TSTP Solution File: SWW245+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWW245+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n032.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 : Fri Sep  1 00:16:42 EDT 2023

% Result   : Theorem 101.27s 101.37s
% Output   : CNFRefutation 101.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :  154
% Syntax   : Number of formulae    :  206 (  22 unt; 145 typ;   0 def)
%            Number of atoms       :  194 ( 169 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  226 (  93   ~; 100   |;  21   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  222 ( 126   >;  96   *;   0   +;   0  <<)
%            Number of predicates  :   70 (  68 usr;   1 prp; 0-5 aty)
%            Number of functors    :   77 (  77 usr;  19 con; 0-5 aty)
%            Number of variables   :   75 (   3 sgn;  29   !;  12   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    hAPP: ( $i * $i ) > $i ).

tff(decl_23,type,
    t_a: $i ).

tff(decl_24,type,
    class_Rings_Oidom: $i > $o ).

tff(decl_25,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

tff(decl_26,type,
    v_c____: $i ).

tff(decl_27,type,
    v_cs____: $i ).

tff(decl_28,type,
    c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).

tff(decl_29,type,
    c_Polynomial_Opoly: ( $i * $i ) > $i ).

tff(decl_30,type,
    v_p: $i ).

tff(decl_31,type,
    tc_Polynomial_Opoly: $i > $i ).

tff(decl_32,type,
    tc_Nat_Onat: $i ).

tff(decl_33,type,
    c_fequal: ( $i * $i ) > $i ).

tff(decl_34,type,
    c_Polynomial_Odegree: ( $i * $i ) > $i ).

tff(decl_35,type,
    c_Nat_OSuc: $i > $i ).

tff(decl_36,type,
    c_If: ( $i * $i * $i * $i ) > $i ).

tff(decl_37,type,
    c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    c_Groups_Otimes__class_Otimes: $i > $i ).

tff(decl_39,type,
    c_Power_Opower__class_Opower: $i > $i ).

tff(decl_40,type,
    class_Groups_Ozero: $i > $o ).

tff(decl_41,type,
    class_Rings_Ocomm__semiring__0: $i > $o ).

tff(decl_42,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).

tff(decl_43,type,
    class_Groups_Ocomm__monoid__add: $i > $o ).

tff(decl_44,type,
    class_Int_Oring__char__0: $i > $o ).

tff(decl_45,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

tff(decl_46,type,
    class_Groups_Omonoid__mult: $i > $o ).

tff(decl_47,type,
    class_Power_Opower: $i > $o ).

tff(decl_48,type,
    class_Rings_Osemiring__0: $i > $o ).

tff(decl_49,type,
    class_Rings_Omult__zero: $i > $o ).

tff(decl_50,type,
    class_Rings_Ono__zero__divisors: $i > $o ).

tff(decl_51,type,
    class_Rings_Ozero__neq__one: $i > $o ).

tff(decl_52,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

tff(decl_53,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

tff(decl_54,type,
    class_Groups_Ocomm__monoid__mult: $i > $o ).

tff(decl_55,type,
    c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    class_Rings_Olinordered__ring__strict: $i > $o ).

tff(decl_57,type,
    c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).

tff(decl_58,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

tff(decl_59,type,
    class_Rings_Ocomm__semiring: $i > $o ).

tff(decl_60,type,
    class_Rings_Osemiring: $i > $o ).

tff(decl_61,type,
    class_Groups_Omonoid__add: $i > $o ).

tff(decl_62,type,
    class_Groups_Oab__semigroup__mult: $i > $o ).

tff(decl_63,type,
    class_Groups_Ocancel__semigroup__add: $i > $o ).

tff(decl_64,type,
    class_Groups_Ocancel__ab__semigroup__add: $i > $o ).

tff(decl_65,type,
    class_Groups_Oab__semigroup__add: $i > $o ).

tff(decl_66,type,
    class_Rings_Oring__no__zero__divisors: $i > $o ).

tff(decl_67,type,
    class_Groups_Olinordered__ab__group__add: $i > $o ).

tff(decl_68,type,
    c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_69,type,
    c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).

tff(decl_70,type,
    c_Groups_Oone__class_Oone: $i > $i ).

tff(decl_71,type,
    c_Nat_Onat_Onat__size: $i > $i ).

tff(decl_72,type,
    c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    class_Groups_Oone: $i > $o ).

tff(decl_74,type,
    tc_Int_Oint: $i ).

tff(decl_75,type,
    c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    class_Rings_Ocomm__ring__1: $i > $o ).

tff(decl_77,type,
    c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).

tff(decl_78,type,
    c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).

tff(decl_79,type,
    c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    c_fTrue: $i ).

tff(decl_82,type,
    c_HOL_Obool_Obool__size: $i > $i ).

tff(decl_83,type,
    c_fFalse: $i ).

tff(decl_84,type,
    c_Polynomial_Ocoeff: ( $i * $i ) > $i ).

tff(decl_85,type,
    class_Rings_Ocomm__ring: $i > $o ).

tff(decl_86,type,
    class_Groups_Oab__group__add: $i > $o ).

tff(decl_87,type,
    class_Groups_Ogroup__add: $i > $o ).

tff(decl_88,type,
    class_Rings_Oring: $i > $o ).

tff(decl_89,type,
    class_Rings_Oring__1: $i > $o ).

tff(decl_90,type,
    c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).

tff(decl_91,type,
    class_Fields_Ofield: $i > $o ).

tff(decl_92,type,
    c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).

tff(decl_93,type,
    class_Rings_Odvd: $i > $o ).

tff(decl_94,type,
    hBOOL: $i > $o ).

tff(decl_95,type,
    c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).

tff(decl_96,type,
    c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(decl_97,type,
    c_Nat_Onat_Onat__case: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    class_Rings_Odivision__ring: $i > $o ).

tff(decl_99,type,
    class_Rings_Odivision__ring__inverse__zero: $i > $o ).

tff(decl_100,type,
    class_Fields_Ofield__inverse__zero: $i > $o ).

tff(decl_101,type,
    c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).

tff(decl_102,type,
    c_Polynomial_OAbs__poly: ( $i * $i ) > $i ).

tff(decl_103,type,
    c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(decl_104,type,
    class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).

tff(decl_105,type,
    class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).

tff(decl_106,type,
    class_Groups_Oordered__ab__group__add: $i > $o ).

tff(decl_107,type,
    class_Rings_Olinordered__idom: $i > $o ).

tff(decl_108,type,
    class_Rings_Olinordered__semidom: $i > $o ).

tff(decl_109,type,
    class_Rings_Olinordered__comm__semiring__strict: $i > $o ).

tff(decl_110,type,
    class_Rings_Olinordered__semiring__strict: $i > $o ).

tff(decl_111,type,
    class_Rings_Olinordered__ring: $i > $o ).

tff(decl_112,type,
    class_Groups_Oordered__comm__monoid__add: $i > $o ).

tff(decl_113,type,
    class_Fields_Olinordered__field: $i > $o ).

tff(decl_114,type,
    class_Fields_Olinordered__field__inverse__zero: $i > $o ).

tff(decl_115,type,
    class_Rings_Oordered__ring: $i > $o ).

tff(decl_116,type,
    class_Divides_Osemiring__div: $i > $o ).

tff(decl_117,type,
    class_Divides_Oring__div: $i > $o ).

tff(decl_118,type,
    c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).

tff(decl_119,type,
    c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).

tff(decl_120,type,
    class_RealVector_Oreal__normed__field: $i > $o ).

tff(decl_121,type,
    class_RealVector_Oreal__field: $i > $o ).

tff(decl_122,type,
    c_Polynomial_Opos__poly: ( $i * $i ) > $o ).

tff(decl_123,type,
    c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).

tff(decl_124,type,
    c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(decl_125,type,
    class_Groups_Oordered__ab__group__add__abs: $i > $o ).

tff(decl_126,type,
    class_Groups_Oabs__if: $i > $o ).

tff(decl_127,type,
    c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).

tff(decl_128,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

tff(decl_129,type,
    class_Groups_Osgn__if: $i > $o ).

tff(decl_130,type,
    class_RealVector_Oreal__normed__div__algebra: $i > $o ).

tff(decl_131,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

tff(decl_132,type,
    c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).

tff(decl_133,type,
    class_Rings_Olinordered__semiring: $i > $o ).

tff(decl_134,type,
    class_Groups_Ocancel__comm__monoid__add: $i > $o ).

tff(decl_135,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_136,type,
    esk2_0: $i ).

tff(decl_137,type,
    esk3_0: $i ).

tff(decl_138,type,
    esk4_0: $i ).

tff(decl_139,type,
    esk5_0: $i ).

tff(decl_140,type,
    esk6_0: $i ).

tff(decl_141,type,
    esk7_0: $i ).

tff(decl_142,type,
    esk8_0: $i ).

tff(decl_143,type,
    esk9_0: $i ).

tff(decl_144,type,
    esk10_0: $i ).

tff(decl_145,type,
    esk11_0: $i ).

tff(decl_146,type,
    esk12_0: $i ).

tff(decl_147,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_148,type,
    esk14_3: ( $i * $i * $i ) > $i ).

tff(decl_149,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_150,type,
    esk16_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_151,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_152,type,
    esk18_1: $i > $i ).

tff(decl_153,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_154,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_155,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_156,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_157,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_158,type,
    esk24_3: ( $i * $i * $i ) > $i ).

tff(decl_159,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_160,type,
    esk26_3: ( $i * $i * $i ) > $i ).

tff(decl_161,type,
    esk27_3: ( $i * $i * $i ) > $i ).

tff(decl_162,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_163,type,
    esk29_3: ( $i * $i * $i ) > $i ).

tff(decl_164,type,
    esk30_3: ( $i * $i * $i ) > $i ).

tff(decl_165,type,
    esk31_3: ( $i * $i * $i ) > $i ).

tff(decl_166,type,
    esk32_3: ( $i * $i * $i ) > $i ).

fof(fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096,axiom,
    ( class_Rings_Oidom(t_a)
   => ( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
     => ? [X5,X6] :
          ( X6 != c_Groups_Ozero__class_Ozero(t_a)
          & ? [X7] :
              ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
               => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X7))),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
              & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
               => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X7))),X5)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
              & ! [X4] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X4),X5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X6,X7)),X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X19] : c_Nat_OSuc(X19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096,axiom,
    ( class_Rings_Oidom(t_a)
   => ( v_c____ != c_Groups_Ozero__class_Ozero(t_a)
     => ? [X5,X6] :
          ( X6 != c_Groups_Ozero__class_Ozero(t_a)
          & ? [X7] :
              ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
               => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X7))),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
              & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
               => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X7))),X5)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
              & ! [X4] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X4),X5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X6,X7)),X4)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096) ).

fof(fact_nat__add__commute,axiom,
    ! [X19,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X22),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_nat__add__assoc,axiom,
    ! [X36,X19,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X19),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X36)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X22] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X22),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

fof(conj_0,conjecture,
    ? [X5,X6] :
      ( X6 != c_Groups_Ozero__class_Ozero(t_a)
      & ? [X7] :
          ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
           => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X7))),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
           => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X7))),X5)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
          & ! [X4] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X4),X5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X6,X7)),X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(tfree_0,hypothesis,
    class_Rings_Oidom(t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X35,X34,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,X35)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X34,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X35)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(c_0_9,plain,
    ! [X102] :
      ( ( esk8_0 != c_Groups_Ozero__class_Ozero(t_a)
        | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
        | ~ class_Rings_Oidom(t_a) )
      & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
        | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,esk9_0))),esk7_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
        | ~ class_Rings_Oidom(t_a) )
      & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
        | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,esk9_0))),esk7_0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
        | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
        | ~ class_Rings_Oidom(t_a) )
      & ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X102),esk7_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk8_0,esk9_0)),X102))
        | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
        | ~ class_Rings_Oidom(t_a) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096])])])])]) ).

fof(c_0_10,plain,
    ! [X614] : c_Nat_OSuc(X614) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X614,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(c_0_11,plain,
    ! [X98] :
      ( ( esk5_0 != c_Groups_Ozero__class_Ozero(t_a)
        | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
        | ~ class_Rings_Oidom(t_a) )
      & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
        | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,esk6_0))),esk4_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
        | ~ class_Rings_Oidom(t_a) )
      & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
        | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,esk6_0))),esk4_0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
        | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
        | ~ class_Rings_Oidom(t_a) )
      & ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X98) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X98),esk4_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk5_0,esk6_0)),X98))
        | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
        | ~ class_Rings_Oidom(t_a) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096])])])])]) ).

cnf(c_0_12,plain,
    ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,esk9_0))),esk7_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
    | ~ class_Rings_Oidom(t_a) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_14,plain,
    ! [X299,X300] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X300,X299) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X299,X300),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(c_0_15,plain,
    ! [X304,X305,X306] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X306,X305),X304) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X306,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X305,X304)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(c_0_16,plain,
    ! [X366] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X366),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

fof(c_0_17,negated_conjecture,
    ~ ? [X5,X6] :
        ( X6 != c_Groups_Ozero__class_Ozero(t_a)
        & ? [X7] :
            ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
             => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X7))),X5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
             => c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X7))),X5)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) )
            & ! [X4] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X4),X5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X6,X7)),X4)) ) ),
    inference(assume_negation,[status(cth)],[conj_0]) ).

cnf(c_0_18,plain,
    ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,esk6_0))),esk4_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Oidom(t_a) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk9_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Oidom(t_a) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).

cnf(c_0_20,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,hypothesis,
    class_Rings_Oidom(t_a),
    inference(split_conjunct,[status(thm)],[tfree_0]) ).

fof(c_0_23,plain,
    ! [X301,X302,X303] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X303,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X302,X301)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X302,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X303,X301)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

cnf(c_0_24,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_25,negated_conjecture,
    ! [X3062,X3063,X3064] :
      ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
        | hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X3062,X3063,X3064)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X3062,X3063,X3064)),X3062)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X3063,X3064)),esk32_3(X3062,X3063,X3064)))
        | X3063 = c_Groups_Ozero__class_Ozero(t_a) )
      & ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X3064,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X3064))),X3062)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
        | hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X3062,X3063,X3064)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X3062,X3063,X3064)),X3062)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X3063,X3064)),esk32_3(X3062,X3063,X3064)))
        | X3063 = c_Groups_Ozero__class_Ozero(t_a) )
      & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
        | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X3064,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X3064))),X3062)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X3062,X3063,X3064)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X3062,X3063,X3064)),X3062)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X3063,X3064)),esk32_3(X3062,X3063,X3064)))
        | X3063 = c_Groups_Ozero__class_Ozero(t_a) )
      & ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X3064,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X3064))),X3062)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
        | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X3064,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X3064))),X3062)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X3062,X3063,X3064)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X3062,X3063,X3064)),X3062)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X3063,X3064)),esk32_3(X3062,X3063,X3064)))
        | X3063 = c_Groups_Ozero__class_Ozero(t_a) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).

cnf(c_0_26,plain,
    ( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk6_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk4_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Oidom(t_a) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_13]),c_0_13]) ).

cnf(c_0_27,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk9_0))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),esk7_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_20]),c_0_22])]) ).

cnf(c_0_28,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[c_0_24,c_0_13]) ).

cnf(c_0_30,negated_conjecture,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | X3 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X1))),X2)) != c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X2,X3,X1)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X2,X3,X1)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X3,X1)),esk32_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_31,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk6_0))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),esk4_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_20]),c_0_21]),c_0_20]),c_0_22])]) ).

cnf(c_0_32,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk9_0))),esk7_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(rw,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_33,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(spm,[status(thm)],[c_0_29,c_0_20]) ).

cnf(c_0_34,negated_conjecture,
    ( X3 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X2,X3,X1)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X2,X3,X1)),X2)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X3,X1)),esk32_3(X2,X3,X1)))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_13]),c_0_13]),c_0_13]) ).

cnf(c_0_35,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk6_0))),esk4_0)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(rw,[status(thm)],[c_0_31,c_0_28]) ).

cnf(c_0_36,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(sr,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_37,negated_conjecture,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | X1 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X3,X1,X2)),X3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),esk32_3(X3,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X3,X1,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_20]),c_0_21]),c_0_20]) ).

cnf(c_0_38,plain,
    c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_35,c_0_33]),c_0_36]) ).

cnf(c_0_39,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,esk6_0))),esk4_0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | ~ class_Rings_Oidom(t_a) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_40,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,esk9_0))),esk7_0)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
    | ~ class_Rings_Oidom(t_a) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_41,negated_conjecture,
    ( X1 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X3,X1,X2)),X3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),esk32_3(X3,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X3,X1,X2)) ),
    inference(sr,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_43,plain,
    ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk7_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk8_0,esk9_0)),X1))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
    | ~ class_Rings_Oidom(t_a) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_44,plain,
    ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk4_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk5_0,esk6_0)),X1))
    | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | ~ class_Rings_Oidom(t_a) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_45,plain,
    ( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk6_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk4_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ class_Rings_Oidom(t_a) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_13]),c_0_13]),c_0_13]) ).

cnf(c_0_46,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,esk9_0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),esk7_0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
    | ~ class_Rings_Oidom(t_a) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_13]),c_0_13]),c_0_13]) ).

cnf(c_0_47,negated_conjecture,
    ( X1 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X3)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),esk32_3(X3,X1,X2)),X3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),esk32_3(X3,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),esk32_3(X3,X1,X2)) ),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_48,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk7_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk8_0,esk9_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_22])]) ).

cnf(c_0_49,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),esk4_0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,esk5_0,esk6_0)),X1)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X1)
    | v_c____ = c_Groups_Ozero__class_Ozero(t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_22])]) ).

cnf(c_0_50,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk6_0))),esk4_0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_c____ = c_Groups_Ozero__class_Ozero(t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_20]),c_0_21]),c_0_20]),c_0_28]),c_0_20]),c_0_22])]) ).

cnf(c_0_51,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk9_0))),esk7_0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_20]),c_0_21]),c_0_20]),c_0_28]),c_0_20]),c_0_22])]) ).

cnf(c_0_52,plain,
    ( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | esk5_0 != c_Groups_Ozero__class_Ozero(t_a)
    | ~ class_Rings_Oidom(t_a) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_53,plain,
    ( esk8_0 != c_Groups_Ozero__class_Ozero(t_a)
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a)
    | ~ class_Rings_Oidom(t_a) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_54,negated_conjecture,
    ( esk8_0 = c_Groups_Ozero__class_Ozero(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk9_0))),esk7_0)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_55,negated_conjecture,
    ( esk5_0 = c_Groups_Ozero__class_Ozero(t_a)
    | v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk6_0))),esk4_0)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ),
    inference(spm,[status(thm)],[c_0_47,c_0_49]) ).

cnf(c_0_56,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk6_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk6_0))),esk4_0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | v_c____ = c_Groups_Ozero__class_Ozero(t_a) ),
    inference(sr,[status(thm)],[c_0_50,c_0_38]) ).

cnf(c_0_57,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(esk9_0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,esk9_0))),esk7_0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | v_c____ != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(sr,[status(thm)],[c_0_51,c_0_38]) ).

cnf(c_0_58,plain,
    ( v_c____ = c_Groups_Ozero__class_Ozero(t_a)
    | esk5_0 != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_22])]) ).

cnf(c_0_59,plain,
    ( v_c____ != c_Groups_Ozero__class_Ozero(t_a)
    | esk8_0 != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_22])]) ).

cnf(c_0_60,plain,
    $false,
    inference(cdclpropres,[status(thm)],[c_0_54,c_0_55,c_0_56,c_0_57,c_0_58,c_0_59]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SWW245+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.10  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Sun Aug 27 22:41:45 EDT 2023
% 0.11/0.30  % CPUTime  : 
% 0.15/0.49  start to proof: theBenchmark
% 101.27/101.37  % Version  : CSE_E---1.5
% 101.27/101.37  % Problem  : theBenchmark.p
% 101.27/101.37  % Proof found
% 101.27/101.37  % SZS status Theorem for theBenchmark.p
% 101.27/101.37  % SZS output start Proof
% See solution above
% 101.37/101.38  % Total time : 100.825000 s
% 101.37/101.38  % SZS output end Proof
% 101.37/101.38  % Total time : 100.866000 s
%------------------------------------------------------------------------------