TSTP Solution File: SWW187+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW187+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 : n017.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 00:16:24 EDT 2023
% Result : Theorem 63.43s 63.52s
% Output : CNFRefutation 63.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 180
% Syntax : Number of formulae : 315 ( 71 unt; 136 typ; 0 def)
% Number of atoms : 380 ( 197 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 351 ( 150 ~; 140 |; 19 &)
% ( 12 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 208 ( 127 >; 81 *; 0 +; 0 <<)
% Number of predicates : 79 ( 77 usr; 1 prp; 0-5 aty)
% Number of functors : 59 ( 59 usr; 9 con; 0-5 aty)
% Number of variables : 340 ( 38 sgn; 190 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
class_Groups_Ozero: $i > $o ).
tff(decl_24,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_26,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_27,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_28,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(decl_32,type,
tc_Nat_Onat: $i ).
tff(decl_33,type,
c_Nat_OSuc: $i > $i ).
tff(decl_34,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_36,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_37,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_38,type,
class_HOL_Oequal: $i > $o ).
tff(decl_39,type,
c_HOL_Oequal__class_Oequal: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
class_Rings_Oidom: $i > $o ).
tff(decl_41,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_42,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_43,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_44,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_45,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_46,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_47,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_48,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_49,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_50,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_51,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_52,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_53,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_54,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_56,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_58,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_59,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_60,type,
class_Orderings_Oord: $i > $o ).
tff(decl_61,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_62,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_63,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_64,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_65,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
c_Nat_Onat_Onat__size: $i > $i ).
tff(decl_67,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_68,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_70,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_71,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_72,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_73,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_74,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_76,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_77,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_78,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_79,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_80,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_81,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_82,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_83,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_84,type,
class_Rings_Oring: $i > $o ).
tff(decl_85,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_86,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_87,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_88,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_89,type,
class_Groups_Oone: $i > $o ).
tff(decl_90,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_91,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_92,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_93,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_94,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_95,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_96,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_97,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_98,type,
c_fFalse: $i ).
tff(decl_99,type,
c_HOL_Obool_Obool__size: $i > $i ).
tff(decl_100,type,
c_fTrue: $i ).
tff(decl_101,type,
class_Rings_Odvd: $i > $o ).
tff(decl_102,type,
class_Fields_Ofield: $i > $o ).
tff(decl_103,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_104,type,
hBOOL: $i > $o ).
tff(decl_105,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_106,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_107,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_108,type,
c_Polynomial_Ocoeff: ( $i * $i ) > $i ).
tff(decl_109,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_110,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_111,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_112,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_113,type,
tc_Int_Oint: $i ).
tff(decl_114,type,
class_Power_Opower: $i > $o ).
tff(decl_115,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_116,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_118,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_119,type,
c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_121,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_122,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_123,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_124,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_125,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_126,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_127,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_128,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_129,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
class_Groups_Ominus: $i > $o ).
tff(decl_131,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_132,type,
tc_HOL_Obool: $i ).
tff(decl_133,type,
class_Enum_Oenum: $i > $o ).
tff(decl_134,type,
t_a: $i ).
tff(decl_135,type,
v_p: $i ).
tff(decl_136,type,
v_h: $i ).
tff(decl_137,type,
v_a: $i ).
tff(decl_138,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_139,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_140,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_142,type,
esk5_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_143,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_145,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_146,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_147,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_148,type,
esk11_1: $i > $i ).
tff(decl_149,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_150,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_151,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_152,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_154,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_156,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk20_2: ( $i * $i ) > $i ).
fof(fact_gr0__conv__Suc,axiom,
! [X25] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25)
<=> ? [X62] : X25 = c_Nat_OSuc(X62) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
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_add__eq__self__zero,axiom,
! [X19,X24] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X19) = X24
=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_nat__add__commute,axiom,
! [X19,X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X19) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_less__zeroE,axiom,
! [X19] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_Zero__neq__Suc,axiom,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_nat__add__assoc,axiom,
! [X30,X19,X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X19),X30) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_nat__neq__iff,axiom,
! [X25,X26] :
( X26 != X25
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_less__le__not__le,axiom,
! [X21,X22,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X22,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X22,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X8,X21,X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_le__diff__conv,axiom,
! [X85,X34,X86] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X86,X34),X85)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X86,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X85,X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_order__refl,axiom,
! [X16,X11] :
( class_Orderings_Opreorder(X11)
=> c_Orderings_Oord__class_Oless__eq(X11,X16,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_smult__0__left,axiom,
! [X13,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Polynomial_Osmult(X11,c_Groups_Ozero__class_Ozero(X11),X13) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X21,X22,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X22,X21)
<=> ( c_Orderings_Oord__class_Oless(X8,X21,X22)
| X22 = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X20,X18,X10,X11] :
( class_Groups_Ocancel__semigroup__add(X11)
=> ( c_Groups_Oplus__class_Oplus(X11,X10,X18) = c_Groups_Oplus__class_Oplus(X11,X10,X20)
=> X18 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(fact_diff__add__0,axiom,
! [X24,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X24)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__diff__left,axiom,
! [X30,X32,X33] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,X32),X30) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X33,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X32,X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_degree__smult__le,axiom,
! [X13,X10,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X11,c_Polynomial_Osmult(X11,X10,X13)),c_Polynomial_Odegree(X11,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__smult__le) ).
fof(fact_synthetic__div__unique__lemma,axiom,
! [X10,X13,X20,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> ( c_Polynomial_Osmult(X11,X20,X13) = c_Polynomial_OpCons(X11,X10,X13)
=> X13 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
fof(tfree_0,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(conj_1,conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) = c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_offset__poly__pCons,axiom,
! [X9,X13,X10,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X11,c_Polynomial_OpCons(X11,X10,X13),X9) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),c_Polynomial_Osmult(X11,X9,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X11,X13,X9)),c_Polynomial_OpCons(X11,X10,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X11,X13,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(fact_degree__add__eq__right,axiom,
! [X17,X13,X11] :
( class_Groups_Ocomm__monoid__add(X11)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X11,X13),c_Polynomial_Odegree(X11,X17))
=> c_Polynomial_Odegree(X11,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),X13,X17)) = c_Polynomial_Odegree(X11,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__add__eq__right) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_diff__is__0__eq,axiom,
! [X25,X26] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X26,X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(conj_0,hypothesis,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Polynomial_Odegree(t_a,v_p),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_pCons__cases,axiom,
! [X13,X11] :
( class_Groups_Ozero(X11)
=> ~ ! [X14,X15] : X13 != c_Polynomial_OpCons(X11,X14,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__cases) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(fact_degree__pCons__eq,axiom,
! [X10,X13,X11] :
( class_Groups_Ozero(X11)
=> ( X13 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))
=> c_Polynomial_Odegree(X11,c_Polynomial_OpCons(X11,X10,X13)) = c_Nat_OSuc(c_Polynomial_Odegree(X11,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__pCons__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X20,X10,X11] :
( class_Rings_Ocomm__semiring__1(X11)
=> c_Groups_Oplus__class_Oplus(X11,X10,X20) = c_Groups_Oplus__class_Oplus(X11,X20,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_le__iff__add,axiom,
! [X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
<=> ? [X35] : X25 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ozero,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Groups_Ozero(X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add,axiom,
! [X90] :
( class_Rings_Ocomm__semiring__0(X90)
=> class_Groups_Ocomm__monoid__add(X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(fact_pCons__eq__0__iff,axiom,
! [X6,X7,X8] :
( class_Groups_Ozero(X8)
=> ( c_Polynomial_OpCons(X8,X7,X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> ( X7 = c_Groups_Ozero__class_Ozero(X8)
& X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_synthetic__div__unique,axiom,
! [X39,X17,X20,X13,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),X13,c_Polynomial_Osmult(X11,X20,X17)) = c_Polynomial_OpCons(X11,X39,X17)
=> ( X39 = hAPP(c_Polynomial_Opoly(X11,X13),X20)
& X17 = c_Polynomial_Osynthetic__div(X11,X13,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X13,X11] :
( class_Groups_Ocomm__monoid__add(X11)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),X13,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X17,X11] :
( class_Groups_Ocomm__monoid__add(X11)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X11),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)),X17) = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_offset__poly__eq__0__iff,axiom,
! [X12,X6,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X8,X6,X12) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(fact_offset__poly__single,axiom,
! [X9,X10,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X11,c_Polynomial_OpCons(X11,X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))),X9) = c_Polynomial_OpCons(X11,X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__single) ).
fof(fact_smult__0__right,axiom,
! [X10,X11] :
( class_Rings_Ocomm__semiring__0(X11)
=> c_Polynomial_Osmult(X11,X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(fact_synthetic__div__eq__0__iff,axiom,
! [X23,X6,X8] :
( class_Rings_Ocomm__semiring__0(X8)
=> ( c_Polynomial_Osynthetic__div(X8,X6,X23) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X8))
<=> c_Polynomial_Odegree(X8,X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
fof(c_0_44,plain,
! [X1594,X1596,X1597] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1594)
| X1594 = c_Nat_OSuc(esk11_1(X1594)) )
& ( X1596 != c_Nat_OSuc(X1597)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1596) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])]) ).
fof(c_0_45,plain,
! [X998] : c_Nat_OSuc(X998) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X998,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_46,plain,
! [X275,X276] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X276,X275) != X276
| X275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])]) ).
fof(c_0_47,plain,
! [X494,X495] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X495,X494) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X494,X495),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
cnf(c_0_48,plain,
( X1 = c_Nat_OSuc(esk11_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,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_45]) ).
fof(c_0_50,plain,
! [X19] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(c_0_51,plain,
! [X422] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X422),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
cnf(c_0_52,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,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_47]) ).
fof(c_0_54,plain,
! [X499,X500,X501] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X501,X500),X499) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X501,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X500,X499)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
cnf(c_0_55,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk11_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_56,plain,
! [X1874,X1875] :
( ( X1875 = X1874
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1875,X1874)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1874,X1875) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1875,X1874)
| X1875 != X1874 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1874,X1875)
| X1875 != X1874 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(c_0_57,plain,
! [X1158] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1158,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_59,plain,
! [X21,X22,X8] :
( class_Orderings_Opreorder(X8)
=> ( c_Orderings_Oord__class_Oless(X8,X22,X21)
<=> ( c_Orderings_Oord__class_Oless__eq(X8,X22,X21)
& ~ c_Orderings_Oord__class_Oless__eq(X8,X21,X22) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(c_0_60,plain,
! [X2710,X2711,X2712] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2712,X2711),X2710)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2712,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2710,X2711)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2712,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2710,X2711))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2712,X2711),X2710) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
fof(c_0_61,plain,
! [X468,X469] :
( ~ class_Orderings_Opreorder(X469)
| c_Orderings_Oord__class_Oless__eq(X469,X468,X468) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(c_0_62,plain,
! [X154,X155] :
( ~ class_Rings_Ocomm__semiring__0(X155)
| c_Polynomial_Osmult(X155,c_Groups_Ozero__class_Ozero(X155),X154) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])]) ).
fof(c_0_63,plain,
! [X21,X22,X8] :
( class_Orderings_Olinorder(X8)
=> ( ~ c_Orderings_Oord__class_Oless(X8,X22,X21)
<=> ( c_Orderings_Oord__class_Oless(X8,X21,X22)
| X22 = X21 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
cnf(c_0_64,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X2 ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_65,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_54]) ).
cnf(c_0_66,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),esk11_1(X1)) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[c_0_55,c_0_53]) ).
cnf(c_0_67,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_69,plain,
! [X259,X260,X261,X262] :
( ~ class_Groups_Ocancel__semigroup__add(X262)
| c_Groups_Oplus__class_Oplus(X262,X261,X260) != c_Groups_Oplus__class_Oplus(X262,X261,X259)
| X260 = X259 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
cnf(c_0_70,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_58,c_0_49]) ).
fof(c_0_71,plain,
! [X1320,X1321,X1322] :
( ( c_Orderings_Oord__class_Oless__eq(X1322,X1321,X1320)
| ~ c_Orderings_Oord__class_Oless(X1322,X1321,X1320)
| ~ class_Orderings_Opreorder(X1322) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1322,X1320,X1321)
| ~ c_Orderings_Oord__class_Oless(X1322,X1321,X1320)
| ~ class_Orderings_Opreorder(X1322) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1322,X1321,X1320)
| c_Orderings_Oord__class_Oless__eq(X1322,X1320,X1321)
| c_Orderings_Oord__class_Oless(X1322,X1321,X1320)
| ~ class_Orderings_Opreorder(X1322) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])]) ).
cnf(c_0_72,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_73,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
fof(c_0_75,plain,
! [X2827,X2828] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2828,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2828,X2827)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(c_0_76,plain,
! [X2862,X2863,X2864] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2864,X2863),X2862) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2864,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2863,X2862)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(c_0_77,plain,
! [X138,X139,X140] :
( ~ class_Rings_Ocomm__semiring__0(X140)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X140,c_Polynomial_Osmult(X140,X139,X138)),c_Polynomial_Odegree(X140,X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__smult__le])]) ).
fof(c_0_78,plain,
! [X212,X213,X214,X215] :
( ~ class_Rings_Ocomm__semiring__0(X215)
| c_Polynomial_Osmult(X215,X214,X213) != c_Polynomial_OpCons(X215,X212,X213)
| X213 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X215)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique__lemma])]) ).
cnf(c_0_79,plain,
( c_Polynomial_Osmult(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_80,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
fof(c_0_81,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).
fof(c_0_82,plain,
! [X109,X110,X111,X112] :
( ~ class_Rings_Ocomm__semiring__0(X112)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X112,c_Polynomial_OpCons(X112,X111,X110),X109) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X112),c_Polynomial_Osmult(X112,X109,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X112,X110,X109)),c_Polynomial_OpCons(X112,X111,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X112,X110,X109))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__pCons])]) ).
fof(c_0_83,plain,
! [X1671,X1672,X1673] :
( ~ class_Groups_Ocomm__monoid__add(X1673)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1673,X1672),c_Polynomial_Odegree(X1673,X1671))
| c_Polynomial_Odegree(X1673,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1673),X1672,X1671)) = c_Polynomial_Odegree(X1673,X1671) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__add__eq__right])]) ).
fof(c_0_84,plain,
! [X1185,X1186,X1187] :
( ( c_Orderings_Oord__class_Oless(X1187,X1186,X1185)
| c_Orderings_Oord__class_Oless(X1187,X1185,X1186)
| X1186 = X1185
| ~ class_Orderings_Olinorder(X1187) )
& ( ~ c_Orderings_Oord__class_Oless(X1187,X1185,X1186)
| ~ c_Orderings_Oord__class_Oless(X1187,X1186,X1185)
| ~ class_Orderings_Olinorder(X1187) )
& ( X1186 != X1185
| ~ c_Orderings_Oord__class_Oless(X1187,X1186,X1185)
| ~ class_Orderings_Olinorder(X1187) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])]) ).
cnf(c_0_85,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) != X3 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_86,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),esk11_1(X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_87,plain,
( X3 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_88,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).
cnf(c_0_89,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_70,c_0_53]) ).
cnf(c_0_90,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_91,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_53]),c_0_74])]) ).
cnf(c_0_92,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_93,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
fof(c_0_94,plain,
! [X279] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X279,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X279,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_95,plain,
! [X2689,X2690] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2690,X2689) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2690,X2689) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2690,X2689)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2690,X2689) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])]) ).
cnf(c_0_96,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(X1,c_Polynomial_Osmult(X1,X2,X3)),c_Polynomial_Odegree(X1,X3))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_97,hypothesis,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)) = c_Polynomial_Odegree(t_a,v_p),
inference(split_conjunct,[status(thm)],[conj_0]) ).
cnf(c_0_98,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Polynomial_Osmult(X1,X2,X3) != c_Polynomial_OpCons(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_99,hypothesis,
c_Polynomial_Osmult(t_a,c_Groups_Ozero__class_Ozero(t_a),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_100,plain,
! [X115,X116] :
( ~ class_Groups_Ozero(X116)
| X115 = c_Polynomial_OpCons(X116,esk2_2(X115,X116),esk3_2(X115,X116)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__cases])])]) ).
cnf(c_0_101,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h)) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_102,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X4,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4)),c_Polynomial_OpCons(X1,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X3,X4)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_103,plain,
( c_Polynomial_Odegree(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)) = c_Polynomial_Odegree(X1,X3)
| ~ class_Groups_Ocomm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Polynomial_Odegree(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_104,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_105,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
fof(c_0_106,plain,
! [X119,X120,X121] :
( ~ class_Groups_Ozero(X121)
| X120 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X121))
| c_Polynomial_Odegree(X121,c_Polynomial_OpCons(X121,X119,X120)) = c_Nat_OSuc(c_Polynomial_Odegree(X121,X120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__pCons__eq])]) ).
cnf(c_0_107,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != esk11_1(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_70]) ).
cnf(c_0_108,plain,
esk11_1(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1)) = X1,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_86]),c_0_88])])]),c_0_89]) ).
fof(c_0_109,plain,
! [X571,X572,X573] :
( ~ class_Rings_Ocomm__semiring__1(X573)
| c_Groups_Oplus__class_Oplus(X573,X572,X571) = c_Groups_Oplus__class_Oplus(X573,X571,X572) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(c_0_110,plain,
! [X338,X339,X341,X342,X343] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X339,X338)
| X338 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X339,esk4_2(X338,X339)) )
& ( X341 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X342,X343)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X342,X341) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])]) ).
cnf(c_0_111,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_74])]) ).
cnf(c_0_112,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_113,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_114,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_115,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,v_p)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_80])]) ).
fof(c_0_116,plain,
! [X280] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X280) = X280,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
cnf(c_0_117,hypothesis,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_OpCons(t_a,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_80])]) ).
cnf(c_0_118,plain,
( X2 = c_Polynomial_OpCons(X1,esk2_2(X2,X1),esk3_2(X2,X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
fof(c_0_119,plain,
! [X2991] :
( ~ class_Rings_Ocomm__semiring__0(X2991)
| class_Groups_Ozero(X2991) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__semiring__0__Groups_Ozero])]) ).
cnf(c_0_120,negated_conjecture,
c_Polynomial_Odegree(t_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_80])]) ).
cnf(c_0_121,plain,
( c_Polynomial_Odegree(X1,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,X3)) = c_Polynomial_Odegree(X1,X3)
| c_Polynomial_Odegree(X1,X2) = c_Polynomial_Odegree(X1,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(X1,X3),c_Polynomial_Odegree(X1,X2))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105])]) ).
fof(c_0_122,plain,
! [X2985] :
( ~ class_Rings_Ocomm__semiring__0(X2985)
| class_Groups_Ocomm__monoid__add(X2985) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add])]) ).
cnf(c_0_123,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X3,X2)) = c_Nat_OSuc(c_Polynomial_Odegree(X1,X2))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_124,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X2)) != X2,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_89]) ).
cnf(c_0_125,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_126,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
cnf(c_0_127,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk4_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_128,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_129,hypothesis,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,v_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_130,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_131,hypothesis,
( esk3_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118])]) ).
cnf(c_0_132,plain,
( class_Groups_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_133,negated_conjecture,
( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p))
| ~ class_Groups_Ocomm__monoid__add(t_a) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_134,plain,
( class_Groups_Ocomm__monoid__add(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_135,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X3,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Groups_Ozero(X1) ),
inference(rw,[status(thm)],[c_0_123,c_0_49]) ).
cnf(c_0_136,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,X1,X2)) != X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_65]),c_0_126])]) ).
cnf(c_0_137,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),esk4_2(c_Polynomial_Odegree(t_a,v_p),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))) = c_Polynomial_Odegree(t_a,v_p),
inference(spm,[status(thm)],[c_0_127,c_0_115]) ).
cnf(c_0_138,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(t_a,v_p),X1),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]) ).
cnf(c_0_139,hypothesis,
esk3_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_80])]) ).
cnf(c_0_140,negated_conjecture,
( c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))))
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_80])]) ).
cnf(c_0_141,plain,
( c_Polynomial_Odegree(X1,c_Polynomial_OpCons(X1,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(X1,X3))
| X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(rw,[status(thm)],[c_0_135,c_0_53]) ).
cnf(c_0_142,hypothesis,
c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_143,hypothesis,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Polynomial_Odegree(t_a,v_p)),c_Polynomial_Odegree(t_a,c_Polynomial_Osmult(t_a,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_125]),c_0_126])]) ).
fof(c_0_144,plain,
! [X186,X187,X188] :
( ( X187 = c_Groups_Ozero__class_Ozero(X188)
| c_Polynomial_OpCons(X188,X187,X186) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188))
| ~ class_Groups_Ozero(X188) )
& ( X186 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188))
| c_Polynomial_OpCons(X188,X187,X186) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188))
| ~ class_Groups_Ozero(X188) )
& ( X187 != c_Groups_Ozero__class_Ozero(X188)
| X186 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188))
| c_Polynomial_OpCons(X188,X187,X186) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X188))
| ~ class_Groups_Ozero(X188) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff])])]) ).
cnf(c_0_145,hypothesis,
( c_Polynomial_OpCons(t_a,esk2_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a) ),
inference(spm,[status(thm)],[c_0_118,c_0_139]) ).
fof(c_0_146,plain,
! [X470,X471,X472,X473,X474] :
( ( X470 = hAPP(c_Polynomial_Opoly(X474,X473),X472)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X474),X473,c_Polynomial_Osmult(X474,X472,X471)) != c_Polynomial_OpCons(X474,X470,X471)
| ~ class_Rings_Ocomm__semiring__0(X474) )
& ( X471 = c_Polynomial_Osynthetic__div(X474,X473,X472)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X474),X473,c_Polynomial_Osmult(X474,X472,X471)) != c_Polynomial_OpCons(X474,X470,X471)
| ~ class_Rings_Ocomm__semiring__0(X474) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique])])]) ).
cnf(c_0_147,negated_conjecture,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p))
| ~ class_Groups_Ozero(t_a) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_97]),c_0_97]),c_0_97]),c_0_142]),c_0_143]) ).
cnf(c_0_148,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X2,X1,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_149,hypothesis,
c_Polynomial_OpCons(t_a,esk2_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_132]),c_0_80])]) ).
cnf(c_0_150,plain,
( X1 = c_Polynomial_Osynthetic__div(X2,X3,X4)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),X3,c_Polynomial_Osmult(X2,X4,X1)) != c_Polynomial_OpCons(X2,X5,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_146]) ).
fof(c_0_151,plain,
! [X163,X164] :
( ~ class_Groups_Ocomm__monoid__add(X164)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X164),X163,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X164))) = X163 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])]) ).
cnf(c_0_152,negated_conjecture,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_a,v_p)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,v_p)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_132]),c_0_80])]) ).
cnf(c_0_153,hypothesis,
( esk2_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_Groups_Ozero__class_Ozero(t_a)
| ~ class_Groups_Ozero(t_a) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
fof(c_0_154,plain,
! [X156,X157] :
( ~ class_Groups_Ocomm__monoid__add(X157)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X157),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X157)),X156) = X156 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])]) ).
cnf(c_0_155,hypothesis,
( X1 = c_Polynomial_Osynthetic__div(t_a,X2,c_Groups_Ozero__class_Ozero(t_a))
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) != c_Polynomial_OpCons(t_a,X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_99]),c_0_80])]) ).
cnf(c_0_156,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
fof(c_0_157,plain,
! [X106,X107,X108] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X108,X107,X106) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X108))
| X107 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X108))
| ~ class_Rings_Ocomm__semiring__0(X108) )
& ( X107 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X108))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X108,X107,X106) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X108))
| ~ class_Rings_Ocomm__semiring__0(X108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__iff])])]) ).
cnf(c_0_158,negated_conjecture,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Groups_Ozero(t_a) ),
inference(spm,[status(thm)],[c_0_152,c_0_141]) ).
fof(c_0_159,plain,
! [X101,X102,X103] :
( ~ class_Rings_Ocomm__semiring__0(X103)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X103,c_Polynomial_OpCons(X103,X102,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X103))),X101) = c_Polynomial_OpCons(X103,X102,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X103))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__single])]) ).
cnf(c_0_160,hypothesis,
esk2_2(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_Groups_Ozero__class_Ozero(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_132]),c_0_80])]) ).
fof(c_0_161,plain,
! [X161,X162] :
( ~ class_Rings_Ocomm__semiring__0(X162)
| c_Polynomial_Osmult(X162,X161,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X162))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X162)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__right])]) ).
cnf(c_0_162,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
fof(c_0_163,plain,
! [X608,X609,X610] :
( ( c_Polynomial_Osynthetic__div(X610,X609,X608) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X610))
| c_Polynomial_Odegree(X610,X609) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__0(X610) )
& ( c_Polynomial_Odegree(X610,X609) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Osynthetic__div(X610,X609,X608) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X610))
| ~ class_Rings_Ocomm__semiring__0(X610) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__eq__0__iff])])]) ).
cnf(c_0_164,hypothesis,
( c_Polynomial_Osynthetic__div(t_a,c_Polynomial_OpCons(t_a,X1,X2),c_Groups_Ozero__class_Ozero(t_a)) = X2
| ~ class_Groups_Ocomm__monoid__add(t_a) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156])]) ).
cnf(c_0_165,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
cnf(c_0_166,negated_conjecture,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_132]),c_0_80])]) ).
cnf(c_0_167,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))),X3) = c_Polynomial_OpCons(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_168,hypothesis,
c_Polynomial_OpCons(t_a,c_Groups_Ozero__class_Ozero(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(rw,[status(thm)],[c_0_149,c_0_160]) ).
cnf(c_0_169,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_161]) ).
cnf(c_0_170,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_162,c_0_134]) ).
cnf(c_0_171,plain,
( c_Polynomial_Odegree(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Osynthetic__div(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
cnf(c_0_172,hypothesis,
c_Polynomial_Osynthetic__div(t_a,c_Polynomial_OpCons(t_a,X1,X2),c_Groups_Ozero__class_Ozero(t_a)) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_134]),c_0_80])]) ).
cnf(c_0_173,negated_conjecture,
v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_80])]) ).
cnf(c_0_174,hypothesis,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_80])]) ).
cnf(c_0_175,hypothesis,
c_Polynomial_Osmult(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(spm,[status(thm)],[c_0_169,c_0_80]) ).
cnf(c_0_176,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),X1) = X1,
inference(spm,[status(thm)],[c_0_170,c_0_80]) ).
cnf(c_0_177,hypothesis,
c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_80])])]) ).
cnf(c_0_178,negated_conjecture,
$false,
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)],[inference(spm,[status(thm)],[c_0_120,c_0_173]),c_0_174]),c_0_175]),c_0_174]),c_0_176]),c_0_177]),c_0_177])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SWW187+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Sun Aug 27 21:35:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 63.43/63.52 % Version : CSE_E---1.5
% 63.43/63.52 % Problem : theBenchmark.p
% 63.43/63.52 % Proof found
% 63.43/63.52 % SZS status Theorem for theBenchmark.p
% 63.43/63.52 % SZS output start Proof
% See solution above
% 63.52/63.54 % Total time : 62.908000 s
% 63.52/63.54 % SZS output end Proof
% 63.52/63.54 % Total time : 62.935000 s
%------------------------------------------------------------------------------