TSTP Solution File: SWW215+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW215+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/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 : n009.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 11:06:52 EDT 2023

% Result   : Theorem 38.67s 16.78s
% Output   : CNFRefutation 38.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  187
% Syntax   : Number of formulae    :  203 (  13 unt; 178 typ;   0 def)
%            Number of atoms       :   46 (   1 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   41 (  20   ~;  13   |;   2   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  287 ( 157   >; 130   *;   0   +;   0  <<)
%            Number of predicates  :   83 (  81 usr;   1 prp; 0-5 aty)
%            Number of functors    :   97 (  97 usr;  21 con; 0-6 aty)
%            Number of variables   :   25 (;  25   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_Polynomial_Opdivmod__rel > c_Rings_Odvd__class_Odvd > c_Orderings_Oord__class_Oless__eq > c_Orderings_Oord__class_Oless > c_SEQ_Odecseq > 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_Odvd > class_Rings_Odivision__ring__inverse__zero > 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_RealVector_Oreal__field > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Oord > class_Orderings_Olinorder > class_Orderings_Odense__linorder > class_Lattices_Oab__semigroup__idem__mult > class_Int_Oring__char__0 > 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_Olinordered__field__inverse__zero > class_Fields_Olinordered__field > class_Fields_Ofield__inverse__zero > class_Fields_Ofield > class_Divides_Osemiring__div > class_Divides_Oring__div > c_RealDef_Opositive > c_Rings_Oinverse__class_Odivide > c_Power_Opower_Opower > c_Polynomial_Osynthetic__div > c_Polynomial_Opcompose > c_Polynomial_Oorder > c_Groups_Oplus__class_Oplus > c_Groups_Ominus__class_Ominus > c_Divides_Odiv__class_Omod > c_Divides_Odiv__class_Odiv > tc_fun > hAPP > c_RealVector_Onorm__class_Onorm > c_RealDef_Oreal > c_Polynomial_Opoly > c_Polynomial_Odegree > c_Groups_Oabs__class_Oabs > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > #nlpp > tc_Polynomial_Opoly > c_Transcendental_Oarctan > c_RComplete_Onatfloor > c_RComplete_Onatceiling > c_Power_Opower__class_Opower > c_Groups_Ozero__class_Ozero > c_Groups_Otimes__class_Otimes > c_Groups_Oone__class_Oone > c_Complex_Oexpi > v_z > v_w____ > v_q____ > v_p > v_m____ > v_e > v_da____ > v_d____ > v_cs____ > tc_RealDef_Oreal > tc_Nat_Onat > tc_Int_Oint > tc_HOL_Obool > tc_Complex_Ocomplex > c_Complex_Oii > #skF_32 > #skF_26 > #skF_49 > #skF_11 > #skF_41 > #skF_31 > #skF_33 > #skF_44 > #skF_18 > #skF_17 > #skF_30 > #skF_15 > #skF_47 > #skF_20 > #skF_56 > #skF_22 > #skF_19 > #skF_36 > #skF_13 > #skF_39 > #skF_10 > #skF_34 > #skF_14 > #skF_29 > #skF_48 > #skF_45 > #skF_35 > #skF_2 > #skF_8 > #skF_7 > #skF_37 > #skF_42 > #skF_9 > #skF_4 > #skF_51 > #skF_28 > #skF_24 > #skF_40 > #skF_23 > #skF_5 > #skF_52 > #skF_50 > #skF_54 > #skF_55 > #skF_3 > #skF_38 > #skF_46 > #skF_12 > #skF_25 > #skF_43 > #skF_27 > #skF_6 > #skF_1 > #skF_21 > #skF_53 > #skF_16

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(class_Groups_Olinordered__ab__group__add,type,
    class_Groups_Olinordered__ab__group__add: $i > $o ).

tff(class_Rings_Ocomm__semiring__1,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

tff('#skF_32',type,
    '#skF_32': ( $i * $i * $i ) > $i ).

tff(c_Orderings_Oord__class_Oless__eq,type,
    c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).

tff(class_Int_Oring__char__0,type,
    class_Int_Oring__char__0: $i > $o ).

tff(class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

tff('#skF_26',type,
    '#skF_26': ( $i * $i * $i ) > $i ).

tff('#skF_49',type,
    '#skF_49': ( $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(c_RealDef_Oreal,type,
    c_RealDef_Oreal: ( $i * $i ) > $i ).

tff('#skF_41',type,
    '#skF_41': ( $i * $i ) > $i ).

tff(class_Rings_Osemiring,type,
    class_Rings_Osemiring: $i > $o ).

tff(tc_HOL_Obool,type,
    tc_HOL_Obool: $i ).

tff('#skF_31',type,
    '#skF_31': ( $i * $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('#skF_44',type,
    '#skF_44': ( $i * $i * $i ) > $i ).

tff('#skF_18',type,
    '#skF_18': $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('#skF_17',type,
    '#skF_17': $i ).

tff(class_Rings_Olinordered__semiring,type,
    class_Rings_Olinordered__semiring: $i > $o ).

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('#skF_30',type,
    '#skF_30': ( $i * $i ) > $i ).

tff(class_Groups_Ocomm__monoid__add,type,
    class_Groups_Ocomm__monoid__add: $i > $o ).

tff('#skF_15',type,
    '#skF_15': $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(class_Rings_Ocomm__ring,type,
    class_Rings_Ocomm__ring: $i > $o ).

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_47',type,
    '#skF_47': ( $i * $i * $i ) > $i ).

tff('#skF_20',type,
    '#skF_20': ( $i * $i ) > $i ).

tff(class_Rings_Odvd,type,
    class_Rings_Odvd: $i > $o ).

tff('#skF_56',type,
    '#skF_56': ( $i * $i * $i ) > $i ).

tff(v_e,type,
    v_e: $i ).

tff(c_Groups_Oone__class_Oone,type,
    c_Groups_Oone__class_Oone: $i > $i ).

tff(c_Polynomial_Osynthetic__div,type,
    c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).

tff('#skF_22',type,
    '#skF_22': $i > $i ).

tff(tc_Int_Oint,type,
    tc_Int_Oint: $i ).

tff(class_Fields_Ofield__inverse__zero,type,
    class_Fields_Ofield__inverse__zero: $i > $o ).

tff(class_Orderings_Odense__linorder,type,
    class_Orderings_Odense__linorder: $i > $o ).

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(c_Power_Opower_Opower,type,
    c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).

tff(v_z,type,
    v_z: $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(class_Groups_Ocomm__monoid__mult,type,
    class_Groups_Ocomm__monoid__mult: $i > $o ).

tff('#skF_19',type,
    '#skF_19': $i ).

tff(c_RComplete_Onatfloor,type,
    c_RComplete_Onatfloor: $i > $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(class_Rings_Olinordered__semidom,type,
    class_Rings_Olinordered__semidom: $i > $o ).

tff('#skF_13',type,
    '#skF_13': ( $i * $i ) > $i ).

tff(c_Complex_Oii,type,
    c_Complex_Oii: $i ).

tff('#skF_39',type,
    '#skF_39': ( $i * $i * $i ) > $i ).

tff(v_cs____,type,
    v_cs____: $i ).

tff('#skF_10',type,
    '#skF_10': $i ).

tff(class_Rings_Odivision__ring,type,
    class_Rings_Odivision__ring: $i > $o ).

tff(c_Complex_Oexpi,type,
    c_Complex_Oexpi: $i > $i ).

tff('#skF_34',type,
    '#skF_34': ( $i * $i ) > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i ) > $i ).

tff(class_Rings_Ocomm__semiring,type,
    class_Rings_Ocomm__semiring: $i > $o ).

tff('#skF_29',type,
    '#skF_29': $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(class_Rings_Oordered__cancel__semiring,type,
    class_Rings_Oordered__cancel__semiring: $i > $o ).

tff(c_Rings_Oinverse__class_Odivide,type,
    c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).

tff('#skF_48',type,
    '#skF_48': ( $i * $i * $i ) > $i ).

tff(class_Groups_Ominus,type,
    class_Groups_Ominus: $i > $o ).

tff(class_Fields_Ofield,type,
    class_Fields_Ofield: $i > $o ).

tff('#skF_45',type,
    '#skF_45': ( $i * $i * $i ) > $i ).

tff(class_Rings_Olinordered__semiring__1,type,
    class_Rings_Olinordered__semiring__1: $i > $o ).

tff(class_Divides_Oring__div,type,
    class_Divides_Oring__div: $i > $o ).

tff('#skF_35',type,
    '#skF_35': ( $i * $i * $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_Orderings_Oord__class_Oless,type,
    c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(c_Divides_Odiv__class_Omod,type,
    c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).

tff(c_Groups_Ozero__class_Ozero,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i * $i * $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_Rings_Odivision__ring__inverse__zero,type,
    class_Rings_Odivision__ring__inverse__zero: $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(class_Power_Opower,type,
    class_Power_Opower: $i > $o ).

tff(c_Rings_Odvd__class_Odvd,type,
    c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).

tff(v_m____,type,
    v_m____: $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i * $i * $i * $i * $i ) > $i ).

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(class_Rings_Osemiring__0,type,
    class_Rings_Osemiring__0: $i > $o ).

tff(c_Polynomial_Opdivmod__rel,type,
    c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $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(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_9',type,
    '#skF_9': $i ).

tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

tff(class_Fields_Olinordered__field,type,
    class_Fields_Olinordered__field: $i > $o ).

tff(c_RComplete_Onatceiling,type,
    c_RComplete_Onatceiling: $i > $i ).

tff(c_Groups_Oabs__class_Oabs,type,
    c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(c_Polynomial_Opoly,type,
    c_Polynomial_Opoly: ( $i * $i ) > $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('#skF_4',type,
    '#skF_4': ( $i * $i * $i * $i ) > $i ).

tff('#skF_51',type,
    '#skF_51': ( $i * $i * $i ) > $i ).

tff(class_Groups_Ozero,type,
    class_Groups_Ozero: $i > $o ).

tff('#skF_28',type,
    '#skF_28': ( $i * $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_23',type,
    '#skF_23': ( $i * $i ) > $i ).

tff(v_da____,type,
    v_da____: $i ).

tff(c_RealVector_Onorm__class_Onorm,type,
    c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).

tff(hAPP,type,
    hAPP: ( $i * $i ) > $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i * $i * $i * $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(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_52',type,
    '#skF_52': ( $i * $i ) > $i ).

tff('#skF_50',type,
    '#skF_50': ( $i * $i * $i ) > $i ).

tff('#skF_54',type,
    '#skF_54': ( $i * $i * $i ) > $i ).

tff('#skF_55',type,
    '#skF_55': ( $i * $i * $i ) > $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i * $i ) > $i ).

tff(c_Polynomial_Odegree,type,
    c_Polynomial_Odegree: ( $i * $i ) > $i ).

tff(hBOOL,type,
    hBOOL: $i > $o ).

tff(class_Divides_Osemiring__div,type,
    class_Divides_Osemiring__div: $i > $o ).

tff('#skF_38',type,
    '#skF_38': ( $i * $i * $i * $i ) > $i ).

tff('#skF_46',type,
    '#skF_46': ( $i * $i * $i ) > $i ).

tff(c_Polynomial_Opcompose,type,
    c_Polynomial_Opcompose: ( $i * $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(v_p,type,
    v_p: $i ).

tff(c_RealDef_Opositive,type,
    c_RealDef_Opositive: $i > $o ).

tff(class_Rings_Oordered__semiring,type,
    class_Rings_Oordered__semiring: $i > $o ).

tff(class_RealVector_Oreal__field,type,
    class_RealVector_Oreal__field: $i > $o ).

tff(class_Rings_Olinordered__idom,type,
    class_Rings_Olinordered__idom: $i > $o ).

tff(class_Fields_Olinordered__field__inverse__zero,type,
    class_Fields_Olinordered__field__inverse__zero: $i > $o ).

tff('#skF_12',type,
    '#skF_12': $i > $i ).

tff(v_q____,type,
    v_q____: $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_43',type,
    '#skF_43': ( $i * $i ) > $i ).

tff(c_Transcendental_Oarctan,type,
    c_Transcendental_Oarctan: $i > $i ).

tff('#skF_27',type,
    '#skF_27': ( $i * $i ) > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(c_Polynomial_Oorder,type,
    c_Polynomial_Oorder: ( $i * $i * $i ) > $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_1',type,
    '#skF_1': ( $i * $i ) > $i ).

tff('#skF_21',type,
    '#skF_21': ( $i * $i ) > $i ).

tff(class_Groups_Oordered__ab__semigroup__add,type,
    class_Groups_Oordered__ab__semigroup__add: $i > $o ).

tff('#skF_53',type,
    '#skF_53': ( $i * $i * $i ) > $i ).

tff('#skF_16',type,
    '#skF_16': ( $i * $i * $i ) > $i ).

tff(f_6195,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

tff(f_35,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I2_J) ).

tff(f_402,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Oorder(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)
          & ( V_x_2 != V_y_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

tff(f_36,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_H_I5_J) ).

tff(f_6186,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

tff(f_66,axiom,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).

tff(f_6488,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f_72,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).

tff(f_393,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/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

tff(c_3470,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_6195]) ).

tff(c_6,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_144,plain,
    ! [T_a_158,V_x_2_157,V_y_2_156] :
      ( c_Orderings_Oord__class_Oless__eq(T_a_158,V_x_2_157,V_y_2_156)
      | ~ c_Orderings_Oord__class_Oless(T_a_158,V_x_2_157,V_y_2_156)
      | ~ class_Orderings_Oorder(T_a_158) ),
    inference(cnfTransformation,[status(thm)],[f_402]) ).

tff(c_8,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_3452,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_6186]) ).

tff(c_5354,plain,
    ! [V_w_3298,V_z_3299] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w_3298,V_z_3299)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z_3299,V_w_3298) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_3698,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(cnfTransformation,[status(thm)],[f_6488]) ).

tff(c_5365,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),
    inference(resolution,[status(thm)],[c_5354,c_3698]) ).

tff(c_35724,plain,
    ! [V_i_3971,V_k_3972,V_j_3973] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_3971,V_k_3972)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j_3973,V_k_3972)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_3971,V_j_3973) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_36093,plain,
    ! [V_i_3975] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_3975,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_3975,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(resolution,[status(thm)],[c_5365,c_35724]) ).

tff(c_136,plain,
    ! [T_a_155,V_y_2_153,V_x_2_154] :
      ( ~ c_Orderings_Oord__class_Oless__eq(T_a_155,V_y_2_153,V_x_2_154)
      | ~ c_Orderings_Oord__class_Oless(T_a_155,V_x_2_154,V_y_2_153)
      | ~ class_Orderings_Opreorder(T_a_155) ),
    inference(cnfTransformation,[status(thm)],[f_393]) ).

tff(c_36115,plain,
    ! [V_i_3975] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),V_i_3975)
      | ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_3975,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(resolution,[status(thm)],[c_36093,c_136]) ).

tff(c_43191,plain,
    ! [V_i_4050] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),V_i_4050)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i_4050,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3452,c_36115]) ).

tff(c_43268,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(resolution,[status(thm)],[c_8,c_43191]) ).

tff(c_43273,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ class_Orderings_Oorder(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_144,c_43268]) ).

tff(c_43288,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3470,c_6,c_43273]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW215+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34  % Computer : n009.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 19:36:39 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 38.67/16.78  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.67/16.79  
% 38.67/16.79  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.80/16.82  
% 38.80/16.82  Inference rules
% 38.80/16.82  ----------------------
% 38.80/16.82  #Ref     : 14
% 38.80/16.82  #Sup     : 8246
% 38.80/16.82  #Fact    : 12
% 38.80/16.82  #Define  : 0
% 38.80/16.82  #Split   : 15
% 38.80/16.82  #Chain   : 0
% 38.80/16.82  #Close   : 0
% 38.80/16.82  
% 38.80/16.82  Ordering : KBO
% 38.80/16.82  
% 38.80/16.82  Simplification rules
% 38.80/16.82  ----------------------
% 38.80/16.82  #Subsume      : 2321
% 38.80/16.82  #Demod        : 5967
% 38.80/16.82  #Tautology    : 4378
% 38.80/16.82  #SimpNegUnit  : 201
% 38.80/16.82  #BackRed      : 1
% 38.80/16.82  
% 38.80/16.82  #Partial instantiations: 0
% 38.80/16.82  #Strategies tried      : 1
% 38.80/16.82  
% 38.80/16.82  Timing (in seconds)
% 38.80/16.82  ----------------------
% 38.80/16.82  Preprocessing        : 2.37
% 38.80/16.82  Parsing              : 1.25
% 38.80/16.82  CNF conversion       : 0.19
% 38.80/16.82  Main loop            : 13.40
% 38.80/16.82  Inferencing          : 1.95
% 38.80/16.82  Reduction            : 7.39
% 38.80/16.82  Demodulation         : 5.66
% 38.80/16.82  BG Simplification    : 0.24
% 38.80/16.82  Subsumption          : 2.95
% 38.80/16.82  Abstraction          : 0.15
% 38.80/16.82  MUC search           : 0.00
% 38.80/16.82  Cooper               : 0.00
% 38.80/16.82  Total                : 15.82
% 38.80/16.82  Index Insertion      : 0.00
% 38.80/16.82  Index Deletion       : 0.00
% 38.80/16.82  Index Matching       : 0.00
% 38.80/16.82  BG Taut test         : 0.00
%------------------------------------------------------------------------------