TSTP Solution File: SCT166+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SCT166+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n003.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 14:11:24 EDT 2023

% Result   : Theorem 1.90s 1.97s
% Output   : CNFRefutation 1.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  150
% Syntax   : Number of formulae    :  180 (  17 unt; 140 typ;   0 def)
%            Number of atoms       :  106 (  28 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  109 (  43   ~;  43   |;  10   &)
%                                         (   3 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  258 ( 110   >; 148   *;   0   +;   0  <<)
%            Number of predicates  :   36 (  34 usr;   1 prp; 0-6 aty)
%            Number of functors    :  106 ( 106 usr;  30 con; 0-6 aty)
%            Number of variables   :  111 (  10 sgn;  62   !;   2   ?;   0   :)

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

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

tff(decl_24,type,
    v_b____: $i ).

tff(decl_25,type,
    v_c____: $i ).

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

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

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

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

tff(decl_30,type,
    c_Product__Type_OPair: ( $i * $i ) > $i ).

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

tff(decl_32,type,
    hBOOL: $i > $o ).

tff(decl_33,type,
    v_Lba____: $i ).

tff(decl_34,type,
    v_P____: $i ).

tff(decl_35,type,
    tc_Nat_Onat: $i ).

tff(decl_36,type,
    c_Orderings_Oord__class_Oless: $i > $i ).

tff(decl_37,type,
    v_h____: $i ).

tff(decl_38,type,
    v_n____: $i ).

tff(decl_39,type,
    c_Arrow__Order__Mirabelle_Omktop: $i ).

tff(decl_40,type,
    v_e____: $i ).

tff(decl_41,type,
    c_Arrow__Order__Mirabelle_Oabove: $i ).

tff(decl_42,type,
    c_Arrow__Order__Mirabelle_Omkbot: $i ).

tff(decl_43,type,
    tc_Arrow__Order__Mirabelle_Oindi: $i ).

tff(decl_44,type,
    tc_HOL_Obool: $i ).

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

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

tff(decl_47,type,
    c_Hilbert__Choice_Oinv__into: ( $i * $i * $i * $i ) > $i ).

tff(decl_48,type,
    c_Groups_Oplus__class_Oplus: $i > $i ).

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

tff(decl_50,type,
    c_Arrow__Order__Mirabelle_OProf: $i ).

tff(decl_51,type,
    v_F: $i ).

tff(decl_52,type,
    c_If: $i > $i ).

tff(decl_53,type,
    c_COMBB: ( $i * $i * $i * $i ) > $i ).

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

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

tff(decl_56,type,
    c_fequal: $i ).

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

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

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

tff(decl_60,type,
    c_Wellfounded_Omeasure: ( $i * $i ) > $i ).

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

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

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

tff(decl_64,type,
    c_Arrow__Order__Mirabelle_OLin: $i ).

tff(decl_65,type,
    c_Finite__Set_Ocard: ( $i * $i ) > $i ).

tff(decl_66,type,
    c_Wellfounded_Olex__prod: ( $i * $i * $i * $i ) > $i ).

tff(decl_67,type,
    c_COMBK: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff(decl_77,type,
    c_COMBI: $i > $i ).

tff(decl_78,type,
    class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).

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

tff(decl_80,type,
    class_Orderings_Opreorder: $i > $o ).

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

tff(decl_82,type,
    c_Wellfounded_Omlex__prod: ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

tff(decl_89,type,
    tc_Product__Type_Ounit: $i ).

tff(decl_90,type,
    tc_Option_Ooption: $i > $i ).

tff(decl_91,type,
    tc_sum: ( $i * $i ) > $i ).

tff(decl_92,type,
    c_Wellfounded_Ofinite__psubset: $i > $i ).

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

tff(decl_94,type,
    c_Set_Oinsert: ( $i * $i * $i ) > $i ).

tff(decl_95,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

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

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

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

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

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

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

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

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

tff(decl_104,type,
    c_Nat_OSuc: $i ).

tff(decl_105,type,
    c_Nat_Onat_Onat__size: $i > $i ).

tff(decl_106,type,
    c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).

tff(decl_107,type,
    c_Int_Oring__1__class_OInts: $i > $i ).

tff(decl_108,type,
    class_Rings_Oring__1: $i > $o ).

tff(decl_109,type,
    class_Int_Oring__char__0: $i > $o ).

tff(decl_110,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

tff(decl_111,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

tff(decl_112,type,
    c_Finite__Set_Ofold__image: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_113,type,
    c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).

tff(decl_114,type,
    c_SetInterval_Oord__class_OatLeastLessThan: ( $i * $i * $i ) > $i ).

tff(decl_115,type,
    c_fFalse: $i ).

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

tff(decl_117,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_118,type,
    esk2_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_119,type,
    esk3_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_120,type,
    esk4_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_121,type,
    esk5_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_122,type,
    esk6_6: ( $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_123,type,
    esk7_0: $i ).

tff(decl_124,type,
    esk8_0: $i ).

tff(decl_125,type,
    esk9_0: $i ).

tff(decl_126,type,
    esk10_0: $i ).

tff(decl_127,type,
    esk11_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_128,type,
    esk12_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_129,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_130,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_131,type,
    esk15_2: ( $i * $i ) > $i ).

tff(decl_132,type,
    esk16_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_133,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_134,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_135,type,
    esk19_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_136,type,
    esk20_1: $i > $i ).

tff(decl_137,type,
    esk21_1: $i > $i ).

tff(decl_138,type,
    esk22_1: $i > $i ).

tff(decl_139,type,
    esk23_1: $i > $i ).

tff(decl_140,type,
    esk24_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_141,type,
    esk25_1: $i > $i ).

tff(decl_142,type,
    esk26_1: $i > $i ).

tff(decl_143,type,
    esk27_1: $i > $i ).

tff(decl_144,type,
    esk28_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_145,type,
    esk29_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_146,type,
    esk30_1: $i > $i ).

tff(decl_147,type,
    esk31_2: ( $i * $i ) > $i ).

tff(decl_148,type,
    esk32_2: ( $i * $i ) > $i ).

tff(decl_149,type,
    esk33_2: ( $i * $i ) > $i ).

tff(decl_150,type,
    esk34_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_151,type,
    esk35_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_152,type,
    esk36_3: ( $i * $i * $i ) > $i ).

tff(decl_153,type,
    esk37_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_154,type,
    esk38_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_155,type,
    esk39_0: $i ).

tff(decl_156,type,
    esk40_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_157,type,
    esk41_1: $i > $i ).

tff(decl_158,type,
    esk42_2: ( $i * $i ) > $i ).

tff(decl_159,type,
    esk43_1: $i > $i ).

tff(decl_160,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_161,type,
    esk45_0: $i ).

fof(fact_range__ex1__eq,axiom,
    ! [X22,X2,X14,X10] :
      ( c_Fun_Oinj__on(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X14),X22),c_Set_Oimage(X10,X14,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))))
      <=> ? [X3] :
            ( X22 = hAPP(X2,X3)
            & ! [X66] :
                ( X22 = hAPP(X2,X66)
               => X66 = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__ex1__eq) ).

fof(fact_range__eqI,axiom,
    ! [X14,X10,X8,X2,X22] :
      ( X22 = hAPP(X2,X8)
     => hBOOL(hAPP(hAPP(c_member(X10),X22),c_Set_Oimage(X14,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_range__eqI) ).

fof(fact_less__irrefl__nat,axiom,
    ! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X46)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(fact_finite,axiom,
    ! [X12,X10] :
      ( class_Finite__Set_Ofinite(X10)
     => c_Finite__Set_Ofinite(X10,X12) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite) ).

fof(fact_injh,axiom,
    c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_injh) ).

fof(fact_finite__nat__set__iff__bounded,axiom,
    ! [X56] :
      ( c_Finite__Set_Ofinite(tc_Nat_Onat,X56)
    <=> ? [X17] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X56))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X17)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(fact_finite__imageD,axiom,
    ! [X12,X2,X14,X10] :
      ( c_Finite__Set_Ofinite(X10,c_Set_Oimage(X14,X10,X2,X12))
     => ( c_Fun_Oinj__on(X14,X10,X2,X12)
       => c_Finite__Set_Ofinite(X14,X12) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageD) ).

fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).

fof(fact_inj__on__def,axiom,
    ! [X12,X2,X14,X10] :
      ( c_Fun_Oinj__on(X10,X14,X2,X12)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => ! [X38] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X38),X12))
             => ( hAPP(X2,X3) = hAPP(X2,X38)
               => X3 = X38 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__def) ).

fof(fact_UNIV__I,axiom,
    ! [X8,X10] : hBOOL(hAPP(hAPP(c_member(X10),X8),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__I) ).

fof(c_0_10,plain,
    ! [X1365,X1366,X1367,X1368,X1370,X1371] :
      ( ( X1365 = hAPP(X1366,esk34_4(X1365,X1366,X1367,X1368))
        | ~ hBOOL(hAPP(hAPP(c_member(X1367),X1365),c_Set_Oimage(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool))) )
      & ( X1365 != hAPP(X1366,X1370)
        | X1370 = esk34_4(X1365,X1366,X1367,X1368)
        | ~ hBOOL(hAPP(hAPP(c_member(X1367),X1365),c_Set_Oimage(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool))) )
      & ( X1365 = hAPP(X1366,esk35_5(X1365,X1366,X1367,X1368,X1371))
        | X1365 != hAPP(X1366,X1371)
        | hBOOL(hAPP(hAPP(c_member(X1367),X1365),c_Set_Oimage(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool))) )
      & ( esk35_5(X1365,X1366,X1367,X1368,X1371) != X1371
        | X1365 != hAPP(X1366,X1371)
        | hBOOL(hAPP(hAPP(c_member(X1367),X1365),c_Set_Oimage(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X1368,X1367,X1366,c_Orderings_Otop__class_Otop(tc_fun(X1368,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__ex1__eq])])])])]) ).

fof(c_0_11,plain,
    ! [X1409,X1410,X1411,X1412,X1413] :
      ( X1413 != hAPP(X1412,X1411)
      | hBOOL(hAPP(hAPP(c_member(X1410),X1413),c_Set_Oimage(X1409,X1410,X1412,c_Orderings_Otop__class_Otop(tc_fun(X1409,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).

cnf(c_0_12,plain,
    ( X3 = esk34_4(X1,X2,X4,X5)
    | X1 != hAPP(X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X1),c_Set_Oimage(X5,X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
    | X1 != hAPP(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_14,plain,
    ! [X46] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),X46)),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

fof(c_0_15,plain,
    ! [X916,X917] :
      ( ~ class_Finite__Set_Ofinite(X917)
      | c_Finite__Set_Ofinite(X917,X916) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).

cnf(c_0_16,plain,
    ( X1 = esk34_4(X2,X3,X4,X5)
    | X2 != hAPP(X3,X1)
    | ~ c_Fun_Oinj__on(X5,X4,X3,c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))) ),
    inference(csr,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,plain,
    c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,v_h____,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[fact_injh]) ).

fof(c_0_18,plain,
    ! [X780] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X780),X780)),
    inference(variable_rename,[status(thm)],[c_0_14]) ).

fof(c_0_19,plain,
    ! [X1603,X1605,X1606,X1607] :
      ( ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1603)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1605),X1603))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1605),esk41_1(X1603))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk42_2(X1606,X1607)),X1606))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X1606) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk42_2(X1606,X1607)),X1607))
        | c_Finite__Set_Ofinite(tc_Nat_Onat,X1606) ) ),
    inference(distribute,[status(thm)],[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_finite__nat__set__iff__bounded])])])])])]) ).

fof(c_0_20,plain,
    ! [X1423,X1424,X1425,X1426] :
      ( ~ c_Finite__Set_Ofinite(X1426,c_Set_Oimage(X1425,X1426,X1424,X1423))
      | ~ c_Fun_Oinj__on(X1425,X1426,X1424,X1423)
      | c_Finite__Set_Ofinite(X1425,X1423) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).

cnf(c_0_21,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).

cnf(c_0_23,plain,
    ( X1 = esk34_4(X2,v_h____,tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi)
    | X2 != hAPP(v_h____,X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

fof(c_0_24,plain,
    ! [X323,X324,X325,X326,X327,X328,X329,X330,X331,X332] :
      ( ( ~ c_Fun_Oinj__on(X326,X325,X324,X323)
        | ~ hBOOL(hAPP(hAPP(c_member(X326),X327),X323))
        | ~ hBOOL(hAPP(hAPP(c_member(X326),X328),X323))
        | hAPP(X324,X327) != hAPP(X324,X328)
        | X327 = X328 )
      & ( hBOOL(hAPP(hAPP(c_member(X332),esk11_4(X329,X330,X331,X332)),X329))
        | c_Fun_Oinj__on(X332,X331,X330,X329) )
      & ( hBOOL(hAPP(hAPP(c_member(X332),esk12_4(X329,X330,X331,X332)),X329))
        | c_Fun_Oinj__on(X332,X331,X330,X329) )
      & ( hAPP(X330,esk11_4(X329,X330,X331,X332)) = hAPP(X330,esk12_4(X329,X330,X331,X332))
        | c_Fun_Oinj__on(X332,X331,X330,X329) )
      & ( esk11_4(X329,X330,X331,X332) != esk12_4(X329,X330,X331,X332)
        | c_Fun_Oinj__on(X332,X331,X330,X329) ) ),
    inference(distribute,[status(thm)],[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_inj__on__def])])])])])]) ).

cnf(c_0_25,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk41_1(X1)))
    | ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_27,plain,
    ! [X117,X118] : hBOOL(hAPP(hAPP(c_member(X118),X117),c_Orderings_Otop__class_Otop(tc_fun(X118,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).

cnf(c_0_28,plain,
    ( c_Finite__Set_Ofinite(X2,X4)
    | ~ c_Finite__Set_Ofinite(X1,c_Set_Oimage(X2,X1,X3,X4))
    | ~ c_Fun_Oinj__on(X2,X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_29,plain,
    c_Finite__Set_Ofinite(tc_Product__Type_Ounit,X1),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_30,plain,
    esk34_4(hAPP(v_h____,X1),v_h____,tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oindi) = X1,
    inference(er,[status(thm)],[c_0_23]) ).

cnf(c_0_31,plain,
    ( hAPP(X1,esk11_4(X2,X1,X3,X4)) = hAPP(X1,esk12_4(X2,X1,X3,X4))
    | c_Fun_Oinj__on(X4,X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_32,plain,
    ( c_Fun_Oinj__on(X4,X3,X2,X1)
    | esk11_4(X1,X2,X3,X4) != esk12_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,plain,
    ( ~ c_Finite__Set_Ofinite(tc_Nat_Onat,X1)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk41_1(X1)),X1)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,plain,
    ( c_Finite__Set_Ofinite(X1,X2)
    | ~ c_Fun_Oinj__on(X1,tc_Product__Type_Ounit,X3,X2) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_36,plain,
    c_Fun_Oinj__on(X1,X2,v_h____,X3),
    inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_30]),c_0_32]) ).

cnf(c_0_37,plain,
    ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_38,plain,
    c_Finite__Set_Ofinite(X1,X2),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_39,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SCT166+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 15:46:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 1.90/1.97  % Version  : CSE_E---1.5
% 1.90/1.97  % Problem  : theBenchmark.p
% 1.90/1.97  % Proof found
% 1.90/1.97  % SZS status Theorem for theBenchmark.p
% 1.90/1.97  % SZS output start Proof
% See solution above
% 1.90/1.98  % Total time : 1.364000 s
% 1.90/1.98  % SZS output end Proof
% 1.90/1.98  % Total time : 1.390000 s
%------------------------------------------------------------------------------