TSTP Solution File: SWW256+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW256+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 00:16:45 EDT 2023
% Result : Theorem 4.37s 4.53s
% Output : CNFRefutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 176
% Syntax : Number of formulae : 249 ( 54 unt; 150 typ; 0 def)
% Number of atoms : 166 ( 87 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 127 ( 60 ~; 45 |; 6 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 198 ( 128 >; 70 *; 0 +; 0 <<)
% Number of predicates : 81 ( 79 usr; 1 prp; 0-3 aty)
% Number of functors : 71 ( 71 usr; 22 con; 0-4 aty)
% Number of variables : 164 ( 23 sgn; 84 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
v_k____: $i ).
tff(decl_24,type,
tc_Nat_Onat: $i ).
tff(decl_25,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_26,type,
v_a____: $i ).
tff(decl_27,type,
tc_Complex_Ocomplex: $i ).
tff(decl_28,type,
class_Power_Opower: $i > $o ).
tff(decl_29,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_30,type,
c_Nat_OSuc: $i > $i ).
tff(decl_31,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_32,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_33,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_34,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_35,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_36,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_37,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_38,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_40,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_41,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_42,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_43,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_44,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_45,type,
class_Groups_Ozero: $i > $o ).
tff(decl_46,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_47,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_48,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_49,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
tc_Int_Oint: $i ).
tff(decl_51,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
class_Groups_Ominus: $i > $o ).
tff(decl_53,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_54,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_55,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_56,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_57,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_58,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_59,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_60,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_61,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_62,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_63,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_64,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_65,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_66,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_67,type,
class_Groups_Oone: $i > $o ).
tff(decl_68,type,
hBOOL: $i > $o ).
tff(decl_69,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_70,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_71,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_72,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_73,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_74,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_75,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_76,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_77,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_78,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_79,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_80,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_81,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_82,type,
class_Rings_Oring: $i > $o ).
tff(decl_83,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_84,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_85,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_86,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_87,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_88,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_90,type,
class_Orderings_Oord: $i > $o ).
tff(decl_91,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_92,type,
v_pa____: $i ).
tff(decl_93,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_94,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_95,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_96,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_97,type,
class_Int_Onumber: $i > $o ).
tff(decl_98,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_99,type,
v_q____: $i ).
tff(decl_100,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_101,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_102,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_103,type,
v_p: $i ).
tff(decl_104,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant: ( $i * $i * $i ) > $o ).
tff(decl_105,type,
v_c____: $i ).
tff(decl_106,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_107,type,
tc_RealDef_Oreal: $i ).
tff(decl_108,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_109,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_110,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_111,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_112,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_113,type,
class_Rings_Oidom: $i > $o ).
tff(decl_114,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_115,type,
class_Fields_Ofield: $i > $o ).
tff(decl_116,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
c_Complex_Oii: $i ).
tff(decl_118,type,
v_s____: $i ).
tff(decl_119,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_120,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_123,type,
class_Rings_Odivision__ring: $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,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_127,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_129,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_130,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_131,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_132,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_133,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_134,type,
class_Rings_Odvd: $i > $o ).
tff(decl_135,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_136,type,
tc_HOL_Obool: $i ).
tff(decl_137,type,
epred1_3: ( $i * $i * $i ) > $o ).
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_3: ( $i * $i * $i ) > $i ).
tff(decl_142,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_143,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_144,type,
esk7_1: $i > $i ).
tff(decl_145,type,
esk8_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_146,type,
esk9_2: ( $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_1: $i > $i ).
tff(decl_150,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_151,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_152,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk16_1: $i > $i ).
tff(decl_154,type,
esk17_0: $i ).
tff(decl_155,type,
esk18_0: $i ).
tff(decl_156,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk20_0: $i ).
tff(decl_158,type,
esk21_1: $i > $i ).
tff(decl_159,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_160,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_161,type,
esk24_0: $i ).
tff(decl_162,type,
esk25_0: $i ).
tff(decl_163,type,
esk26_0: $i ).
tff(decl_164,type,
esk27_0: $i ).
tff(decl_165,type,
esk28_0: $i ).
tff(decl_166,type,
esk29_0: $i ).
tff(decl_167,type,
esk30_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_168,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_169,type,
esk32_3: ( $i * $i * $i ) > $i ).
tff(decl_170,type,
esk33_3: ( $i * $i * $i ) > $i ).
tff(decl_171,type,
esk34_3: ( $i * $i * $i ) > $i ).
fof(conj_0,conjecture,
? [X3,X81] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X81),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X81),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_Suc__eq__plus1,axiom,
! [X4] : c_Nat_OSuc(X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_less__iff__Suc__add,axiom,
! [X9,X14] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X9)
<=> ? [X53] : X9 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_Zero__neq__Suc,axiom,
! [X11] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X4] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_zero__less__diff,axiom,
! [X14,X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X14,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_gr0I,axiom,
! [X4] :
( X4 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_power__0,axiom,
! [X5,X6] :
( class_Power_Opower(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),c_Groups_Oone__class_Oone(X6)) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_add__is__0,axiom,
! [X9,X14] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X14 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X9 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_nat__add__assoc,axiom,
! [X12,X4,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X4),X12) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_nat__add__commute,axiom,
! [X4,X11] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_inverse__nonzero__iff__nonzero,axiom,
! [X10,X6] :
( class_Rings_Odivision__ring__inverse__zero(X6)
=> ( c_Rings_Oinverse__class_Oinverse(X6,X10) = c_Groups_Ozero__class_Ozero(X6)
<=> X10 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(fact_inverse__i,axiom,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__i) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(fact_complex__i__not__zero,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).
fof(fact_dvd__mult__left,axiom,
! [X34,X21,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X5),X21),X34)
=> c_Rings_Odvd__class_Odvd(X6,X5,X34) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_power__one,axiom,
! [X4,X6] :
( class_Groups_Omonoid__mult(X6)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X6),c_Groups_Oone__class_Oone(X6)),X4) = c_Groups_Oone__class_Oone(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_dvd__triv__right,axiom,
! [X21,X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> c_Rings_Odvd__class_Odvd(X6,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X6),X21),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(fact_add__diff__inverse,axiom,
! [X4,X11] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X4)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X4)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_diff__mult__distrib,axiom,
! [X12,X4,X11] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X4)),X12) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X12),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_dvd__0__left,axiom,
! [X5,X6] :
( class_Rings_Ocomm__semiring__1(X6)
=> ( c_Rings_Odvd__class_Odvd(X6,c_Groups_Ozero__class_Ozero(X6),X5)
=> X5 = c_Groups_Ozero__class_Ozero(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(fact_less__irrefl__nat,axiom,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(c_0_26,negated_conjecture,
~ ? [X3,X81] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X81),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X81),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_27,negated_conjecture,
! [X2945,X2946] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2945),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2945),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2946),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2946),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_28,plain,
! [X688] : c_Nat_OSuc(X688) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X688,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_29,plain,
! [X667,X668,X670,X671,X672] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X668,X667)
| X667 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X668,esk3_2(X667,X668))) )
& ( X670 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X671,X672))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X671,X670) ) ),
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_less__iff__Suc__add])])])])]) ).
fof(c_0_30,plain,
! [X217] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X217),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
cnf(c_0_31,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,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_28]) ).
fof(c_0_33,plain,
! [X1030] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1030) = X1030,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(c_0_34,plain,
! [X1388,X1389] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1389,X1388))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1388,X1389) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1388,X1389)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1389,X1388)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
fof(c_0_35,plain,
! [X1039] :
( X1039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1039) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(c_0_36,plain,
! [X1353,X1354] :
( ~ class_Power_Opower(X1354)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1354),X1353),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1354) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(c_0_37,plain,
! [X1008,X1009] :
( ~ class_Rings_Ocomm__semiring__1(X1009)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1009),X1008),c_Groups_Oone__class_Oone(X1009)) = X1008 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(c_0_38,plain,
! [X1027,X1028] :
( ( X1028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1028,X1027) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X1027 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1028,X1027) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X1028 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1027 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1028,X1027) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])]) ).
fof(c_0_39,plain,
! [X1490,X1491,X1492] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1492,X1491),X1490) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1492,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1491,X1490)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
cnf(c_0_40,plain,
( X2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk3_2(X2,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_41,plain,
! [X1496,X1497] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1497,X1496) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1496,X1497),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
cnf(c_0_42,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_43,plain,
! [X2279,X2280] :
( ( c_Rings_Oinverse__class_Oinverse(X2280,X2279) != c_Groups_Ozero__class_Ozero(X2280)
| X2279 = c_Groups_Ozero__class_Ozero(X2280)
| ~ class_Rings_Odivision__ring__inverse__zero(X2280) )
& ( X2279 != c_Groups_Ozero__class_Ozero(X2280)
| c_Rings_Oinverse__class_Oinverse(X2280,X2279) = c_Groups_Ozero__class_Ozero(X2280)
| ~ class_Rings_Odivision__ring__inverse__zero(X2280) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonzero__iff__nonzero])])]) ).
cnf(c_0_44,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_45,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_33]) ).
cnf(c_0_46,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_48,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_49,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
cnf(c_0_50,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_51,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(c_0_52,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_53,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_39]) ).
cnf(c_0_54,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk3_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[c_0_40,c_0_32]) ).
cnf(c_0_55,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_41]) ).
cnf(c_0_56,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_42,c_0_32]) ).
cnf(c_0_57,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_58,plain,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
inference(split_conjunct,[status(thm)],[fact_inverse__i]) ).
cnf(c_0_59,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero]) ).
cnf(c_0_60,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_complex__i__not__zero]) ).
cnf(c_0_61,negated_conjecture,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_45]) ).
cnf(c_0_62,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_63,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_64,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_65,plain,
! [X2815,X2816,X2817,X2818] :
( ~ class_Rings_Ocomm__semiring__1(X2818)
| ~ c_Rings_Odvd__class_Odvd(X2818,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2818),X2817),X2816),X2815)
| c_Rings_Odvd__class_Odvd(X2818,X2817,X2815) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__left])]) ).
fof(c_0_66,plain,
! [X1037,X1038] :
( ~ class_Groups_Omonoid__mult(X1038)
| hAPP(hAPP(c_Power_Opower__class_Opower(X1038),c_Groups_Oone__class_Oone(X1038)),X1037) = c_Groups_Oone__class_Oone(X1038) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(c_0_67,plain,
! [X2836,X2837,X2838] :
( ~ class_Rings_Ocomm__semiring__1(X2838)
| c_Rings_Odvd__class_Odvd(X2838,X2837,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2838),X2836),X2837)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__right])]) ).
cnf(c_0_68,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_69,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),esk3_2(X2,X1))) = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_53]),c_0_55]) ).
cnf(c_0_70,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_56,c_0_55]) ).
cnf(c_0_71,plain,
c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]),c_0_60]) ).
cnf(c_0_72,negated_conjecture,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_k____) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64]),c_0_63]),c_0_64]) ).
cnf(c_0_73,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).
cnf(c_0_76,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_78,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),v_k____),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72])]) ).
fof(c_0_79,plain,
! [X4,X11] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X4)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X4)) = X11 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(c_0_80,plain,
! [X144,X145,X146] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X146,X145)),X144) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X146),X144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X145),X144)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(c_0_81,plain,
! [X2842,X2843] :
( ~ class_Rings_Ocomm__semiring__1(X2843)
| ~ c_Rings_Odvd__class_Odvd(X2843,c_Groups_Ozero__class_Ozero(X2843),X2842)
| X2842 = c_Groups_Ozero__class_Ozero(X2843) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])]) ).
cnf(c_0_82,negated_conjecture,
( c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X3),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_61]),c_0_51])]) ).
cnf(c_0_83,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),X1) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,plain,
c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_64]),c_0_51])]) ).
cnf(c_0_85,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,v_k____) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
fof(c_0_86,plain,
! [X692,X693] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X693,X692)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X692,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X693,X692)) = X693 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])]) ).
fof(c_0_87,plain,
! [X4] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X4),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
cnf(c_0_88,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_90,negated_conjecture,
c_Rings_Odvd__class_Odvd(tc_Complex_Ocomplex,X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_64]),c_0_84])]) ).
cnf(c_0_91,negated_conjecture,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(spm,[status(thm)],[c_0_85,c_0_55]) ).
cnf(c_0_92,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_93,plain,
! [X595] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X595,X595),
inference(variable_rename,[status(thm)],[c_0_87]) ).
cnf(c_0_94,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)),X2)) ),
inference(spm,[status(thm)],[c_0_46,c_0_88]) ).
cnf(c_0_95,negated_conjecture,
X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_51])]) ).
cnf(c_0_96,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_k____),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_97,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_98,plain,
$false,
inference(sr,[status(thm)],[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(rw,[status(thm)],[c_0_94,c_0_95]),c_0_95]),c_0_95]),c_0_95]),c_0_95]),c_0_95]),c_0_96])]),c_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW256+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n015.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 17:58:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 4.37/4.53 % Version : CSE_E---1.5
% 4.37/4.53 % Problem : theBenchmark.p
% 4.37/4.53 % Proof found
% 4.37/4.53 % SZS status Theorem for theBenchmark.p
% 4.37/4.53 % SZS output start Proof
% See solution above
% 4.37/4.55 % Total time : 3.899000 s
% 4.37/4.55 % SZS output end Proof
% 4.37/4.55 % Total time : 3.942000 s
%------------------------------------------------------------------------------