TSTP Solution File: SWW225+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWW225+1 : TPTP v8.1.2. 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 : n023.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 11:06:53 EDT 2023
% Result : Theorem 58.83s 33.16s
% Output : CNFRefutation 58.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 208
% Syntax : Number of formulae : 228 ( 16 unt; 198 typ; 0 def)
% Number of atoms : 50 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 12 |; 1 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 301 ( 182 >; 119 *; 0 +; 0 <<)
% Number of predicates : 77 ( 75 usr; 1 prp; 0-3 aty)
% Number of functors : 123 ( 123 usr; 16 con; 0-4 aty)
% Number of variables : 30 (; 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Orderings_Oord__class_Oless__eq > c_Orderings_Oord__class_Oless > 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__1 > 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_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__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_Nat_Osemiring__char__0 > class_Int_Oring__char__0 > class_Int_Onumber__ring > class_Int_Onumber > 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_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 > class_Divides_Osemiring__div > c_SEQ_Osubseq > c_Nat__Numeral_Oneg > c_Nat_Osemiring__1__class_Oof__nat__aux > c_Rings_Oinverse__class_Odivide > c_Power_Opower_Opower > c_Groups_Oplus__class_Oplus > c_Groups_Ominus__class_Ominus > c_Divides_Odiv__class_Odiv > tc_fun > hAPP > c_RealVector_Onorm__class_Onorm > c_Nat__Transfer_Otsub > c_Int_Onumber__class_Onumber__of > c_Groups_Oabs__class_Oabs > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > c_Complex_Orcis > #nlpp > v_g____ > tc_Polynomial_Opoly > c_RealDef_Oreal > c_RComplete_Onatfloor > c_RComplete_Onatceiling > c_Power_Opower__class_Opower > c_Nat_Osemiring__1__class_Oof__nat > c_Nat_OSuc > c_Int_Osucc > c_Int_Opred > c_Groups_Ozero__class_Ozero > c_Groups_Otimes__class_Otimes > c_Groups_Oone__class_Oone > c_Complex_Oexpi > c_Complex_Ocis > v_z____ > v_w____ > v_r > v_f____ > v_d____ > v_N2____ > v_N1____ > tc_RealDef_Oreal > tc_Nat_Onat > tc_Int_Oint > tc_HOL_Obool > tc_Complex_Ocomplex > c_Int_OPls > c_Complex_Oii > #skF_76 > #skF_47 > #skF_26 > #skF_11 > #skF_64 > #skF_22 > #skF_80 > #skF_6 > #skF_33 > #skF_66 > #skF_53 > #skF_17 > #skF_20 > #skF_62 > #skF_63 > #skF_72 > #skF_70 > #skF_52 > #skF_60 > #skF_31 > #skF_38 > #skF_79 > #skF_78 > #skF_13 > #skF_39 > #skF_69 > #skF_77 > #skF_14 > #skF_34 > #skF_58 > #skF_74 > #skF_32 > #skF_12 > #skF_56 > #skF_48 > #skF_18 > #skF_45 > #skF_19 > #skF_28 > #skF_35 > #skF_49 > #skF_65 > #skF_43 > #skF_10 > #skF_37 > #skF_42 > #skF_8 > #skF_51 > #skF_36 > #skF_57 > #skF_71 > #skF_23 > #skF_24 > #skF_46 > #skF_67 > #skF_5 > #skF_59 > #skF_50 > #skF_54 > #skF_2 > #skF_40 > #skF_27 > #skF_68 > #skF_3 > #skF_44 > #skF_75 > #skF_25 > #skF_41 > #skF_7 > #skF_29 > #skF_61 > #skF_1 > #skF_16 > #skF_21 > #skF_55 > #skF_9 > #skF_30 > #skF_15 > #skF_73 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_Groups_Olinordered__ab__group__add,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff('#skF_76',type,
'#skF_76': ( $i * $i ) > $i ).
tff(class_Rings_Ocomm__semiring__1,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(c_Orderings_Oord__class_Oless__eq,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff('#skF_47',type,
'#skF_47': ( $i * $i ) > $i ).
tff(c_Int_Opred,type,
c_Int_Opred: $i > $i ).
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('#skF_26',type,
'#skF_26': ( $i * $i * $i ) > $i ).
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_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(class_Rings_Olinordered__semiring__strict,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff('#skF_64',type,
'#skF_64': ( $i * $i * $i ) > $i ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff('#skF_22',type,
'#skF_22': ( $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(tc_HOL_Obool,type,
tc_HOL_Obool: $i ).
tff('#skF_80',type,
'#skF_80': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i ) > $i ).
tff(class_Rings_Ocomm__ring__1,type,
class_Rings_Ocomm__ring__1: $i > $o ).
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('#skF_66',type,
'#skF_66': $i > $i ).
tff(c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $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(class_Groups_Ocomm__monoid__add,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
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(c_Nat_Osemiring__1__class_Oof__nat__aux,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: ( $i * $i * $i * $i ) > $i ).
tff(class_Groups_Omonoid__mult,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(tc_Polynomial_Opoly,type,
tc_Polynomial_Opoly: $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_62',type,
'#skF_62': $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(tc_Int_Oint,type,
tc_Int_Oint: $i ).
tff('#skF_72',type,
'#skF_72': ( $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(class_Rings_Olinordered__ring,type,
class_Rings_Olinordered__ring: $i > $o ).
tff('#skF_70',type,
'#skF_70': ( $i * $i ) > $i ).
tff(c_Power_Opower_Opower,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(tc_RealDef_Oreal,type,
tc_RealDef_Oreal: $i ).
tff(v_d____,type,
v_d____: $i ).
tff(class_Rings_Ocomm__semiring__0,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff('#skF_52',type,
'#skF_52': ( $i * $i * $i ) > $i ).
tff(c_RealDef_Oreal,type,
c_RealDef_Oreal: $i > $i ).
tff(class_Int_Onumber,type,
class_Int_Onumber: $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('#skF_31',type,
'#skF_31': ( $i * $i ) > $i ).
tff('#skF_38',type,
'#skF_38': ( $i * $i ) > $i ).
tff(c_RComplete_Onatfloor,type,
c_RComplete_Onatfloor: $i > $i ).
tff('#skF_79',type,
'#skF_79': ( $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(c_Int_OPls,type,
c_Int_OPls: $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff(c_Complex_Oii,type,
c_Complex_Oii: $i ).
tff(v_g____,type,
v_g____: $i > $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i * $i ) > $i ).
tff(c_SEQ_Omonoseq,type,
c_SEQ_Omonoseq: ( $i * $i ) > $o ).
tff('#skF_69',type,
'#skF_69': ( $i * $i ) > $i ).
tff(c_Complex_Oexpi,type,
c_Complex_Oexpi: $i > $i ).
tff(c_SEQ_Oincseq,type,
c_SEQ_Oincseq: ( $i * $i ) > $o ).
tff('#skF_77',type,
'#skF_77': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff(v_N1____,type,
v_N1____: $i ).
tff(v_N2____,type,
v_N2____: $i ).
tff(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).
tff('#skF_34',type,
'#skF_34': $i > $i ).
tff('#skF_58',type,
'#skF_58': $i > $i ).
tff(class_Rings_Ocomm__semiring,type,
class_Rings_Ocomm__semiring: $i > $o ).
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_32',type,
'#skF_32': $i > $i ).
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('#skF_56',type,
'#skF_56': $i > $i ).
tff('#skF_48',type,
'#skF_48': ( $i * $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff(class_Fields_Ofield,type,
class_Fields_Ofield: $i > $o ).
tff('#skF_45',type,
'#skF_45': $i ).
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_28',type,
'#skF_28': $i > $i ).
tff('#skF_35',type,
'#skF_35': ( $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('#skF_49',type,
'#skF_49': ( $i * $i ) > $i ).
tff(c_Groups_Ominus__class_Ominus,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Oord__class_Oless,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
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('#skF_65',type,
'#skF_65': ( $i * $i * $i ) > $i ).
tff('#skF_43',type,
'#skF_43': $i > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
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(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff('#skF_37',type,
'#skF_37': ( $i * $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': ( $i * $i ) > $i ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(c_Complex_Orcis,type,
c_Complex_Orcis: ( $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(c_Groups_Oplus__class_Oplus,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
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_36',type,
'#skF_36': ( $i * $i ) > $i ).
tff('#skF_57',type,
'#skF_57': $i > $i ).
tff('#skF_71',type,
'#skF_71': ( $i * $i ) > $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(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
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('#skF_23',type,
'#skF_23': $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_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(class_Rings_Osemiring__1,type,
class_Rings_Osemiring__1: $i > $o ).
tff(class_Rings_Olinordered__semiring__1__strict,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff('#skF_46',type,
'#skF_46': ( $i * $i * $i * $i ) > $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_67',type,
'#skF_67': $i > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i ) > $i ).
tff(v_z____,type,
v_z____: $i ).
tff(hAPP,type,
hAPP: ( $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_50',type,
'#skF_50': ( $i * $i * $i ) > $i ).
tff('#skF_54',type,
'#skF_54': ( $i * $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(v_w____,type,
v_w____: $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(c_Nat__Numeral_Oneg,type,
c_Nat__Numeral_Oneg: $i > $o ).
tff('#skF_40',type,
'#skF_40': ( $i * $i ) > $i ).
tff(class_Rings_Oordered__semiring,type,
class_Rings_Oordered__semiring: $i > $o ).
tff('#skF_27',type,
'#skF_27': $i > $i ).
tff('#skF_68',type,
'#skF_68': ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i * $i ) > $i ).
tff('#skF_44',type,
'#skF_44': $i ).
tff(class_Rings_Olinordered__idom,type,
class_Rings_Olinordered__idom: $i > $o ).
tff('#skF_75',type,
'#skF_75': ( $i * $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i ) > $i ).
tff(class_Groups_Oab__group__add,type,
class_Groups_Oab__group__add: $i > $o ).
tff('#skF_41',type,
'#skF_41': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $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('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff(c_Int_Osucc,type,
c_Int_Osucc: $i > $i ).
tff(class_Groups_Oordered__ab__semigroup__add,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff('#skF_55',type,
'#skF_55': $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': $i > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i ) > $i ).
tff('#skF_73',type,
'#skF_73': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(c_Complex_Ocis,type,
c_Complex_Ocis: $i > $i ).
tff(f_33,axiom,
c_SEQ_Osubseq(v_f____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fz_I1_J) ).
tff(f_5653,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
tff(f_1176,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
tff(f_3072,axiom,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__def) ).
tff(f_5939,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f_1037,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
tff(f_1438,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
tff(f_5595,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
tff(f_378,axiom,
! [V_n_2,V_fa_2] :
( c_SEQ_Osubseq(V_fa_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,hAPP(V_fa_2,V_n_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_seq__suble) ).
tff(f_1154,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
& ~ 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_4,plain,
c_SEQ_Osubseq(v_f____),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_3318,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_5653]) ).
tff(c_17775,plain,
! [T_a_3355,V_x_3356,V_y_3357] :
( c_Orderings_Oord__class_Oless(T_a_3355,V_x_3356,V_y_3357)
| c_Orderings_Oord__class_Oless__eq(T_a_3355,V_y_3357,V_x_3356)
| ~ class_Orderings_Olinorder(T_a_3355) ),
inference(cnfTransformation,[status(thm)],[f_1176]) ).
tff(c_1704,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(cnfTransformation,[status(thm)],[f_3072]) ).
tff(c_3544,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(cnfTransformation,[status(thm)],[f_5939]) ).
tff(c_3604,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(demodulation,[status(thm),theory(equality)],[c_1704,c_1704,c_3544]) ).
tff(c_17935,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[c_17775,c_3604]) ).
tff(c_18063,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(demodulation,[status(thm),theory(equality)],[c_3318,c_17935]) ).
tff(c_542,plain,
! [V_n_2_538,V_m_2_537] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2_538,V_m_2_537)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2_538),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2_537)) ),
inference(cnfTransformation,[status(thm)],[f_1037]) ).
tff(c_80983,plain,
! [V_n_2_4198,V_m_2_4199] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2_4198,V_m_2_4199)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_n_2_4198),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),V_m_2_4199)) ),
inference(demodulation,[status(thm),theory(equality)],[c_1704,c_1704,c_542]) ).
tff(c_81117,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(resolution,[status(thm)],[c_18063,c_80983]) ).
tff(c_719,plain,
! [V_m_729,V_n_728] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_729,V_n_728)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_729),c_Nat_OSuc(V_n_728)) ),
inference(cnfTransformation,[status(thm)],[f_1438]) ).
tff(c_81352,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),
inference(resolution,[status(thm)],[c_81117,c_719]) ).
tff(c_3202,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnfTransformation,[status(thm)],[f_5595]) ).
tff(c_183,plain,
! [V_n_2_206,V_fa_2_207] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2_206,hAPP(V_fa_2_207,V_n_2_206))
| ~ c_SEQ_Osubseq(V_fa_2_207) ),
inference(cnfTransformation,[status(thm)],[f_378]) ).
tff(c_17110,plain,
! [T_a_3345,V_y_2_3346,V_x_2_3347] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a_3345,V_y_2_3346,V_x_2_3347)
| ~ c_Orderings_Oord__class_Oless(T_a_3345,V_x_2_3347,V_y_2_3346)
| ~ class_Orderings_Opreorder(T_a_3345) ),
inference(cnfTransformation,[status(thm)],[f_1154]) ).
tff(c_17236,plain,
! [V_fa_2_207,V_n_2_206] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2_207,V_n_2_206),V_n_2_206)
| ~ class_Orderings_Opreorder(tc_Nat_Onat)
| ~ c_SEQ_Osubseq(V_fa_2_207) ),
inference(resolution,[status(thm)],[c_183,c_17110]) ).
tff(c_17465,plain,
! [V_fa_2_207,V_n_2_206] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2_207,V_n_2_206),V_n_2_206)
| ~ c_SEQ_Osubseq(V_fa_2_207) ),
inference(demodulation,[status(thm),theory(equality)],[c_3202,c_17236]) ).
tff(c_96839,plain,
~ c_SEQ_Osubseq(v_f____),
inference(resolution,[status(thm)],[c_81352,c_17465]) ).
tff(c_96880,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_96839]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% 0.14/0.14 % 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
% 0.14/0.36 % Computer : n023.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 19:34:22 EDT 2023
% 0.14/0.36 % CPUTime :
% 58.83/33.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.83/33.16
% 58.83/33.16 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.83/33.20
% 58.83/33.20 Inference rules
% 58.83/33.20 ----------------------
% 58.83/33.20 #Ref : 31
% 58.83/33.20 #Sup : 20619
% 58.83/33.20 #Fact : 18
% 58.83/33.20 #Define : 0
% 58.83/33.20 #Split : 12
% 58.83/33.20 #Chain : 0
% 58.83/33.20 #Close : 0
% 58.83/33.20
% 58.83/33.20 Ordering : KBO
% 58.83/33.20
% 58.83/33.20 Simplification rules
% 58.83/33.20 ----------------------
% 58.83/33.20 #Subsume : 6718
% 58.83/33.20 #Demod : 14380
% 58.83/33.20 #Tautology : 6870
% 58.83/33.20 #SimpNegUnit : 968
% 58.83/33.20 #BackRed : 27
% 58.83/33.20
% 58.83/33.20 #Partial instantiations: 0
% 58.83/33.20 #Strategies tried : 1
% 58.83/33.20
% 58.83/33.20 Timing (in seconds)
% 58.83/33.20 ----------------------
% 58.83/33.20 Preprocessing : 2.23
% 58.83/33.20 Parsing : 1.16
% 58.83/33.20 CNF conversion : 0.18
% 58.83/33.20 Main loop : 29.84
% 58.83/33.20 Inferencing : 3.82
% 58.83/33.20 Reduction : 16.99
% 58.83/33.20 Demodulation : 13.39
% 58.83/33.20 BG Simplification : 0.28
% 58.83/33.20 Subsumption : 7.11
% 58.83/33.20 Abstraction : 0.25
% 58.83/33.20 MUC search : 0.00
% 58.83/33.20 Cooper : 0.00
% 58.83/33.20 Total : 32.12
% 58.91/33.20 Index Insertion : 0.00
% 58.91/33.20 Index Deletion : 0.00
% 58.91/33.20 Index Matching : 0.00
% 58.91/33.20 BG Taut test : 0.00
%------------------------------------------------------------------------------