c_5405]) ).
tff(c_5421,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(demodulation,[status(thm),theory(equality)],[c_4481,c_5417]) ).
tff(c_3271,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnfTransformation,[status(thm)],[f_5532]) ).
tff(c_8,plain,
! [B_n_6] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n_6))),v_r)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_276176,plain,
! [V_i_977098,V_k_977099,V_j_977100] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_977098),V_k_977099))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j_977100),V_k_977099))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_977098),V_j_977100)) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_276594,plain,
! [V_i_978023] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_978023),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_978023),v_r)) ),
inference(resolution,[status(thm)],[c_20099,c_276176]) ).
tff(c_66,plain,
! [T_a_78,V_x_2_77] :
( ( c_Groups_Ozero__class_Ozero(T_a_78) = V_x_2_77 )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a_78,V_x_2_77)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_RealVector_Oreal__normed__vector(T_a_78) ),
inference(cnfTransformation,[status(thm)],[f_184]) ).
tff(c_282118,plain,
! [T_a_994612,V_x_2_994613] :
( ( c_Groups_Ozero__class_Ozero(T_a_994612) = V_x_2_994613 )
| ~ class_RealVector_Oreal__normed__vector(T_a_994612)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a_994612,V_x_2_994613)),v_r)) ),
inference(resolution,[status(thm)],[c_276594,c_66]) ).
tff(c_282172,plain,
! [B_n_6] :
( ( hAPP(v_s,B_n_6) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[c_8,c_282118]) ).
tff(c_282214,plain,
! [B_n_6] : ( hAPP(v_s,B_n_6) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(demodulation,[status(thm),theory(equality)],[c_3271,c_282172]) ).
tff(c_3223,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5508]) ).
tff(c_42622,plain,
! [T_a_3903,V_y_2_3904,V_x_2_3905] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a_3903,V_y_2_3904),V_x_2_3905))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a_3903,V_x_2_3905),V_y_2_3904))
| ~ class_Orderings_Opreorder(T_a_3903) ),
inference(cnfTransformation,[status(thm)],[f_1075]) ).
tff(c_42740,plain,
! [B_n_6] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n_6))))
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_8,c_42622]) ).
tff(c_42944,plain,
! [B_n_6] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n_6)))),
inference(demodulation,[status(thm),theory(equality)],[c_3223,c_42740]) ).
tff(c_282245,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_r),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))),
inference(demodulation,[status(thm),theory(equality)],[c_282214,c_42944]) ).
tff(c_282270,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_38149,c_5421,c_282245]) ).
tff(c_282271,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r,
inference(splitRight,[status(thm)],[c_38094]) ).
tff(c_282391,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r),v_r)),
inference(demodulation,[status(thm),theory(equality)],[c_282271,c_3445]) ).
tff(c_282397,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_592,c_282391]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW204+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Apr 9 05:14:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 136.03/101.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 136.03/101.08
% 136.03/101.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------