TSTP Solution File: NUM623+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM623+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n020.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 10:39:21 EDT 2023

% Result   : Theorem 0.73s 0.84s
% Output   : CNFRefutation 0.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   88
% Syntax   : Number of formulae    :  147 (  29 unt;  67 typ;   0 def)
%            Number of atoms       :  256 (  64 equ)
%            Maximal formula atoms :   32 (   3 avg)
%            Number of connectives :  290 ( 114   ~; 117   |;  39   &)
%                                         (   6 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   89 (  48   >;  41   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   58 (  58 usr;  19 con; 0-4 aty)
%            Number of variables   :   83 (   1 sgn;  46   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aSet0: $i > $o ).

tff(decl_23,type,
    aElement0: $i > $o ).

tff(decl_24,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_25,type,
    isFinite0: $i > $o ).

tff(decl_26,type,
    slcrc0: $i ).

tff(decl_27,type,
    isCountable0: $i > $o ).

tff(decl_28,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff(decl_29,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_30,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(decl_31,type,
    szNzAzT0: $i ).

tff(decl_32,type,
    sz00: $i ).

tff(decl_33,type,
    szszuzczcdt0: $i > $i ).

tff(decl_34,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_35,type,
    iLess0: ( $i * $i ) > $o ).

tff(decl_36,type,
    sbrdtbr0: $i > $i ).

tff(decl_37,type,
    szmzizndt0: $i > $i ).

tff(decl_38,type,
    szmzazxdt0: $i > $i ).

tff(decl_39,type,
    slbdtrb0: $i > $i ).

tff(decl_40,type,
    slbdtsldtrb0: ( $i * $i ) > $i ).

tff(decl_41,type,
    aFunction0: $i > $o ).

tff(decl_42,type,
    szDzozmdt0: $i > $i ).

tff(decl_43,type,
    sdtlpdtrp0: ( $i * $i ) > $i ).

tff(decl_44,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(decl_45,type,
    sdtlcdtrc0: ( $i * $i ) > $i ).

tff(decl_46,type,
    sdtexdt0: ( $i * $i ) > $i ).

tff(decl_47,type,
    szDzizrdt0: $i > $i ).

tff(decl_48,type,
    xT: $i ).

tff(decl_49,type,
    xK: $i ).

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

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

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

tff(decl_53,type,
    xN: $i ).

tff(decl_54,type,
    xC: $i ).

tff(decl_55,type,
    xe: $i ).

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

tff(decl_57,type,
    xO: $i ).

tff(decl_58,type,
    xQ: $i ).

tff(decl_59,type,
    xp: $i ).

tff(decl_60,type,
    xP: $i ).

tff(decl_61,type,
    xn: $i ).

tff(decl_62,type,
    xx: $i ).

tff(decl_63,type,
    xm: $i ).

tff(decl_64,type,
    esk1_1: $i > $i ).

tff(decl_65,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk5_1: $i > $i ).

tff(decl_69,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_72,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_73,type,
    esk10_1: $i > $i ).

tff(decl_74,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_75,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_76,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_77,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_78,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_79,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_80,type,
    esk17_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_82,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_83,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk21_3: ( $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk22_1: $i > $i ).

tff(decl_86,type,
    esk23_1: $i > $i ).

tff(decl_87,type,
    esk24_1: $i > $i ).

tff(decl_88,type,
    esk25_1: $i > $i ).

fof(m__4982,hypothesis,
    ! [X1] :
      ( aElementOf0(X1,xO)
     => ? [X2] :
          ( aElementOf0(X2,szNzAzT0)
          & aElementOf0(X2,sdtlbdtrb0(xd,szDzizrdt0(xd)))
          & sdtlpdtrp0(xe,X2) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4982) ).

fof(mDefSeg,axiom,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => ! [X2] :
          ( X2 = slbdtrb0(X1)
        <=> ( aSet0(X2)
            & ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( aElementOf0(X3,szNzAzT0)
                  & sdtlseqdt0(szszuzczcdt0(X3),X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).

fof(mDefMin,axiom,
    ! [X1] :
      ( ( aSubsetOf0(X1,szNzAzT0)
        & X1 != slcrc0 )
     => ! [X2] :
          ( X2 = szmzizndt0(X1)
        <=> ( aElementOf0(X2,X1)
            & ! [X3] :
                ( aElementOf0(X3,X1)
               => sdtlseqdt0(X2,X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).

fof(mDefEmp,axiom,
    ! [X1] :
      ( X1 = slcrc0
    <=> ( aSet0(X1)
        & ~ ? [X2] : aElementOf0(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

fof(m__4660,hypothesis,
    ( aFunction0(xe)
    & szDzozmdt0(xe) = szNzAzT0
    & ! [X1] :
        ( aElementOf0(X1,szNzAzT0)
       => sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).

fof(mCardNum,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
      <=> isFinite0(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).

fof(mCardSeg,axiom,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => sbrdtbr0(slbdtrb0(X1)) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSeg) ).

fof(m__5365,hypothesis,
    ( aElementOf0(xx,szNzAzT0)
    & aElementOf0(xx,xO) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5365) ).

fof(mSegFin,axiom,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => isFinite0(slbdtrb0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegFin) ).

fof(mDefSub,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aSubsetOf0(X2,X1)
        <=> ( aSet0(X2)
            & ! [X3] :
                ( aElementOf0(X3,X2)
               => aElementOf0(X3,X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).

fof(m__3821,hypothesis,
    ! [X1,X2] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X2,szNzAzT0)
        & X1 != X2 )
     => szmzizndt0(sdtlpdtrp0(xN,X1)) != szmzizndt0(sdtlpdtrp0(xN,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3821) ).

fof(m__5106,hypothesis,
    aSubsetOf0(xQ,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).

fof(mNATSet,axiom,
    ( aSet0(szNzAzT0)
    & isCountable0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

fof(m__5147,hypothesis,
    xp = szmzizndt0(xQ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).

fof(m__3671,hypothesis,
    ! [X1] :
      ( aElementOf0(X1,szNzAzT0)
     => ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).

fof(m__5389,hypothesis,
    ( aElementOf0(xm,szNzAzT0)
    & xx = sdtlpdtrp0(xe,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).

fof(m__5401,hypothesis,
    xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5401) ).

fof(mLessASymm,axiom,
    ! [X1,X2] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aElementOf0(X2,szNzAzT0) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).

fof(m__5173,hypothesis,
    aElementOf0(xp,xQ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).

fof(m__5481,hypothesis,
    ( aElementOf0(xp,sdtlpdtrp0(xN,xm))
    & aElementOf0(xx,xQ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5481) ).

fof(m__,conjecture,
    xp = xx,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(c_0_21,hypothesis,
    ! [X198] :
      ( ( aElementOf0(esk25_1(X198),szNzAzT0)
        | ~ aElementOf0(X198,xO) )
      & ( aElementOf0(esk25_1(X198),sdtlbdtrb0(xd,szDzizrdt0(xd)))
        | ~ aElementOf0(X198,xO) )
      & ( sdtlpdtrp0(xe,esk25_1(X198)) = X198
        | ~ aElementOf0(X198,xO) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4982])])])]) ).

fof(c_0_22,plain,
    ! [X98,X99,X100,X101,X102] :
      ( ( aSet0(X99)
        | X99 != slbdtrb0(X98)
        | ~ aElementOf0(X98,szNzAzT0) )
      & ( aElementOf0(X100,szNzAzT0)
        | ~ aElementOf0(X100,X99)
        | X99 != slbdtrb0(X98)
        | ~ aElementOf0(X98,szNzAzT0) )
      & ( sdtlseqdt0(szszuzczcdt0(X100),X98)
        | ~ aElementOf0(X100,X99)
        | X99 != slbdtrb0(X98)
        | ~ aElementOf0(X98,szNzAzT0) )
      & ( ~ aElementOf0(X101,szNzAzT0)
        | ~ sdtlseqdt0(szszuzczcdt0(X101),X98)
        | aElementOf0(X101,X99)
        | X99 != slbdtrb0(X98)
        | ~ aElementOf0(X98,szNzAzT0) )
      & ( ~ aElementOf0(esk9_2(X98,X102),X102)
        | ~ aElementOf0(esk9_2(X98,X102),szNzAzT0)
        | ~ sdtlseqdt0(szszuzczcdt0(esk9_2(X98,X102)),X98)
        | ~ aSet0(X102)
        | X102 = slbdtrb0(X98)
        | ~ aElementOf0(X98,szNzAzT0) )
      & ( aElementOf0(esk9_2(X98,X102),szNzAzT0)
        | aElementOf0(esk9_2(X98,X102),X102)
        | ~ aSet0(X102)
        | X102 = slbdtrb0(X98)
        | ~ aElementOf0(X98,szNzAzT0) )
      & ( sdtlseqdt0(szszuzczcdt0(esk9_2(X98,X102)),X98)
        | aElementOf0(esk9_2(X98,X102),X102)
        | ~ aSet0(X102)
        | X102 = slbdtrb0(X98)
        | ~ aElementOf0(X98,szNzAzT0) ) ),
    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)],[mDefSeg])])])])])]) ).

fof(c_0_23,plain,
    ! [X86,X87,X88,X89] :
      ( ( aElementOf0(X87,X86)
        | X87 != szmzizndt0(X86)
        | ~ aSubsetOf0(X86,szNzAzT0)
        | X86 = slcrc0 )
      & ( ~ aElementOf0(X88,X86)
        | sdtlseqdt0(X87,X88)
        | X87 != szmzizndt0(X86)
        | ~ aSubsetOf0(X86,szNzAzT0)
        | X86 = slcrc0 )
      & ( aElementOf0(esk7_2(X86,X89),X86)
        | ~ aElementOf0(X89,X86)
        | X89 = szmzizndt0(X86)
        | ~ aSubsetOf0(X86,szNzAzT0)
        | X86 = slcrc0 )
      & ( ~ sdtlseqdt0(X89,esk7_2(X86,X89))
        | ~ aElementOf0(X89,X86)
        | X89 = szmzizndt0(X86)
        | ~ aSubsetOf0(X86,szNzAzT0)
        | X86 = slcrc0 ) ),
    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)],[mDefMin])])])])])]) ).

fof(c_0_24,plain,
    ! [X9,X10,X11] :
      ( ( aSet0(X9)
        | X9 != slcrc0 )
      & ( ~ aElementOf0(X10,X9)
        | X9 != slcrc0 )
      & ( ~ aSet0(X11)
        | aElementOf0(esk1_1(X11),X11)
        | X11 = slcrc0 ) ),
    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)],[mDefEmp])])])])])]) ).

fof(c_0_25,hypothesis,
    ! [X195] :
      ( aFunction0(xe)
      & szDzozmdt0(xe) = szNzAzT0
      & ( ~ aElementOf0(X195,szNzAzT0)
        | sdtlpdtrp0(xe,X195) = szmzizndt0(sdtlpdtrp0(xN,X195)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4660])])]) ).

fof(c_0_26,plain,
    ! [X75] :
      ( ( ~ aElementOf0(sbrdtbr0(X75),szNzAzT0)
        | isFinite0(X75)
        | ~ aSet0(X75) )
      & ( ~ isFinite0(X75)
        | aElementOf0(sbrdtbr0(X75),szNzAzT0)
        | ~ aSet0(X75) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardNum])])]) ).

fof(c_0_27,plain,
    ! [X111] :
      ( ~ aElementOf0(X111,szNzAzT0)
      | sbrdtbr0(slbdtrb0(X111)) = X111 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardSeg])]) ).

cnf(c_0_28,hypothesis,
    ( aElementOf0(esk25_1(X1),szNzAzT0)
    | ~ aElementOf0(X1,xO) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,hypothesis,
    aElementOf0(xx,xO),
    inference(split_conjunct,[status(thm)],[m__5365]) ).

fof(c_0_30,plain,
    ! [X104] :
      ( ~ aElementOf0(X104,szNzAzT0)
      | isFinite0(slbdtrb0(X104)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSegFin])]) ).

cnf(c_0_31,plain,
    ( aSet0(X1)
    | X1 != slbdtrb0(X2)
    | ~ aElementOf0(X2,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_32,plain,
    ! [X15,X16,X17,X18] :
      ( ( aSet0(X16)
        | ~ aSubsetOf0(X16,X15)
        | ~ aSet0(X15) )
      & ( ~ aElementOf0(X17,X16)
        | aElementOf0(X17,X15)
        | ~ aSubsetOf0(X16,X15)
        | ~ aSet0(X15) )
      & ( aElementOf0(esk2_2(X15,X18),X18)
        | ~ aSet0(X18)
        | aSubsetOf0(X18,X15)
        | ~ aSet0(X15) )
      & ( ~ aElementOf0(esk2_2(X15,X18),X15)
        | ~ aSet0(X18)
        | aSubsetOf0(X18,X15)
        | ~ aSet0(X15) ) ),
    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)],[mDefSub])])])])])]) ).

cnf(c_0_33,plain,
    ( sdtlseqdt0(X3,X1)
    | X2 = slcrc0
    | ~ aElementOf0(X1,X2)
    | X3 != szmzizndt0(X2)
    | ~ aSubsetOf0(X2,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_34,plain,
    ( ~ aElementOf0(X1,X2)
    | X2 != slcrc0 ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_35,hypothesis,
    ! [X178,X179] :
      ( ~ aElementOf0(X178,szNzAzT0)
      | ~ aElementOf0(X179,szNzAzT0)
      | X178 = X179
      | szmzizndt0(sdtlpdtrp0(xN,X178)) != szmzizndt0(sdtlpdtrp0(xN,X179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3821])]) ).

cnf(c_0_36,hypothesis,
    ( sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1))
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_37,plain,
    ( aElementOf0(sbrdtbr0(X1),szNzAzT0)
    | ~ isFinite0(X1)
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_38,plain,
    ( sbrdtbr0(slbdtrb0(X1)) = X1
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_39,hypothesis,
    aElementOf0(esk25_1(xx),szNzAzT0),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_40,hypothesis,
    ( sdtlpdtrp0(xe,esk25_1(X1)) = X1
    | ~ aElementOf0(X1,xO) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_41,plain,
    ( isFinite0(slbdtrb0(X1))
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_42,plain,
    ( aSet0(slbdtrb0(X1))
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(er,[status(thm)],[c_0_31]) ).

cnf(c_0_43,plain,
    ( aElementOf0(X1,X3)
    | ~ aElementOf0(X1,X2)
    | ~ aSubsetOf0(X2,X3)
    | ~ aSet0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_44,hypothesis,
    aSubsetOf0(xQ,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__5106]) ).

cnf(c_0_45,plain,
    aSet0(szNzAzT0),
    inference(split_conjunct,[status(thm)],[mNATSet]) ).

cnf(c_0_46,plain,
    ( sdtlseqdt0(X1,X2)
    | X1 != szmzizndt0(X3)
    | ~ aSubsetOf0(X3,szNzAzT0)
    | ~ aElementOf0(X2,X3) ),
    inference(csr,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_47,hypothesis,
    xp = szmzizndt0(xQ),
    inference(split_conjunct,[status(thm)],[m__5147]) ).

fof(c_0_48,hypothesis,
    ! [X175] :
      ( ( aSubsetOf0(sdtlpdtrp0(xN,X175),szNzAzT0)
        | ~ aElementOf0(X175,szNzAzT0) )
      & ( isCountable0(sdtlpdtrp0(xN,X175))
        | ~ aElementOf0(X175,szNzAzT0) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3671])])]) ).

cnf(c_0_49,hypothesis,
    ( X1 = X2
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,szNzAzT0)
    | szmzizndt0(sdtlpdtrp0(xN,X1)) != szmzizndt0(sdtlpdtrp0(xN,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_50,hypothesis,
    aElementOf0(xm,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__5389]) ).

cnf(c_0_51,hypothesis,
    xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
    inference(split_conjunct,[status(thm)],[m__5401]) ).

cnf(c_0_52,hypothesis,
    ( szmzizndt0(sdtlpdtrp0(xN,sbrdtbr0(X1))) = sdtlpdtrp0(xe,sbrdtbr0(X1))
    | ~ isFinite0(X1)
    | ~ aSet0(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_53,hypothesis,
    sbrdtbr0(slbdtrb0(esk25_1(xx))) = esk25_1(xx),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_54,hypothesis,
    sdtlpdtrp0(xe,esk25_1(xx)) = xx,
    inference(spm,[status(thm)],[c_0_40,c_0_29]) ).

cnf(c_0_55,hypothesis,
    isFinite0(slbdtrb0(esk25_1(xx))),
    inference(spm,[status(thm)],[c_0_41,c_0_39]) ).

cnf(c_0_56,hypothesis,
    aSet0(slbdtrb0(esk25_1(xx))),
    inference(spm,[status(thm)],[c_0_42,c_0_39]) ).

fof(c_0_57,plain,
    ! [X66,X67] :
      ( ~ aElementOf0(X66,szNzAzT0)
      | ~ aElementOf0(X67,szNzAzT0)
      | ~ sdtlseqdt0(X66,X67)
      | ~ sdtlseqdt0(X67,X66)
      | X66 = X67 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLessASymm])]) ).

cnf(c_0_58,hypothesis,
    ( aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X1,xQ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).

cnf(c_0_59,hypothesis,
    aElementOf0(xp,xQ),
    inference(split_conjunct,[status(thm)],[m__5173]) ).

cnf(c_0_60,hypothesis,
    ( sdtlseqdt0(X1,X2)
    | X1 != xp
    | ~ aElementOf0(X2,xQ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_44])]) ).

cnf(c_0_61,hypothesis,
    ( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_62,hypothesis,
    ( X1 = xm
    | szmzizndt0(sdtlpdtrp0(xN,X1)) != xx
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).

cnf(c_0_63,hypothesis,
    szmzizndt0(sdtlpdtrp0(xN,esk25_1(xx))) = xx,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_55]),c_0_56])]) ).

cnf(c_0_64,plain,
    ( X1 = X2
    | ~ aElementOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,szNzAzT0)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_65,hypothesis,
    aElementOf0(xp,szNzAzT0),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_66,hypothesis,
    ( sdtlseqdt0(xp,X1)
    | ~ aElementOf0(X1,xQ) ),
    inference(er,[status(thm)],[c_0_60]) ).

cnf(c_0_67,hypothesis,
    aElementOf0(xx,xQ),
    inference(split_conjunct,[status(thm)],[m__5481]) ).

fof(c_0_68,negated_conjecture,
    xp != xx,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_69,plain,
    ( sdtlseqdt0(szmzizndt0(X1),X2)
    | ~ aSubsetOf0(X1,szNzAzT0)
    | ~ aElementOf0(X2,X1) ),
    inference(er,[status(thm)],[c_0_46]) ).

cnf(c_0_70,hypothesis,
    aSubsetOf0(sdtlpdtrp0(xN,esk25_1(xx)),szNzAzT0),
    inference(spm,[status(thm)],[c_0_61,c_0_39]) ).

cnf(c_0_71,hypothesis,
    esk25_1(xx) = xm,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_39]),c_0_63])]) ).

cnf(c_0_72,hypothesis,
    ( X1 = xp
    | ~ sdtlseqdt0(xp,X1)
    | ~ sdtlseqdt0(X1,xp)
    | ~ aElementOf0(X1,szNzAzT0) ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_73,hypothesis,
    sdtlseqdt0(xp,xx),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_74,hypothesis,
    aElementOf0(xx,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__5365]) ).

cnf(c_0_75,negated_conjecture,
    xp != xx,
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_76,hypothesis,
    ( sdtlseqdt0(xx,X1)
    | ~ aElementOf0(X1,sdtlpdtrp0(xN,xm)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_63]),c_0_71]) ).

cnf(c_0_77,hypothesis,
    aElementOf0(xp,sdtlpdtrp0(xN,xm)),
    inference(split_conjunct,[status(thm)],[m__5481]) ).

cnf(c_0_78,hypothesis,
    ~ sdtlseqdt0(xx,xp),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74])]),c_0_75]) ).

cnf(c_0_79,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM623+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n020.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri Aug 25 18:00:30 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.21/0.64  start to proof: theBenchmark
% 0.73/0.84  % Version  : CSE_E---1.5
% 0.73/0.84  % Problem  : theBenchmark.p
% 0.73/0.84  % Proof found
% 0.73/0.84  % SZS status Theorem for theBenchmark.p
% 0.73/0.84  % SZS output start Proof
% See solution above
% 0.73/0.85  % Total time : 0.187000 s
% 0.73/0.85  % SZS output end Proof
% 0.73/0.85  % Total time : 0.193000 s
%------------------------------------------------------------------------------