TSTP Solution File: NUM554+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM554+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/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 10:38:39 EDT 2023

% Result   : Theorem 0.82s 0.95s
% Output   : CNFRefutation 0.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   55
% Syntax   : Number of formulae    :  129 (  31 unt;  37 typ;   0 def)
%            Number of atoms       :  414 (  77 equ)
%            Maximal formula atoms :   54 (   4 avg)
%            Number of connectives :  552 ( 230   ~; 252   |;  46   &)
%                                         (   7 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   45 (  27   >;  18   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   29 (  29 usr;  10 con; 0-3 aty)
%            Number of variables   :  133 (   0 sgn;  59   !;   0   ?;   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,
    xk: $i ).

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

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

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

tff(decl_45,type,
    xQ: $i ).

tff(decl_46,type,
    xy: $i ).

tff(decl_47,type,
    xP: $i ).

tff(decl_48,type,
    esk1_1: $i > $i ).

tff(decl_49,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk5_1: $i > $i ).

tff(decl_53,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_57,type,
    esk10_1: $i > $i ).

tff(decl_58,type,
    esk11_3: ( $i * $i * $i ) > $i ).

fof(mDefSel,axiom,
    ! [X1,X2] :
      ( ( aSet0(X1)
        & aElementOf0(X2,szNzAzT0) )
     => ! [X3] :
          ( X3 = slbdtsldtrb0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aSubsetOf0(X4,X1)
                  & sbrdtbr0(X4) = X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).

fof(mDiffCons,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aSet0(X2) )
     => ( ~ aElementOf0(X1,X2)
       => sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDiffCons) ).

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).

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

fof(m__2270,hypothesis,
    aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).

fof(m__2202,hypothesis,
    aElementOf0(xk,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).

fof(m__2202_02,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & xk != sz00 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).

fof(mDefDiff,axiom,
    ! [X1,X2] :
      ( ( aSet0(X1)
        & aElement0(X2) )
     => ! [X3] :
          ( X3 = sdtmndt0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aElement0(X4)
                  & aElementOf0(X4,X1)
                  & X4 != X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

fof(m__2256,hypothesis,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).

fof(mFConsSet,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ! [X2] :
          ( ( aSet0(X2)
            & isFinite0(X2) )
         => isFinite0(sdtpldt0(X2,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFConsSet) ).

fof(mDefCons,axiom,
    ! [X1,X2] :
      ( ( aSet0(X1)
        & aElement0(X2) )
     => ! [X3] :
          ( X3 = sdtpldt0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aElement0(X4)
                  & ( aElementOf0(X4,X1)
                    | X4 = X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).

fof(m__2357,hypothesis,
    xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).

fof(mFDiffSet,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ! [X2] :
          ( ( aSet0(X2)
            & isFinite0(X2) )
         => isFinite0(sdtmndt0(X2,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).

fof(m__2304,hypothesis,
    ( aElement0(xy)
    & aElementOf0(xy,xQ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2304) ).

fof(m__2291,hypothesis,
    ( aSet0(xQ)
    & isFinite0(xQ)
    & sbrdtbr0(xQ) = xk ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).

fof(m__2323,hypothesis,
    ~ aElementOf0(xx,xQ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2323) ).

fof(mCardDiff,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( ( isFinite0(X1)
            & aElementOf0(X2,X1) )
         => szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardDiff) ).

fof(m__,conjecture,
    aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(c_0_18,plain,
    ! [X110,X111,X112,X113,X114,X115] :
      ( ( aSet0(X112)
        | X112 != slbdtsldtrb0(X110,X111)
        | ~ aSet0(X110)
        | ~ aElementOf0(X111,szNzAzT0) )
      & ( aSubsetOf0(X113,X110)
        | ~ aElementOf0(X113,X112)
        | X112 != slbdtsldtrb0(X110,X111)
        | ~ aSet0(X110)
        | ~ aElementOf0(X111,szNzAzT0) )
      & ( sbrdtbr0(X113) = X111
        | ~ aElementOf0(X113,X112)
        | X112 != slbdtsldtrb0(X110,X111)
        | ~ aSet0(X110)
        | ~ aElementOf0(X111,szNzAzT0) )
      & ( ~ aSubsetOf0(X114,X110)
        | sbrdtbr0(X114) != X111
        | aElementOf0(X114,X112)
        | X112 != slbdtsldtrb0(X110,X111)
        | ~ aSet0(X110)
        | ~ aElementOf0(X111,szNzAzT0) )
      & ( ~ aElementOf0(esk11_3(X110,X111,X115),X115)
        | ~ aSubsetOf0(esk11_3(X110,X111,X115),X110)
        | sbrdtbr0(esk11_3(X110,X111,X115)) != X111
        | ~ aSet0(X115)
        | X115 = slbdtsldtrb0(X110,X111)
        | ~ aSet0(X110)
        | ~ aElementOf0(X111,szNzAzT0) )
      & ( aSubsetOf0(esk11_3(X110,X111,X115),X110)
        | aElementOf0(esk11_3(X110,X111,X115),X115)
        | ~ aSet0(X115)
        | X115 = slbdtsldtrb0(X110,X111)
        | ~ aSet0(X110)
        | ~ aElementOf0(X111,szNzAzT0) )
      & ( sbrdtbr0(esk11_3(X110,X111,X115)) = X111
        | aElementOf0(esk11_3(X110,X111,X115),X115)
        | ~ aSet0(X115)
        | X115 = slbdtsldtrb0(X110,X111)
        | ~ aSet0(X110)
        | ~ aElementOf0(X111,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)],[mDefSel])])])])])]) ).

cnf(c_0_19,plain,
    ( aSubsetOf0(X1,X2)
    | ~ aElementOf0(X1,X3)
    | X3 != slbdtsldtrb0(X2,X4)
    | ~ aSet0(X2)
    | ~ aElementOf0(X4,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_20,plain,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aSet0(X2) )
     => ( ~ aElementOf0(X1,X2)
       => sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
    inference(fof_simplification,[status(thm)],[mDiffCons]) ).

fof(c_0_21,plain,
    ! [X5,X6] :
      ( ~ aSet0(X5)
      | ~ aElementOf0(X6,X5)
      | aElement0(X6) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).

fof(c_0_22,plain,
    ! [X13,X14,X15,X16] :
      ( ( aSet0(X14)
        | ~ aSubsetOf0(X14,X13)
        | ~ aSet0(X13) )
      & ( ~ aElementOf0(X15,X14)
        | aElementOf0(X15,X13)
        | ~ aSubsetOf0(X14,X13)
        | ~ aSet0(X13) )
      & ( aElementOf0(esk2_2(X13,X16),X16)
        | ~ aSet0(X16)
        | aSubsetOf0(X16,X13)
        | ~ aSet0(X13) )
      & ( ~ aElementOf0(esk2_2(X13,X16),X13)
        | ~ aSet0(X16)
        | aSubsetOf0(X16,X13)
        | ~ aSet0(X13) ) ),
    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_23,plain,
    ( aSubsetOf0(X1,X2)
    | ~ aElementOf0(X1,slbdtsldtrb0(X2,X3))
    | ~ aElementOf0(X3,szNzAzT0)
    | ~ aSet0(X2) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_24,hypothesis,
    aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
    inference(split_conjunct,[status(thm)],[m__2270]) ).

cnf(c_0_25,hypothesis,
    aElementOf0(xk,szNzAzT0),
    inference(split_conjunct,[status(thm)],[m__2202]) ).

cnf(c_0_26,hypothesis,
    aSet0(xS),
    inference(split_conjunct,[status(thm)],[m__2202_02]) ).

fof(c_0_27,plain,
    ! [X33,X34,X35,X36,X37,X38] :
      ( ( aSet0(X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( aElement0(X36)
        | ~ aElementOf0(X36,X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( aElementOf0(X36,X33)
        | ~ aElementOf0(X36,X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( X36 != X34
        | ~ aElementOf0(X36,X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( ~ aElement0(X37)
        | ~ aElementOf0(X37,X33)
        | X37 = X34
        | aElementOf0(X37,X35)
        | X35 != sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( ~ aElementOf0(esk4_3(X33,X34,X38),X38)
        | ~ aElement0(esk4_3(X33,X34,X38))
        | ~ aElementOf0(esk4_3(X33,X34,X38),X33)
        | esk4_3(X33,X34,X38) = X34
        | ~ aSet0(X38)
        | X38 = sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( aElement0(esk4_3(X33,X34,X38))
        | aElementOf0(esk4_3(X33,X34,X38),X38)
        | ~ aSet0(X38)
        | X38 = sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( aElementOf0(esk4_3(X33,X34,X38),X33)
        | aElementOf0(esk4_3(X33,X34,X38),X38)
        | ~ aSet0(X38)
        | X38 = sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) )
      & ( esk4_3(X33,X34,X38) != X34
        | aElementOf0(esk4_3(X33,X34,X38),X38)
        | ~ aSet0(X38)
        | X38 = sdtmndt0(X33,X34)
        | ~ aSet0(X33)
        | ~ aElement0(X34) ) ),
    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)],[mDefDiff])])])])])]) ).

fof(c_0_28,plain,
    ! [X42,X43] :
      ( ~ aElement0(X42)
      | ~ aSet0(X43)
      | aElementOf0(X42,X43)
      | sdtmndt0(sdtpldt0(X43,X42),X42) = X43 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).

cnf(c_0_29,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_30,hypothesis,
    aElementOf0(xx,xS),
    inference(split_conjunct,[status(thm)],[m__2256]) ).

fof(c_0_31,plain,
    ! [X48,X49] :
      ( ~ aElement0(X48)
      | ~ aSet0(X49)
      | ~ isFinite0(X49)
      | isFinite0(sdtpldt0(X49,X48)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFConsSet])])]) ).

fof(c_0_32,plain,
    ! [X26,X27,X28,X29,X30,X31] :
      ( ( aSet0(X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( aElement0(X29)
        | ~ aElementOf0(X29,X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( aElementOf0(X29,X26)
        | X29 = X27
        | ~ aElementOf0(X29,X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( ~ aElementOf0(X30,X26)
        | ~ aElement0(X30)
        | aElementOf0(X30,X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( X30 != X27
        | ~ aElement0(X30)
        | aElementOf0(X30,X28)
        | X28 != sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( ~ aElementOf0(esk3_3(X26,X27,X31),X26)
        | ~ aElement0(esk3_3(X26,X27,X31))
        | ~ aElementOf0(esk3_3(X26,X27,X31),X31)
        | ~ aSet0(X31)
        | X31 = sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( esk3_3(X26,X27,X31) != X27
        | ~ aElement0(esk3_3(X26,X27,X31))
        | ~ aElementOf0(esk3_3(X26,X27,X31),X31)
        | ~ aSet0(X31)
        | X31 = sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( aElement0(esk3_3(X26,X27,X31))
        | aElementOf0(esk3_3(X26,X27,X31),X31)
        | ~ aSet0(X31)
        | X31 = sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) )
      & ( aElementOf0(esk3_3(X26,X27,X31),X26)
        | esk3_3(X26,X27,X31) = X27
        | aElementOf0(esk3_3(X26,X27,X31),X31)
        | ~ aSet0(X31)
        | X31 = sdtpldt0(X26,X27)
        | ~ aSet0(X26)
        | ~ aElement0(X27) ) ),
    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)],[mDefCons])])])])])]) ).

cnf(c_0_33,plain,
    ( aElementOf0(X1,X3)
    | ~ aElementOf0(X1,X2)
    | ~ aSubsetOf0(X2,X3)
    | ~ aSet0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_34,hypothesis,
    aSubsetOf0(xQ,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_35,plain,
    ( aElementOf0(X1,X2)
    | ~ aElementOf0(X1,X3)
    | X3 != sdtmndt0(X2,X4)
    | ~ aSet0(X2)
    | ~ aElement0(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_36,plain,
    ( aSet0(X1)
    | X1 != sdtmndt0(X2,X3)
    | ~ aSet0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_37,plain,
    ( aElementOf0(X1,X2)
    | sdtmndt0(sdtpldt0(X2,X1),X1) = X2
    | ~ aElement0(X1)
    | ~ aSet0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_38,hypothesis,
    xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
    inference(split_conjunct,[status(thm)],[m__2357]) ).

cnf(c_0_39,hypothesis,
    aElement0(xx),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_26])]) ).

cnf(c_0_40,plain,
    ( isFinite0(sdtpldt0(X2,X1))
    | ~ aElement0(X1)
    | ~ aSet0(X2)
    | ~ isFinite0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

fof(c_0_41,plain,
    ! [X50,X51] :
      ( ~ aElement0(X50)
      | ~ aSet0(X51)
      | ~ isFinite0(X51)
      | isFinite0(sdtmndt0(X51,X50)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])]) ).

cnf(c_0_42,plain,
    ( aElementOf0(X1,X3)
    | X1 != X2
    | ~ aElement0(X1)
    | X3 != sdtpldt0(X4,X2)
    | ~ aSet0(X4)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_43,plain,
    ( aSet0(X1)
    | X1 != sdtpldt0(X2,X3)
    | ~ aSet0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_44,plain,
    ( aSubsetOf0(X2,X1)
    | ~ aElementOf0(esk2_2(X1,X2),X1)
    | ~ aSet0(X2)
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_45,hypothesis,
    ( aElementOf0(X1,xS)
    | ~ aElementOf0(X1,xQ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_26])]) ).

cnf(c_0_46,plain,
    ( aElementOf0(X1,X2)
    | ~ aElementOf0(X1,sdtmndt0(X2,X3))
    | ~ aElement0(X3)
    | ~ aSet0(X2) ),
    inference(er,[status(thm)],[c_0_35]) ).

cnf(c_0_47,plain,
    ( aElementOf0(esk2_2(X1,X2),X2)
    | aSubsetOf0(X2,X1)
    | ~ aSet0(X2)
    | ~ aSet0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_48,plain,
    ( aSet0(sdtmndt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aSet0(X1) ),
    inference(er,[status(thm)],[c_0_36]) ).

cnf(c_0_49,plain,
    ( aElementOf0(X1,X2)
    | X1 = X3
    | ~ aElementOf0(X1,X4)
    | X4 != sdtpldt0(X2,X3)
    | ~ aSet0(X2)
    | ~ aElement0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_50,hypothesis,
    ( sdtmndt0(xP,xx) = sdtmndt0(xQ,xy)
    | aElementOf0(xx,sdtmndt0(xQ,xy))
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).

cnf(c_0_51,hypothesis,
    aElement0(xy),
    inference(split_conjunct,[status(thm)],[m__2304]) ).

cnf(c_0_52,hypothesis,
    aSet0(xQ),
    inference(split_conjunct,[status(thm)],[m__2291]) ).

fof(c_0_53,hypothesis,
    ~ aElementOf0(xx,xQ),
    inference(fof_simplification,[status(thm)],[m__2323]) ).

cnf(c_0_54,hypothesis,
    ( isFinite0(xP)
    | ~ isFinite0(sdtmndt0(xQ,xy))
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_39])]) ).

cnf(c_0_55,plain,
    ( isFinite0(sdtmndt0(X2,X1))
    | ~ aElement0(X1)
    | ~ aSet0(X2)
    | ~ isFinite0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_56,hypothesis,
    isFinite0(xQ),
    inference(split_conjunct,[status(thm)],[m__2291]) ).

cnf(c_0_57,plain,
    ( aElementOf0(X1,sdtpldt0(X2,X1))
    | ~ aElement0(X1)
    | ~ aSet0(X2) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_42])]) ).

cnf(c_0_58,plain,
    ( aSet0(sdtpldt0(X1,X2))
    | ~ aElement0(X2)
    | ~ aSet0(X1) ),
    inference(er,[status(thm)],[c_0_43]) ).

cnf(c_0_59,hypothesis,
    ( aSubsetOf0(X1,xS)
    | ~ aElementOf0(esk2_2(xS,X1),xQ)
    | ~ aSet0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_26])]) ).

cnf(c_0_60,plain,
    ( aSubsetOf0(sdtmndt0(X1,X2),X3)
    | aElementOf0(esk2_2(X3,sdtmndt0(X1,X2)),X1)
    | ~ aElement0(X2)
    | ~ aSet0(X1)
    | ~ aSet0(X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).

cnf(c_0_61,plain,
    ( X1 = X2
    | aElementOf0(X1,X3)
    | ~ aElementOf0(X1,sdtpldt0(X3,X2))
    | ~ aElement0(X2)
    | ~ aSet0(X3) ),
    inference(er,[status(thm)],[c_0_49]) ).

fof(c_0_62,plain,
    ! [X77,X78] :
      ( ~ aSet0(X77)
      | ~ isFinite0(X77)
      | ~ aElementOf0(X78,X77)
      | szszuzczcdt0(sbrdtbr0(sdtmndt0(X77,X78))) = sbrdtbr0(X77) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])]) ).

cnf(c_0_63,hypothesis,
    ( sdtmndt0(xP,xx) = sdtmndt0(xQ,xy)
    | aElementOf0(xx,sdtmndt0(xQ,xy)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_48]),c_0_51]),c_0_52])]) ).

cnf(c_0_64,hypothesis,
    ~ aElementOf0(xx,xQ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_65,hypothesis,
    ( isFinite0(xP)
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_51]),c_0_52])]) ).

cnf(c_0_66,hypothesis,
    ( aElementOf0(xx,xP)
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_38]),c_0_39])]) ).

cnf(c_0_67,hypothesis,
    ( aSet0(xP)
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_38]),c_0_39])]) ).

cnf(c_0_68,hypothesis,
    ( aSubsetOf0(sdtmndt0(xQ,X1),xS)
    | ~ aElement0(X1)
    | ~ aSet0(sdtmndt0(xQ,X1)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_52]),c_0_26])]) ).

cnf(c_0_69,hypothesis,
    ( X1 = xx
    | aElementOf0(X1,sdtmndt0(xQ,xy))
    | ~ aElementOf0(X1,xP)
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_38]),c_0_39])]) ).

cnf(c_0_70,plain,
    ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
    | ~ aSet0(X1)
    | ~ isFinite0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_71,hypothesis,
    sdtmndt0(xP,xx) = sdtmndt0(xQ,xy),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_63]),c_0_51]),c_0_52])]),c_0_64]) ).

cnf(c_0_72,hypothesis,
    isFinite0(xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_48]),c_0_51]),c_0_52])]) ).

cnf(c_0_73,hypothesis,
    aElementOf0(xx,xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_48]),c_0_51]),c_0_52])]) ).

cnf(c_0_74,hypothesis,
    aSet0(xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_48]),c_0_51]),c_0_52])]) ).

cnf(c_0_75,hypothesis,
    ( aElementOf0(X1,xS)
    | ~ aElementOf0(X1,sdtmndt0(xQ,X2))
    | ~ aElement0(X2)
    | ~ aSet0(sdtmndt0(xQ,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_68]),c_0_26])]) ).

cnf(c_0_76,hypothesis,
    ( X1 = xx
    | aElementOf0(X1,sdtmndt0(xQ,xy))
    | ~ aElementOf0(X1,xP) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_48]),c_0_51]),c_0_52])]) ).

cnf(c_0_77,plain,
    ( aElementOf0(X1,X4)
    | ~ aSubsetOf0(X1,X2)
    | sbrdtbr0(X1) != X3
    | X4 != slbdtsldtrb0(X2,X3)
    | ~ aSet0(X2)
    | ~ aElementOf0(X3,szNzAzT0) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_78,hypothesis,
    szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_73]),c_0_74])]) ).

cnf(c_0_79,hypothesis,
    sbrdtbr0(xQ) = xk,
    inference(split_conjunct,[status(thm)],[m__2291]) ).

cnf(c_0_80,hypothesis,
    aElementOf0(xy,xQ),
    inference(split_conjunct,[status(thm)],[m__2304]) ).

cnf(c_0_81,hypothesis,
    ( X1 = xx
    | aElementOf0(X1,xS)
    | ~ aElementOf0(X1,xP)
    | ~ aSet0(sdtmndt0(xQ,xy)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_51])]) ).

fof(c_0_82,negated_conjecture,
    ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_83,plain,
    ( aElementOf0(X1,slbdtsldtrb0(X2,sbrdtbr0(X1)))
    | ~ aSubsetOf0(X1,X2)
    | ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
    | ~ aSet0(X2) ),
    inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_77])]) ).

cnf(c_0_84,hypothesis,
    sbrdtbr0(xP) = xk,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_78]),c_0_79]),c_0_56]),c_0_80]),c_0_52])]) ).

cnf(c_0_85,hypothesis,
    ( X1 = xx
    | aElementOf0(X1,xS)
    | ~ aElementOf0(X1,xP) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_48]),c_0_51]),c_0_52])]) ).

cnf(c_0_86,negated_conjecture,
    ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    inference(split_conjunct,[status(thm)],[c_0_82]) ).

cnf(c_0_87,hypothesis,
    ( aElementOf0(xP,slbdtsldtrb0(X1,xk))
    | ~ aSubsetOf0(xP,X1)
    | ~ aSet0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_25])]) ).

cnf(c_0_88,hypothesis,
    ( esk2_2(X1,xP) = xx
    | aSubsetOf0(xP,X1)
    | aElementOf0(esk2_2(X1,xP),xS)
    | ~ aSet0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_47]),c_0_74])]) ).

cnf(c_0_89,negated_conjecture,
    ~ aSubsetOf0(xP,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_26])]) ).

cnf(c_0_90,hypothesis,
    esk2_2(xS,xP) = xx,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_88]),c_0_74]),c_0_26])]),c_0_89]) ).

cnf(c_0_91,hypothesis,
    $false,
    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_44,c_0_90]),c_0_30]),c_0_74]),c_0_26])]),c_0_89]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM554+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n020.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   : Fri Aug 25 11:12:45 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.82/0.95  % Version  : CSE_E---1.5
% 0.82/0.95  % Problem  : theBenchmark.p
% 0.82/0.95  % Proof found
% 0.82/0.95  % SZS status Theorem for theBenchmark.p
% 0.82/0.95  % SZS output start Proof
% See solution above
% 0.92/0.97  % Total time : 0.396000 s
% 0.92/0.97  % SZS output end Proof
% 0.92/0.97  % Total time : 0.400000 s
%------------------------------------------------------------------------------