TSTP Solution File: SCT097-1 by CSE

TSTP Solution File: SCT097-1 by CSE_E---1.5

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SCT097-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:11:11 EDT 2023

% Result   : Unsatisfiable 0.92s 1.02s
% Output   : CNFRefutation 0.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  198
% Syntax   : Number of formulae    :  204 (   6 unt; 194 typ;   0 def)
%            Number of atoms       :   14 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   11 (   7   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :   15 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  377 ( 174   >; 203   *;   0   +;   0  <<)
%            Number of predicates  :   84 (  83 usr;   1 prp; 0-6 aty)
%            Number of functors    :  111 ( 111 usr;  20 con; 0-7 aty)
%            Number of variables   :    4 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    class_Ring__and__Field_Oordered__field: $i > $o ).

tff(decl_23,type,
    class_Ring__and__Field_Odivision__by__zero: $i > $o ).

tff(decl_24,type,
    c_HOL_Ozero__class_Ozero: $i > $i ).

tff(decl_25,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(decl_26,type,
    c_HOL_Oinverse__class_Odivide: $i > $i ).

tff(decl_27,type,
    hAPP: ( $i * $i ) > $i ).

tff(decl_28,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(decl_29,type,
    c_HOL_Oplus__class_Oplus: $i > $i ).

tff(decl_30,type,
    class_OrderedGroup_Ocomm__monoid__add: $i > $o ).

tff(decl_31,type,
    tc_bool: $i ).

tff(decl_32,type,
    tc_fun: ( $i * $i ) > $i ).

tff(decl_33,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

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

tff(decl_35,type,
    class_Lattices_Obounded__lattice: $i > $o ).

tff(decl_36,type,
    class_Ring__and__Field_Oordered__ring__strict: $i > $o ).

tff(decl_37,type,
    c_HOL_Otimes__class_Otimes: $i > $i ).

tff(decl_38,type,
    c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).

tff(decl_39,type,
    tc_prod: ( $i * $i ) > $i ).

tff(decl_40,type,
    c_HOL_Oone__class_Oone: $i > $i ).

tff(decl_41,type,
    c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).

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

tff(decl_43,type,
    c_Pair: ( $i * $i * $i * $i ) > $i ).

tff(decl_44,type,
    c_Set_Oinsert: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    c_Relation_ODomain: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    c_HOL_Ouminus__class_Ouminus: $i > $i ).

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

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

tff(decl_49,type,
    c_HOL_Ominus__class_Ominus: $i > $i ).

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

tff(decl_51,type,
    c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    tc_nat: $i ).

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

tff(decl_54,type,
    c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).

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

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

tff(decl_57,type,
    c_in: $i > $i ).

tff(decl_58,type,
    c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).

tff(decl_59,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

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

tff(decl_61,type,
    c_Finite__Set_Osetsum: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_66,type,
    c_HOL_Oord__class_Oless: $i > $i ).

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

tff(decl_68,type,
    class_OrderedGroup_Oordered__ab__group__add: $i > $o ).

tff(decl_69,type,
    class_Ring__and__Field_Oring__1: $i > $o ).

tff(decl_70,type,
    class_Int_Onumber__ring: $i > $o ).

tff(decl_71,type,
    class_Ring__and__Field_Oordered__semiring: $i > $o ).

tff(decl_72,type,
    class_OrderedGroup_Oab__group__add: $i > $o ).

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

tff(decl_74,type,
    class_Ring__and__Field_Ocomm__ring__1: $i > $o ).

tff(decl_75,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

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

tff(decl_77,type,
    class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).

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

tff(decl_79,type,
    class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).

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

tff(decl_81,type,
    class_Ring__and__Field_Ofield: $i > $o ).

tff(decl_82,type,
    class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).

tff(decl_83,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

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

tff(decl_85,type,
    c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_86,type,
    c_Relation_ORange: ( $i * $i * $i ) > $i ).

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

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

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

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

tff(decl_91,type,
    c_Relation_OId: $i > $i ).

tff(decl_92,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

tff(decl_93,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: ( $i * $i * $i ) > $i ).

tff(decl_94,type,
    c_Nat_Osemiring__1__class_Oof__nat: $i > $i ).

tff(decl_95,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

tff(decl_96,type,
    class_Power_Opower: $i > $o ).

tff(decl_97,type,
    class_Orderings_Olinorder: $i > $o ).

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

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

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

tff(decl_101,type,
    class_Lattices_Oupper__semilattice: $i > $o ).

tff(decl_102,type,
    class_Ring__and__Field_Osgn__if: $i > $o ).

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

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

tff(decl_105,type,
    c_List_Osko__Recdef__Xtfl__wf__induct__1__1: ( $i * $i * $i ) > $i ).

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

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

tff(decl_108,type,
    c_Relation_Oconverse: ( $i * $i * $i ) > $i ).

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

tff(decl_110,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: ( $i * $i * $i ) > $i ).

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

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

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

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

tff(decl_115,type,
    class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).

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

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

tff(decl_118,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

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

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

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

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

tff(decl_123,type,
    class_Orderings_Otop: $i > $o ).

tff(decl_124,type,
    class_Ring__and__Field_Omult__mono: $i > $o ).

tff(decl_125,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

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

tff(decl_127,type,
    class_Orderings_Opreorder: $i > $o ).

tff(decl_128,type,
    c_Wellfounded_Oacc: ( $i * $i ) > $i ).

tff(decl_129,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: ( $i * $i * $i ) > $i ).

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

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

tff(decl_132,type,
    c_List_Osko__Recdef__Xcuts__eq__1__1: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_133,type,
    c_Recdef_Ocut: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_134,type,
    c_Relation_OId__on: ( $i * $i ) > $i ).

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

tff(decl_136,type,
    class_Ring__and__Field_Ocomm__ring: $i > $o ).

tff(decl_137,type,
    class_OrderedGroup_Oab__semigroup__mult: $i > $o ).

tff(decl_138,type,
    class_Ring__and__Field_Ocomm__semiring: $i > $o ).

tff(decl_139,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_140,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2: ( $i * $i * $i * $i ) > $i ).

tff(decl_141,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_142,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2: ( $i * $i * $i * $i ) > $i ).

tff(decl_143,type,
    class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).

tff(decl_144,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

tff(decl_145,type,
    class_HOL_Oord: $i > $o ).

tff(decl_146,type,
    c_HOL_OIf: $i > $i ).

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

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

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

tff(decl_150,type,
    c_Equiv__Relations_Ocongruent2: ( $i * $i * $i * $i * $i * $i ) > $o ).

tff(decl_151,type,
    c_ATP__Linkup_Osko__Finite__Set__Xsetsum__0_H__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_152,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

tff(decl_153,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: ( $i * $i * $i ) > $i ).

tff(decl_154,type,
    c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: ( $i * $i * $i ) > $i ).

tff(decl_155,type,
    c_ATP__Linkup_Osko__Relation__XImageE__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_156,type,
    c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_157,type,
    c_ATP__Linkup_Osko__Finite__Set__Xsetprod__1_H__1__1: ( $i * $i * $i * $i ) > $i ).

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

tff(decl_159,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: ( $i * $i * $i ) > $i ).

tff(decl_160,type,
    v_sko__Wellfounded__Xacc__Xinducts__1: ( $i * $i ) > $i ).

tff(decl_161,type,
    t_a: $i ).

tff(decl_162,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: ( $i * $i * $i ) > $i ).

tff(decl_163,type,
    c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: ( $i * $i * $i ) > $i ).

tff(decl_164,type,
    v_sko__Wellfounded__Xacc__Xinduct__1: ( $i * $i ) > $i ).

tff(decl_165,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: ( $i * $i * $i ) > $i ).

tff(decl_166,type,
    c_ATP__Linkup_Osko__Finite__Set__Xsetprod__pos__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_167,type,
    c_ATP__Linkup_Osko__Finite__Set__Xsetprod__zero__iff__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_168,type,
    c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_169,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_170,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_171,type,
    v_sko__Transitive__Closure__Xrtrancl__Xcases__1: ( $i * $i * $i ) > $i ).

tff(decl_172,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: ( $i * $i ) > $i ).

tff(decl_173,type,
    c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_174,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_175,type,
    v_sko__Transitive__Closure__Xtrancl__Xcases__1: ( $i * $i * $i ) > $i ).

tff(decl_176,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_177,type,
    c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_178,type,
    c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_179,type,
    c_ATP__Linkup_Osko__Relation__XIdE__1__1: ( $i * $i ) > $i ).

tff(decl_180,type,
    c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: ( $i * $i ) > $i ).

tff(decl_181,type,
    c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: ( $i * $i ) > $i ).

tff(decl_182,type,
    c_ATP__Linkup_Osko__Relation__XId__onE__1__1: ( $i * $i * $i ) > $i ).

tff(decl_183,type,
    v_r: $i ).

tff(decl_184,type,
    t_b: $i ).

tff(decl_185,type,
    c_Relation_Oirrefl: ( $i * $i ) > $o ).

tff(decl_186,type,
    c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: ( $i * $i ) > $i ).

tff(decl_187,type,
    c_Equiv__Relations_Ocongruent: ( $i * $i * $i * $i ) > $o ).

tff(decl_188,type,
    c_Wellfounded_Omlex__prod: ( $i * $i * $i ) > $i ).

tff(decl_189,type,
    c_Nitpick_Orefl_H: ( $i * $i ) > $o ).

tff(decl_190,type,
    c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: ( $i * $i ) > $i ).

tff(decl_191,type,
    c_ATP__Linkup_Osko__Relation__XDomainE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_192,type,
    c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_193,type,
    c_ATP__Linkup_Osko__Relation__XRangeE__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_194,type,
    c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: ( $i * $i * $i * $i ) > $i ).

tff(decl_195,type,
    c_fequal: $i > $i ).

tff(decl_196,type,
    c_Relation_Oinv__image: ( $i * $i * $i * $i ) > $i ).

tff(decl_197,type,
    class_Nat_Osemiring__char__0: $i > $o ).

tff(decl_198,type,
    c_Wellfounded_Omeasure: ( $i * $i ) > $i ).

tff(decl_199,type,
    tc_Arrow__Order__Mirabelle_Oalt: $i ).

tff(decl_200,type,
    v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: ( $i * $i ) > $i ).

tff(decl_201,type,
    c_Arrow__Order__Mirabelle_Omktop: $i ).

tff(decl_202,type,
    v_c____: $i ).

tff(decl_203,type,
    v_d____: $i ).

tff(decl_204,type,
    v_P____: $i ).

tff(decl_205,type,
    v_F: $i > $i ).

tff(decl_206,type,
    v_h____: $i ).

tff(decl_207,type,
    tc_Arrow__Order__Mirabelle_Oindi: $i ).

tff(decl_208,type,
    v_n____: $i ).

tff(decl_209,type,
    v_e____: $i ).

tff(decl_210,type,
    c_Arrow__Order__Mirabelle_Oabove: $i ).

tff(decl_211,type,
    c_Arrow__Order__Mirabelle_Omkbot: $i ).

tff(decl_212,type,
    v_b____: $i ).

tff(decl_213,type,
    v_a____: $i ).

tff(decl_214,type,
    v_Lab____: $i ).

tff(decl_215,type,
    v_Lba____: $i ).

cnf(cls_CHAINED_1,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).

cnf(cls_conjecture_0,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_CHAINED_0,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),X1),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
    | ~ c_lessequals(X1,v_n____,tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

cnf(cls_le__refl_0,axiom,
    c_lessequals(X1,X1,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

cnf(c_0_4,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))))
    | ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))) ),
    cls_CHAINED_1 ).

cnf(c_0_5,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_e____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omktop,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_fequal(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Oabove,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_c____),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),hAPP(c_COMBC(c_COMBB(c_Arrow__Order__Mirabelle_Omkbot,v_P____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_Arrow__Order__Mirabelle_Oalt,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_e____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))),
    cls_conjecture_0 ).

cnf(c_0_6,plain,
    ~ hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),v_n____),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____)))),
    inference(sr,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,axiom,
    ( hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_b____,v_a____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F(hAPP(c_COMBC(hAPP(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),X1),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lab____),tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____))))
    | ~ c_lessequals(X1,v_n____,tc_nat) ),
    cls_CHAINED_0 ).

cnf(c_0_8,axiom,
    c_lessequals(X1,X1,tc_nat),
    cls_le__refl_0 ).

cnf(c_0_9,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : SCT097-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Thu Aug 24 15:03:36 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 0.92/1.02  % Version  : CSE_E---1.5
% 0.92/1.02  % Problem  : theBenchmark.p
% 0.92/1.02  % Proof found
% 0.92/1.02  % SZS status Theorem for theBenchmark.p
% 0.92/1.02  % SZS output start Proof
% See solution above
% 0.92/1.03  % Total time : 0.406000 s
% 0.92/1.03  % SZS output end Proof
% 0.92/1.03  % Total time : 0.454000 s
%------------------------------------------------------------------------------