TSTP Solution File: NUM556+3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM556+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n012.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 : Tue May 21 01:14:40 EDT 2024

% Result   : Theorem 0.14s 0.46s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   73 (  23 unt;   0 def)
%            Number of atoms       :  410 (  85 equ)
%            Maximal formula atoms :   67 (   5 avg)
%            Number of connectives :  504 ( 167   ~; 167   |; 129   &)
%                                         (  10 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  11 con; 0-3 aty)
%            Number of variables   :   95 (   0 sgn  69   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(m__2202_02,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & xk != sz00 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).

fof(m__2357,hypothesis,
    ( aSet0(sdtmndt0(xQ,xy))
    & ! [X1] :
        ( aElementOf0(X1,sdtmndt0(xQ,xy))
      <=> ( aElement0(X1)
          & aElementOf0(X1,xQ)
          & X1 != xy ) )
    & aSet0(xP)
    & ! [X1] :
        ( aElementOf0(X1,xP)
      <=> ( aElement0(X1)
          & ( aElementOf0(X1,sdtmndt0(xQ,xy))
            | X1 = xx ) ) )
    & xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).

fof(mEOfElem,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( aElementOf0(X2,X1)
         => aElement0(X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

fof(mDiffCons,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aSet0(X2) )
     => ( ~ aElementOf0(X1,X2)
       => sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).

fof(m__2411,hypothesis,
    ( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
    & aSet0(sdtmndt0(xQ,xy))
    & ! [X1] :
        ( aElementOf0(X1,sdtmndt0(xQ,xy))
      <=> ( aElement0(X1)
          & aElementOf0(X1,xQ)
          & X1 != xy ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2411) ).

fof(mFConsSet,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ! [X2] :
          ( ( aSet0(X2)
            & isFinite0(X2) )
         => isFinite0(sdtpldt0(X2,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).

fof(m__2256,hypothesis,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).

fof(mFDiffSet,axiom,
    ! [X1] :
      ( aElement0(X1)
     => ! [X2] :
          ( ( aSet0(X2)
            & isFinite0(X2) )
         => isFinite0(sdtmndt0(X2,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).

fof(m__2270,hypothesis,
    ( aSet0(xQ)
    & ! [X1] :
        ( aElementOf0(X1,xQ)
       => aElementOf0(X1,xS) )
    & aSubsetOf0(xQ,xS)
    & sbrdtbr0(xQ) = xk
    & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).

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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

fof(mCardDiff,axiom,
    ! [X1] :
      ( aSet0(X1)
     => ! [X2] :
          ( ( isFinite0(X1)
            & aElementOf0(X2,X1) )
         => szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).

fof(m__2291,hypothesis,
    ( aSet0(xQ)
    & isFinite0(xQ)
    & sbrdtbr0(xQ) = xk ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).

fof(m__2304,hypothesis,
    ( aElement0(xy)
    & aElementOf0(xy,xQ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).

fof(m__,conjecture,
    ( ( ! [X1] :
          ( aElementOf0(X1,xP)
         => aElementOf0(X1,xS) )
      | aSubsetOf0(xP,xS) )
    & sbrdtbr0(xP) = xk ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__2227,hypothesis,
    ( aSet0(slbdtsldtrb0(xS,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
         => ( aSet0(X1)
            & ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,xS) )
            & aSubsetOf0(X1,xS)
            & sbrdtbr0(X1) = xk ) )
        & ( ( ( ( aSet0(X1)
                & ! [X2] :
                    ( aElementOf0(X2,X1)
                   => aElementOf0(X2,xS) ) )
              | aSubsetOf0(X1,xS) )
            & sbrdtbr0(X1) = xk )
         => aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [X1] :
        ( ( aElementOf0(X1,slbdtsldtrb0(xT,xk))
         => ( aSet0(X1)
            & ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,xT) )
            & aSubsetOf0(X1,xT)
            & sbrdtbr0(X1) = xk ) )
        & ( ( ( ( aSet0(X1)
                & ! [X2] :
                    ( aElementOf0(X2,X1)
                   => aElementOf0(X2,xT) ) )
              | aSubsetOf0(X1,xT) )
            & sbrdtbr0(X1) = xk )
         => aElementOf0(X1,slbdtsldtrb0(xT,xk)) ) )
    & ! [X1] :
        ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
       => aElementOf0(X1,slbdtsldtrb0(xT,xk)) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ~ ( ! [X1] :
            ( ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
             => ( aSet0(X1)
                & ! [X2] :
                    ( aElementOf0(X2,X1)
                   => aElementOf0(X2,xS) )
                & aSubsetOf0(X1,xS)
                & sbrdtbr0(X1) = xk ) )
            & ( ( ( ( aSet0(X1)
                    & ! [X2] :
                        ( aElementOf0(X2,X1)
                       => aElementOf0(X2,xS) ) )
                  | aSubsetOf0(X1,xS) )
                & sbrdtbr0(X1) = xk )
             => aElementOf0(X1,slbdtsldtrb0(xS,xk)) ) )
       => ( ~ ? [X1] : aElementOf0(X1,slbdtsldtrb0(xS,xk))
          | slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).

fof(c_0_15,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & xk != sz00 ),
    inference(fof_simplification,[status(thm)],[m__2202_02]) ).

fof(c_0_16,hypothesis,
    ( aSet0(sdtmndt0(xQ,xy))
    & ! [X1] :
        ( aElementOf0(X1,sdtmndt0(xQ,xy))
      <=> ( aElement0(X1)
          & aElementOf0(X1,xQ)
          & X1 != xy ) )
    & aSet0(xP)
    & ! [X1] :
        ( aElementOf0(X1,xP)
      <=> ( aElement0(X1)
          & ( aElementOf0(X1,sdtmndt0(xQ,xy))
            | X1 = xx ) ) )
    & xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
    inference(fof_simplification,[status(thm)],[m__2357]) ).

fof(c_0_17,plain,
    ! [X7,X8] :
      ( ~ aSet0(X7)
      | ~ aElementOf0(X8,X7)
      | aElement0(X8) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])])]) ).

fof(c_0_18,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & xk != sz00 ),
    inference(fof_nnf,[status(thm)],[c_0_15]) ).

fof(c_0_19,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_20,hypothesis,
    ( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
    & aSet0(sdtmndt0(xQ,xy))
    & ! [X1] :
        ( aElementOf0(X1,sdtmndt0(xQ,xy))
      <=> ( aElement0(X1)
          & aElementOf0(X1,xQ)
          & X1 != xy ) ) ),
    inference(fof_simplification,[status(thm)],[m__2411]) ).

fof(c_0_21,plain,
    ! [X52,X53] :
      ( ~ aElement0(X52)
      | ~ aSet0(X53)
      | ~ isFinite0(X53)
      | isFinite0(sdtpldt0(X53,X52)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFConsSet])])])]) ).

fof(c_0_22,hypothesis,
    ! [X146,X147] :
      ( aSet0(sdtmndt0(xQ,xy))
      & ( aElement0(X146)
        | ~ aElementOf0(X146,sdtmndt0(xQ,xy)) )
      & ( aElementOf0(X146,xQ)
        | ~ aElementOf0(X146,sdtmndt0(xQ,xy)) )
      & ( X146 != xy
        | ~ aElementOf0(X146,sdtmndt0(xQ,xy)) )
      & ( ~ aElement0(X146)
        | ~ aElementOf0(X146,xQ)
        | X146 = xy
        | aElementOf0(X146,sdtmndt0(xQ,xy)) )
      & aSet0(xP)
      & ( aElement0(X147)
        | ~ aElementOf0(X147,xP) )
      & ( aElementOf0(X147,sdtmndt0(xQ,xy))
        | X147 = xx
        | ~ aElementOf0(X147,xP) )
      & ( ~ aElementOf0(X147,sdtmndt0(xQ,xy))
        | ~ aElement0(X147)
        | aElementOf0(X147,xP) )
      & ( X147 != xx
        | ~ aElement0(X147)
        | aElementOf0(X147,xP) )
      & xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])]) ).

cnf(c_0_23,plain,
    ( aElement0(X2)
    | ~ aSet0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,hypothesis,
    aElementOf0(xx,xS),
    inference(split_conjunct,[status(thm)],[m__2256]) ).

cnf(c_0_25,hypothesis,
    aSet0(xS),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_26,plain,
    ! [X46,X47] :
      ( ~ aElement0(X46)
      | ~ aSet0(X47)
      | aElementOf0(X46,X47)
      | sdtmndt0(sdtpldt0(X47,X46),X46) = X47 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).

fof(c_0_27,hypothesis,
    ! [X148] :
      ( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
      & aSet0(sdtmndt0(xQ,xy))
      & ( aElement0(X148)
        | ~ aElementOf0(X148,sdtmndt0(xQ,xy)) )
      & ( aElementOf0(X148,xQ)
        | ~ aElementOf0(X148,sdtmndt0(xQ,xy)) )
      & ( X148 != xy
        | ~ aElementOf0(X148,sdtmndt0(xQ,xy)) )
      & ( ~ aElement0(X148)
        | ~ aElementOf0(X148,xQ)
        | X148 = xy
        | aElementOf0(X148,sdtmndt0(xQ,xy)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])]) ).

cnf(c_0_28,plain,
    ( isFinite0(sdtpldt0(X2,X1))
    | ~ aElement0(X1)
    | ~ aSet0(X2)
    | ~ isFinite0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_29,hypothesis,
    xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_30,hypothesis,
    aElement0(xx),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_31,hypothesis,
    aSet0(sdtmndt0(xQ,xy)),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_32,plain,
    ! [X54,X55] :
      ( ~ aElement0(X54)
      | ~ aSet0(X55)
      | ~ isFinite0(X55)
      | isFinite0(sdtmndt0(X55,X54)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])])]) ).

fof(c_0_33,hypothesis,
    ! [X145] :
      ( aSet0(xQ)
      & ( ~ aElementOf0(X145,xQ)
        | aElementOf0(X145,xS) )
      & aSubsetOf0(xQ,xS)
      & sbrdtbr0(xQ) = xk
      & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2270])])])]) ).

cnf(c_0_34,hypothesis,
    ( aElementOf0(X1,xP)
    | X1 != xx
    | ~ aElement0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

fof(c_0_35,plain,
    ! [X1,X2] :
      ( ( aSet0(X1)
        & aElement0(X2) )
     => ! [X3] :
          ( X3 = sdtmndt0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aElement0(X4)
                  & aElementOf0(X4,X1)
                  & X4 != X2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[mDefDiff]) ).

fof(c_0_36,plain,
    ! [X85,X86] :
      ( ~ aSet0(X85)
      | ~ isFinite0(X85)
      | ~ aElementOf0(X86,X85)
      | szszuzczcdt0(sbrdtbr0(sdtmndt0(X85,X86))) = sbrdtbr0(X85) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])])]) ).

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_26]) ).

cnf(c_0_38,hypothesis,
    ~ aElementOf0(xx,sdtmndt0(xQ,xy)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_39,hypothesis,
    ( isFinite0(xP)
    | ~ isFinite0(sdtmndt0(xQ,xy)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).

cnf(c_0_40,plain,
    ( isFinite0(sdtmndt0(X2,X1))
    | ~ aElement0(X1)
    | ~ aSet0(X2)
    | ~ isFinite0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_41,hypothesis,
    isFinite0(xQ),
    inference(split_conjunct,[status(thm)],[m__2291]) ).

cnf(c_0_42,hypothesis,
    aElement0(xy),
    inference(split_conjunct,[status(thm)],[m__2304]) ).

cnf(c_0_43,hypothesis,
    aSet0(xQ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_44,hypothesis,
    ( aElementOf0(xx,xP)
    | ~ aElement0(xx) ),
    inference(er,[status(thm)],[c_0_34]) ).

fof(c_0_45,plain,
    ! [X37,X38,X39,X40,X41,X42] :
      ( ( aSet0(X39)
        | X39 != sdtmndt0(X37,X38)
        | ~ aSet0(X37)
        | ~ aElement0(X38) )
      & ( aElement0(X40)
        | ~ aElementOf0(X40,X39)
        | X39 != sdtmndt0(X37,X38)
        | ~ aSet0(X37)
        | ~ aElement0(X38) )
      & ( aElementOf0(X40,X37)
        | ~ aElementOf0(X40,X39)
        | X39 != sdtmndt0(X37,X38)
        | ~ aSet0(X37)
        | ~ aElement0(X38) )
      & ( X40 != X38
        | ~ aElementOf0(X40,X39)
        | X39 != sdtmndt0(X37,X38)
        | ~ aSet0(X37)
        | ~ aElement0(X38) )
      & ( ~ aElement0(X41)
        | ~ aElementOf0(X41,X37)
        | X41 = X38
        | aElementOf0(X41,X39)
        | X39 != sdtmndt0(X37,X38)
        | ~ aSet0(X37)
        | ~ aElement0(X38) )
      & ( ~ aElementOf0(esk4_3(X37,X38,X42),X42)
        | ~ aElement0(esk4_3(X37,X38,X42))
        | ~ aElementOf0(esk4_3(X37,X38,X42),X37)
        | esk4_3(X37,X38,X42) = X38
        | ~ aSet0(X42)
        | X42 = sdtmndt0(X37,X38)
        | ~ aSet0(X37)
        | ~ aElement0(X38) )
      & ( aElement0(esk4_3(X37,X38,X42))
        | aElementOf0(esk4_3(X37,X38,X42),X42)
        | ~ aSet0(X42)
        | X42 = sdtmndt0(X37,X38)
        | ~ aSet0(X37)
        | ~ aElement0(X38) )
      & ( aElementOf0(esk4_3(X37,X38,X42),X37)
        | aElementOf0(esk4_3(X37,X38,X42),X42)
        | ~ aSet0(X42)
        | X42 = sdtmndt0(X37,X38)
        | ~ aSet0(X37)
        | ~ aElement0(X38) )
      & ( esk4_3(X37,X38,X42) != X38
        | aElementOf0(esk4_3(X37,X38,X42),X42)
        | ~ aSet0(X42)
        | X42 = sdtmndt0(X37,X38)
        | ~ aSet0(X37)
        | ~ aElement0(X38) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[c_0_35])])])])])])]) ).

fof(c_0_46,negated_conjecture,
    ~ ( ( ! [X1] :
            ( aElementOf0(X1,xP)
           => aElementOf0(X1,xS) )
        | aSubsetOf0(xP,xS) )
      & sbrdtbr0(xP) = xk ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_47,plain,
    ( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
    | ~ aSet0(X1)
    | ~ isFinite0(X1)
    | ~ aElementOf0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_48,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_37,c_0_29]),c_0_30]),c_0_31])]),c_0_38]) ).

cnf(c_0_49,hypothesis,
    isFinite0(xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42]),c_0_43])]) ).

cnf(c_0_50,hypothesis,
    aElementOf0(xx,xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_30])]) ).

cnf(c_0_51,hypothesis,
    aSet0(xP),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_52,plain,
    ( aElementOf0(X1,X2)
    | ~ aElementOf0(X1,X3)
    | X3 != sdtmndt0(X2,X4)
    | ~ aSet0(X2)
    | ~ aElement0(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

fof(c_0_53,negated_conjecture,
    ( ( aElementOf0(esk16_0,xP)
      | sbrdtbr0(xP) != xk )
    & ( ~ aElementOf0(esk16_0,xS)
      | sbrdtbr0(xP) != xk )
    & ( ~ aSubsetOf0(xP,xS)
      | sbrdtbr0(xP) != xk ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])])]) ).

cnf(c_0_54,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_47,c_0_48]),c_0_49]),c_0_50]),c_0_51])]) ).

cnf(c_0_55,hypothesis,
    sbrdtbr0(xQ) = xk,
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_56,hypothesis,
    aElementOf0(xy,xQ),
    inference(split_conjunct,[status(thm)],[m__2304]) ).

fof(c_0_57,hypothesis,
    ! [X131,X132,X133,X135,X136,X137,X139,X140,X141,X142] :
      ( aSet0(slbdtsldtrb0(xS,xk))
      & ( aSet0(X131)
        | ~ aElementOf0(X131,slbdtsldtrb0(xS,xk)) )
      & ( ~ aElementOf0(X132,X131)
        | aElementOf0(X132,xS)
        | ~ aElementOf0(X131,slbdtsldtrb0(xS,xk)) )
      & ( aSubsetOf0(X131,xS)
        | ~ aElementOf0(X131,slbdtsldtrb0(xS,xk)) )
      & ( sbrdtbr0(X131) = xk
        | ~ aElementOf0(X131,slbdtsldtrb0(xS,xk)) )
      & ( aElementOf0(esk12_1(X133),X133)
        | ~ aSet0(X133)
        | sbrdtbr0(X133) != xk
        | aElementOf0(X133,slbdtsldtrb0(xS,xk)) )
      & ( ~ aElementOf0(esk12_1(X133),xS)
        | ~ aSet0(X133)
        | sbrdtbr0(X133) != xk
        | aElementOf0(X133,slbdtsldtrb0(xS,xk)) )
      & ( ~ aSubsetOf0(X133,xS)
        | sbrdtbr0(X133) != xk
        | aElementOf0(X133,slbdtsldtrb0(xS,xk)) )
      & aSet0(slbdtsldtrb0(xT,xk))
      & ( aSet0(X135)
        | ~ aElementOf0(X135,slbdtsldtrb0(xT,xk)) )
      & ( ~ aElementOf0(X136,X135)
        | aElementOf0(X136,xT)
        | ~ aElementOf0(X135,slbdtsldtrb0(xT,xk)) )
      & ( aSubsetOf0(X135,xT)
        | ~ aElementOf0(X135,slbdtsldtrb0(xT,xk)) )
      & ( sbrdtbr0(X135) = xk
        | ~ aElementOf0(X135,slbdtsldtrb0(xT,xk)) )
      & ( aElementOf0(esk13_1(X137),X137)
        | ~ aSet0(X137)
        | sbrdtbr0(X137) != xk
        | aElementOf0(X137,slbdtsldtrb0(xT,xk)) )
      & ( ~ aElementOf0(esk13_1(X137),xT)
        | ~ aSet0(X137)
        | sbrdtbr0(X137) != xk
        | aElementOf0(X137,slbdtsldtrb0(xT,xk)) )
      & ( ~ aSubsetOf0(X137,xT)
        | sbrdtbr0(X137) != xk
        | aElementOf0(X137,slbdtsldtrb0(xT,xk)) )
      & ( ~ aElementOf0(X139,slbdtsldtrb0(xS,xk))
        | aElementOf0(X139,slbdtsldtrb0(xT,xk)) )
      & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
      & ( aSet0(X140)
        | ~ aElementOf0(X140,slbdtsldtrb0(xS,xk)) )
      & ( ~ aElementOf0(X141,X140)
        | aElementOf0(X141,xS)
        | ~ aElementOf0(X140,slbdtsldtrb0(xS,xk)) )
      & ( aSubsetOf0(X140,xS)
        | ~ aElementOf0(X140,slbdtsldtrb0(xS,xk)) )
      & ( sbrdtbr0(X140) = xk
        | ~ aElementOf0(X140,slbdtsldtrb0(xS,xk)) )
      & ( aElementOf0(esk14_1(X142),X142)
        | ~ aSet0(X142)
        | sbrdtbr0(X142) != xk
        | aElementOf0(X142,slbdtsldtrb0(xS,xk)) )
      & ( ~ aElementOf0(esk14_1(X142),xS)
        | ~ aSet0(X142)
        | sbrdtbr0(X142) != xk
        | aElementOf0(X142,slbdtsldtrb0(xS,xk)) )
      & ( ~ aSubsetOf0(X142,xS)
        | sbrdtbr0(X142) != xk
        | aElementOf0(X142,slbdtsldtrb0(xS,xk)) )
      & aElementOf0(esk15_0,slbdtsldtrb0(xS,xk))
      & slbdtsldtrb0(xS,xk) != slcrc0 ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[m__2227])])])])])])]) ).

cnf(c_0_58,plain,
    ( aElementOf0(X1,X2)
    | ~ aElementOf0(X1,sdtmndt0(X2,X3))
    | ~ aElement0(X3)
    | ~ aSet0(X2) ),
    inference(er,[status(thm)],[c_0_52]) ).

cnf(c_0_59,hypothesis,
    ( aElementOf0(X1,sdtmndt0(xQ,xy))
    | X1 = xx
    | ~ aElementOf0(X1,xP) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_60,negated_conjecture,
    ( aElementOf0(esk16_0,xP)
    | sbrdtbr0(xP) != xk ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_61,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_47,c_0_54]),c_0_55]),c_0_41]),c_0_56]),c_0_43])]) ).

cnf(c_0_62,hypothesis,
    ( aElementOf0(X1,xS)
    | ~ aElementOf0(X1,X2)
    | ~ aElementOf0(X2,slbdtsldtrb0(xS,xk)) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_63,hypothesis,
    ( aElementOf0(X1,slbdtsldtrb0(xS,xk))
    | ~ aSubsetOf0(X1,xS)
    | sbrdtbr0(X1) != xk ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

cnf(c_0_64,hypothesis,
    ( X1 = xx
    | aElementOf0(X1,xQ)
    | ~ aElementOf0(X1,xP) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_42]),c_0_43])]) ).

cnf(c_0_65,negated_conjecture,
    aElementOf0(esk16_0,xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).

cnf(c_0_66,negated_conjecture,
    ( ~ aElementOf0(esk16_0,xS)
    | sbrdtbr0(xP) != xk ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_67,hypothesis,
    ( aElementOf0(X1,xS)
    | sbrdtbr0(X2) != xk
    | ~ aSubsetOf0(X2,xS)
    | ~ aElementOf0(X1,X2) ),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_68,hypothesis,
    ( esk16_0 = xx
    | aElementOf0(esk16_0,xQ) ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_69,hypothesis,
    aSubsetOf0(xQ,xS),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_70,negated_conjecture,
    ~ aElementOf0(esk16_0,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_61])]) ).

cnf(c_0_71,hypothesis,
    esk16_0 = xx,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_55]),c_0_69])]),c_0_70]) ).

cnf(c_0_72,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71]),c_0_24])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : NUM556+3 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.10  % Command    : run_E %s %d THM
% 0.09/0.30  % Computer : n012.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Mon May 20 04:36:52 EDT 2024
% 0.09/0.30  % CPUTime    : 
% 0.14/0.40  Running first-order theorem proving
% 0.14/0.40  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46  # Version: 3.1.0
% 0.14/0.46  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46  # Starting new_bool_3 with 300s (1) cores
% 0.14/0.46  # Starting new_bool_1 with 300s (1) cores
% 0.14/0.46  # Starting sh5l with 300s (1) cores
% 0.14/0.46  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 17001 completed with status 0
% 0.14/0.46  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.14/0.46  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46  # No SInE strategy applied
% 0.14/0.46  # Search class: FGHSF-FSLM31-MFFFFFNN
% 0.14/0.46  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.46  # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 811s (1) cores
% 0.14/0.46  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.46  # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.14/0.46  # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 0.14/0.46  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 136s (1) cores
% 0.14/0.46  # SAT001_MinMin_p005000_rr_RG with pid 17010 completed with status 0
% 0.14/0.46  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.14/0.46  # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.14/0.46  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.14/0.46  # No SInE strategy applied
% 0.14/0.46  # Search class: FGHSF-FSLM31-MFFFFFNN
% 0.14/0.46  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.46  # Starting G-E--_110_C45_F1_PI_AE_Q4_CS_SP_PS_S4S with 811s (1) cores
% 0.14/0.46  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.14/0.46  # Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.14/0.46  # Preprocessing time       : 0.003 s
% 0.14/0.46  # Presaturation interreduction done
% 0.14/0.46  
% 0.14/0.46  # Proof found!
% 0.14/0.46  # SZS status Theorem
% 0.14/0.46  # SZS output start CNFRefutation
% See solution above
% 0.14/0.46  # Parsed axioms                        : 72
% 0.14/0.46  # Removed by relevancy pruning/SinE    : 0
% 0.14/0.46  # Initial clauses                      : 174
% 0.14/0.46  # Removed in clause preprocessing      : 6
% 0.14/0.46  # Initial clauses in saturation        : 168
% 0.14/0.46  # Processed clauses                    : 591
% 0.14/0.46  # ...of these trivial                  : 6
% 0.14/0.46  # ...subsumed                          : 104
% 0.14/0.46  # ...remaining for further processing  : 481
% 0.14/0.46  # Other redundant clauses eliminated   : 47
% 0.14/0.46  # Clauses deleted for lack of memory   : 0
% 0.14/0.46  # Backward-subsumed                    : 5
% 0.14/0.46  # Backward-rewritten                   : 18
% 0.14/0.46  # Generated clauses                    : 842
% 0.14/0.46  # ...of the previous two non-redundant : 705
% 0.14/0.46  # ...aggressively subsumed             : 0
% 0.14/0.46  # Contextual simplify-reflections      : 25
% 0.14/0.46  # Paramodulations                      : 797
% 0.14/0.46  # Factorizations                       : 0
% 0.14/0.46  # NegExts                              : 0
% 0.14/0.46  # Equation resolutions                 : 48
% 0.14/0.46  # Disequality decompositions           : 0
% 0.14/0.46  # Total rewrite steps                  : 636
% 0.14/0.46  # ...of those cached                   : 585
% 0.14/0.46  # Propositional unsat checks           : 0
% 0.14/0.46  #    Propositional check models        : 0
% 0.14/0.46  #    Propositional check unsatisfiable : 0
% 0.14/0.46  #    Propositional clauses             : 0
% 0.14/0.46  #    Propositional clauses after purity: 0
% 0.14/0.46  #    Propositional unsat core size     : 0
% 0.14/0.46  #    Propositional preprocessing time  : 0.000
% 0.14/0.46  #    Propositional encoding time       : 0.000
% 0.14/0.46  #    Propositional solver time         : 0.000
% 0.14/0.46  #    Success case prop preproc time    : 0.000
% 0.14/0.46  #    Success case prop encoding time   : 0.000
% 0.14/0.46  #    Success case prop solver time     : 0.000
% 0.14/0.46  # Current number of processed clauses  : 273
% 0.14/0.46  #    Positive orientable unit clauses  : 50
% 0.14/0.46  #    Positive unorientable unit clauses: 0
% 0.14/0.46  #    Negative unit clauses             : 13
% 0.14/0.46  #    Non-unit-clauses                  : 210
% 0.14/0.46  # Current number of unprocessed clauses: 434
% 0.14/0.46  # ...number of literals in the above   : 1870
% 0.14/0.46  # Current number of archived formulas  : 0
% 0.14/0.46  # Current number of archived clauses   : 178
% 0.14/0.46  # Clause-clause subsumption calls (NU) : 7271
% 0.14/0.46  # Rec. Clause-clause subsumption calls : 3283
% 0.14/0.46  # Non-unit clause-clause subsumptions  : 85
% 0.14/0.46  # Unit Clause-clause subsumption calls : 1163
% 0.14/0.46  # Rewrite failures with RHS unbound    : 0
% 0.14/0.46  # BW rewrite match attempts            : 6
% 0.14/0.46  # BW rewrite match successes           : 5
% 0.14/0.46  # Condensation attempts                : 0
% 0.14/0.46  # Condensation successes               : 0
% 0.14/0.46  # Termbank termtop insertions          : 25620
% 0.14/0.46  # Search garbage collected termcells   : 2906
% 0.14/0.46  
% 0.14/0.46  # -------------------------------------------------
% 0.14/0.46  # User time                : 0.045 s
% 0.14/0.46  # System time              : 0.005 s
% 0.14/0.46  # Total time               : 0.050 s
% 0.14/0.46  # Maximum resident set size: 2328 pages
% 0.14/0.46  
% 0.14/0.46  # -------------------------------------------------
% 0.14/0.46  # User time                : 0.201 s
% 0.14/0.46  # System time              : 0.015 s
% 0.14/0.46  # Total time               : 0.215 s
% 0.14/0.46  # Maximum resident set size: 1780 pages
% 0.14/0.46  % E---3.1 exiting
% 0.14/0.46  % E exiting
%------------------------------------------------------------------------------