TSTP Solution File: SWW240+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW240+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 : n016.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 00:16:41 EDT 2023
% Result : Theorem 38.58s 38.78s
% Output : CNFRefutation 38.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 154
% Syntax : Number of formulae : 194 ( 18 unt; 140 typ; 0 def)
% Number of atoms : 91 ( 44 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 31 ~; 26 |; 0 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 234 ( 133 >; 101 *; 0 +; 0 <<)
% Number of predicates : 76 ( 74 usr; 1 prp; 0-3 aty)
% Number of functors : 66 ( 66 usr; 7 con; 0-5 aty)
% Number of variables : 91 ( 2 sgn; 53 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_24,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_26,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_27,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_28,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_29,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_30,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_31,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_32,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_33,type,
tc_Nat_Onat: $i ).
tff(decl_34,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_35,type,
class_Groups_Oone: $i > $o ).
tff(decl_36,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_37,type,
class_Rings_Oidom: $i > $o ).
tff(decl_38,type,
class_Groups_Ozero: $i > $o ).
tff(decl_39,type,
class_Power_Opower: $i > $o ).
tff(decl_40,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_43,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_44,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_45,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_47,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_48,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_49,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_50,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_51,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_52,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_53,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_54,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_55,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_56,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_57,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_58,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_59,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_60,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_61,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_62,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_63,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_64,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_65,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_66,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_67,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_68,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_69,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_70,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_71,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_72,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_73,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_74,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_75,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_76,type,
hBOOL: $i > $o ).
tff(decl_77,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_78,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_79,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_80,type,
class_Rings_Oring: $i > $o ).
tff(decl_81,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_82,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_83,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).
tff(decl_85,type,
tc_Int_Oint: $i ).
tff(decl_86,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_87,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_88,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_90,type,
c_Groups_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_91,type,
class_Groups_Osgn__if: $i > $o ).
tff(decl_92,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_93,type,
class_Groups_Ominus: $i > $o ).
tff(decl_94,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_95,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_96,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_97,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_98,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_99,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_100,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_101,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_102,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_103,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_104,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_105,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_106,type,
c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).
tff(decl_107,type,
class_Orderings_Oord: $i > $o ).
tff(decl_108,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_109,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_110,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_111,type,
class_Rings_Odvd: $i > $o ).
tff(decl_112,type,
c_Nat_OSuc: $i > $i ).
tff(decl_113,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_115,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_116,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_117,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_118,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
c_SMT_Oz3div: ( $i * $i ) > $i ).
tff(decl_120,type,
class_Fields_Ofield: $i > $o ).
tff(decl_121,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_122,type,
c_SMT_Oz3mod: ( $i * $i ) > $i ).
tff(decl_123,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_124,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_125,type,
tc_HOL_Obool: $i ).
tff(decl_126,type,
t_a: $i ).
tff(decl_127,type,
v_n: $i ).
tff(decl_128,type,
v_p: $i ).
tff(decl_129,type,
v_x: $i ).
tff(decl_130,type,
epred1_3: ( $i * $i * $i ) > $o ).
tff(decl_131,type,
epred2_3: ( $i * $i * $i ) > $o ).
tff(decl_132,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_133,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_134,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_135,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_136,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_137,type,
esk6_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_138,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_139,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_140,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_141,type,
esk10_1: $i > $i ).
tff(decl_142,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_144,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_145,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_146,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_147,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_148,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_150,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_151,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_152,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_154,type,
esk23_3: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_156,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_157,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_158,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_159,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_160,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_161,type,
esk30_3: ( $i * $i * $i ) > $i ).
fof(clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__1,axiom,
! [X86] :
( class_Rings_Ocomm__ring__1(X86)
=> class_Rings_Ocomm__semiring__1(X86) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X6) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(tfree_0,hypothesis,
class_Rings_Ocomm__ring__1(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Ozero__class_Ozero(X7)),X6) = c_Groups_Ozero__class_Ozero(X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Ozero__class_Ozero(X7)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X6,X12,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> c_Groups_Oplus__class_Oplus(X7,X12,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),c_Groups_Oplus__class_Oplus(X7,X6,c_Groups_Oone__class_Oone(X7))),X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(conj_0,conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X10,X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),X10) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X10),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X87] :
( class_Rings_Ocomm__semiring__1(X87)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X87)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(fact_poly__mult,axiom,
! [X4,X8,X9,X7] :
( class_Rings_Ocomm__semiring__0(X7)
=> hAPP(c_Polynomial_Opoly(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X7)),X9),X8)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),hAPP(c_Polynomial_Opoly(X7,X9),X4)),hAPP(c_Polynomial_Opoly(X7,X8),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(fact_poly__monom,axiom,
! [X4,X5,X6,X7] :
( class_Rings_Ocomm__semiring__1(X7)
=> hAPP(c_Polynomial_Opoly(X7,c_Polynomial_Omonom(X7,X6,X5)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X6),hAPP(hAPP(c_Power_Opower__class_Opower(X7),X4),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(fact_nat__mult__1,axiom,
! [X5] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__0,axiom,
! [X86] :
( class_Rings_Ocomm__ring__1(X86)
=> class_Rings_Ocomm__semiring__0(X86) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__0) ).
fof(c_0_14,plain,
! [X2977] :
( ~ class_Rings_Ocomm__ring__1(X2977)
| class_Rings_Ocomm__semiring__1(X2977) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__1])]) ).
fof(c_0_15,plain,
! [X235,X236] :
( ~ class_Rings_Ocomm__semiring__1(X236)
| c_Groups_Oplus__class_Oplus(X236,c_Groups_Ozero__class_Ozero(X236),X235) = X235 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
cnf(c_0_16,plain,
( class_Rings_Ocomm__semiring__1(X1)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,hypothesis,
class_Rings_Ocomm__ring__1(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
fof(c_0_18,plain,
! [X483,X484] :
( ~ class_Rings_Ocomm__semiring__1(X484)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X484),c_Groups_Ozero__class_Ozero(X484)),X483) = c_Groups_Ozero__class_Ozero(X484) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(c_0_19,plain,
! [X253,X254] :
( ~ class_Rings_Ocomm__semiring__1(X254)
| c_Groups_Oplus__class_Oplus(X254,X253,c_Groups_Ozero__class_Ozero(X254)) = X253 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(c_0_20,plain,
! [X497,X498,X499] :
( ~ class_Rings_Ocomm__semiring__1(X499)
| c_Groups_Oplus__class_Oplus(X499,X498,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X499),X497),X498)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X499),c_Groups_Oplus__class_Oplus(X499,X497,c_Groups_Oone__class_Oone(X499))),X498) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
cnf(c_0_21,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,hypothesis,
class_Rings_Ocomm__semiring__1(t_a),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_26,plain,
! [X175,X176,X177] :
( ~ class_Rings_Ocomm__semiring__1(X177)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X177),X176),X175) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X177),X175),X176) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(c_0_27,plain,
! [X90,X91] :
( hAPP(X91,esk1_2(X90,X91)) != hAPP(X90,esk1_2(X90,X91))
| X91 = X90 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
cnf(c_0_28,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1))),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,hypothesis,
c_Groups_Oplus__class_Oplus(t_a,c_Groups_Ozero__class_Ozero(t_a),X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,hypothesis,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Ozero__class_Ozero(t_a)),X1) = c_Groups_Ozero__class_Ozero(t_a),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_31,hypothesis,
c_Groups_Oplus__class_Oplus(t_a,X1,c_Groups_Ozero__class_Ozero(t_a)) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_32,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n)),v_p)),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_34,plain,
! [X3039] :
( ~ class_Rings_Ocomm__semiring__1(X3039)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X3039)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).
fof(c_0_35,plain,
! [X97,X98,X99,X100] :
( ~ class_Rings_Ocomm__semiring__0(X100)
| hAPP(c_Polynomial_Opoly(X100,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X100)),X99),X98)),X97) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X100),hAPP(c_Polynomial_Opoly(X100,X99),X97)),hAPP(c_Polynomial_Opoly(X100,X98),X97)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])]) ).
fof(c_0_36,plain,
! [X93,X94,X95,X96] :
( ~ class_Rings_Ocomm__semiring__1(X96)
| hAPP(c_Polynomial_Opoly(X96,c_Polynomial_Omonom(X96,X95,X94)),X93) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X96),X95),hAPP(hAPP(c_Power_Opower__class_Opower(X96),X93),X94)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__monom])]) ).
cnf(c_0_37,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,hypothesis,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31]),c_0_22])]) ).
fof(c_0_39,plain,
! [X712] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X712) = X712,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
cnf(c_0_40,negated_conjecture,
( hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),v_p),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n))),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x))
| ~ class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(t_a)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X4)),hAPP(c_Polynomial_Opoly(X1,X3),X4))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
( hAPP(c_Polynomial_Opoly(X1,c_Polynomial_Omonom(X1,X2,X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,hypothesis,
( hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)) = X1
| hAPP(X1,esk1_2(X1,hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)))) != esk1_2(X1,hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a))) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(t_a)),v_p),c_Polynomial_Omonom(t_a,c_Groups_Oone__class_Oone(t_a),v_n))),v_x) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),v_x),v_n)),hAPP(c_Polynomial_Opoly(t_a,v_p),v_x)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_22])]) ).
cnf(c_0_47,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Polynomial_Opoly(X1,X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X5))) = hAPP(c_Polynomial_Opoly(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X1)),X2),c_Polynomial_Omonom(X1,X4,X5))),X3)
| ~ class_Rings_Ocomm__semiring__0(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,hypothesis,
hAPP(c_Groups_Otimes__class_Otimes(t_a),c_Groups_Oone__class_Oone(t_a)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,hypothesis,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),X2),X1),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
fof(c_0_50,plain,
! [X2978] :
( ~ class_Rings_Ocomm__ring__1(X2978)
| class_Rings_Ocomm__semiring__0(X2978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__ring__1__Rings_Ocomm__semiring__0])]) ).
cnf(c_0_51,negated_conjecture,
~ class_Rings_Ocomm__semiring__0(t_a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_45]),c_0_22])]),c_0_49]) ).
cnf(c_0_52,plain,
( class_Rings_Ocomm__semiring__0(X1)
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW240+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
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sun Aug 27 18:20:29 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.59 start to proof: theBenchmark
% 38.58/38.78 % Version : CSE_E---1.5
% 38.58/38.78 % Problem : theBenchmark.p
% 38.58/38.78 % Proof found
% 38.58/38.78 % SZS status Theorem for theBenchmark.p
% 38.58/38.78 % SZS output start Proof
% See solution above
% 38.71/38.79 % Total time : 38.112000 s
% 38.71/38.79 % SZS output end Proof
% 38.71/38.79 % Total time : 38.153000 s
%------------------------------------------------------------------------------