TSTP Solution File: NUM579+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM579+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n025.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 Aug 22 10:52:12 EDT 2023

% Result   : Theorem 91.41s 69.65s
% Output   : CNFRefutation 91.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   85
% Syntax   : Number of formulae    :  151 (  36 unt;  73 typ;   1 def)
%            Number of atoms       :  218 (  21 equ)
%            Maximal formula atoms :   28 (   2 avg)
%            Number of connectives :  216 (  76   ~;  68   |;  39   &)
%                                         (   5 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  129 (  61   >;  68   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   64 (  64 usr;  12 con; 0-4 aty)
%            Number of variables   :   58 (;  58   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aFunction0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > sdtlpdtrp0 > sdtlcdtrc0 > sdtlbdtrb0 > sdtexdt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > szDzozmdt0 > szDzizrdt0 > slbdtrb0 > sbrdtbr0 > xk > xc > xT > xS > xN > xK > szNzAzT0 > sz00 > slcrc0 > #skF_41 > #skF_7 > #skF_11 > #skF_17 > #skF_31 > #skF_33 > #skF_6 > #skF_1 > #skF_18 > #skF_37 > #skF_40 > #skF_38 > #skF_4 > #skF_29 > #skF_12 > #skF_30 > #skF_32 > #skF_23 > #skF_39 > #skF_35 > #skF_5 > #skF_19 > #skF_10 > #skF_8 > #skF_20 > #skF_28 > #skF_26 > #skF_24 > #skF_34 > #skF_15 > #skF_13 > #skF_14 > #skF_25 > #skF_3 > #skF_2 > #skF_27 > #skF_36 > #skF_21 > #skF_9 > #skF_22 > #skF_16

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(xk,type,
    xk: $i ).

tff('#skF_41',type,
    '#skF_41': $i ).

tff('#skF_7',type,
    '#skF_7': $i > $i ).

tff('#skF_11',type,
    '#skF_11': ( $i * $i ) > $i ).

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

tff('#skF_17',type,
    '#skF_17': ( $i * $i * $i ) > $i ).

tff('#skF_31',type,
    '#skF_31': ( $i * $i * $i ) > $i ).

tff('#skF_33',type,
    '#skF_33': ( $i * $i * $i ) > $i ).

tff(aSet0,type,
    aSet0: $i > $o ).

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

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

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

tff('#skF_6',type,
    '#skF_6': ( $i * $i * $i ) > $i ).

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

tff('#skF_1',type,
    '#skF_1': $i > $i ).

tff('#skF_18',type,
    '#skF_18': ( $i * $i * $i ) > $i ).

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

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

tff('#skF_37',type,
    '#skF_37': $i > $i ).

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

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

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

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

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

tff('#skF_40',type,
    '#skF_40': $i ).

tff('#skF_38',type,
    '#skF_38': ( $i * $i ) > $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

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

tff('#skF_29',type,
    '#skF_29': ( $i * $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i ) > $i ).

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

tff('#skF_30',type,
    '#skF_30': ( $i * $i * $i ) > $i ).

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

tff('#skF_32',type,
    '#skF_32': ( $i * $i * $i * $i ) > $i ).

tff('#skF_23',type,
    '#skF_23': ( $i * $i * $i ) > $i ).

tff('#skF_39',type,
    '#skF_39': $i ).

tff('#skF_35',type,
    '#skF_35': ( $i * $i * $i ) > $i ).

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

tff('#skF_5',type,
    '#skF_5': ( $i * $i * $i ) > $i ).

tff('#skF_19',type,
    '#skF_19': ( $i * $i * $i ) > $i ).

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

tff('#skF_10',type,
    '#skF_10': ( $i * $i ) > $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

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

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

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

tff('#skF_20',type,
    '#skF_20': ( $i * $i * $i ) > $i ).

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

tff('#skF_28',type,
    '#skF_28': ( $i * $i ) > $i ).

tff('#skF_26',type,
    '#skF_26': $i > $i ).

tff('#skF_24',type,
    '#skF_24': ( $i * $i ) > $i ).

tff('#skF_34',type,
    '#skF_34': ( $i * $i * $i ) > $i ).

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i ) > $i ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i * $i ) > $i ).

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

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

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

tff('#skF_25',type,
    '#skF_25': ( $i * $i ) > $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i * $i ) > $i ).

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

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

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

tff('#skF_27',type,
    '#skF_27': $i > $i ).

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

tff('#skF_36',type,
    '#skF_36': ( $i * $i * $i * $i ) > $i ).

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

tff('#skF_21',type,
    '#skF_21': ( $i * $i * $i ) > $i ).

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

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

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

tff('#skF_22',type,
    '#skF_22': ( $i * $i * $i * $i ) > $i ).

tff('#skF_16',type,
    '#skF_16': ( $i * $i * $i ) > $i ).

tff(f_988,negated_conjecture,
    ~ ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ! [W1] :
            ( ( aSet0(W1)
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2] :
                  ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W2] :
                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ! [W2] :
                  ( aElementOf0(W2,W1)
                 => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ( sbrdtbr0(W1) = xk )
              & aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
           => ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2] :
                    ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
             => ( ( aSet0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W2] :
                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & ( aElementOf0(W2,W1)
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )
               => ( ( ( ! [W2] :
                          ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                         => aElementOf0(W2,xS) )
                      | aSubsetOf0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))),xS) )
                    & ( sbrdtbr0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) = xK ) )
                  | aElementOf0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))),slbdtsldtrb0(xS,xK)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_252,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => sdtlseqdt0(sz00,W0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).

tff(f_824,hypothesis,
    ( aElementOf0(xk,szNzAzT0)
    & ( szszuzczcdt0(xk) = xK ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).

tff(f_324,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
      <=> isFinite0(W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).

tff(f_886,hypothesis,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aSet0(sdtlpdtrp0(xN,W0))
        & ! [W1] :
            ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
           => aElementOf0(W1,szNzAzT0) )
        & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).

tff(f_39,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).

tff(f_342,axiom,
    ! [W0] :
      ( ( aSet0(W0)
        & isFinite0(W0) )
     => ! [W1] :
          ( aElement0(W1)
         => ( ~ aElementOf0(W1,W0)
           => ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).

tff(f_674,hypothesis,
    ( aSet0(xS)
    & ! [W0] :
        ( aElementOf0(W0,xS)
       => aElementOf0(W0,szNzAzT0) )
    & aSubsetOf0(xS,szNzAzT0)
    & isCountable0(xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).

tff(f_212,axiom,
    aElementOf0(sz00,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).

tff(f_873,hypothesis,
    ( aFunction0(xN)
    & ( szDzozmdt0(xN) = szNzAzT0 )
    & ( sdtlpdtrp0(xN,sz00) = xS )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => aElementOf0(W1,szNzAzT0) ) )
              | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
            & isCountable0(sdtlpdtrp0(xN,W0)) )
         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            & ! [W1] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
               => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).

tff(f_899,hypothesis,
    ! [W0,W1] :
      ( ( aElementOf0(W0,szNzAzT0)
        & aElementOf0(W1,szNzAzT0) )
     => ( sdtlseqdt0(W1,W0)
       => ( ! [W2] :
              ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
             => aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
          & aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).

tff(f_84,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
               => aElementOf0(W2,W0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).

tff(c_8442,plain,
    aElementOf0('#skF_39',szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_126,plain,
    ! [W0_80] :
      ( sdtlseqdt0(sz00,W0_80)
      | ~ aElementOf0(W0_80,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_8430,plain,
    ! [W2_614] :
      ( aElementOf0(W2_614,sdtmndt0(sdtlpdtrp0(xN,'#skF_39'),szmzizndt0(sdtlpdtrp0(xN,'#skF_39'))))
      | ~ aElementOf0(W2_614,'#skF_40') ),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_8458,plain,
    ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,'#skF_39')),sdtmndt0(sdtlpdtrp0(xN,'#skF_39'),szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_9206,plain,
    ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,'#skF_39')),'#skF_40'),
    inference(resolution,[status(thm)],[c_8430,c_8458]) ).

tff(c_8440,plain,
    aSet0('#skF_40'),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_8320,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_824]) ).

tff(c_8426,plain,
    sbrdtbr0('#skF_40') = xk,
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_8919,plain,
    ! [W0_657] :
      ( isFinite0(W0_657)
      | ~ aElementOf0(sbrdtbr0(W0_657),szNzAzT0)
      | ~ aSet0(W0_657) ),
    inference(cnfTransformation,[status(thm)],[f_324]) ).

tff(c_8928,plain,
    ( isFinite0('#skF_40')
    | ~ aElementOf0(xk,szNzAzT0)
    | ~ aSet0('#skF_40') ),
    inference(superposition,[status(thm),theory(equality)],[c_8426,c_8919]) ).

tff(c_8934,plain,
    isFinite0('#skF_40'),
    inference(demodulation,[status(thm),theory(equality)],[c_8440,c_8320,c_8928]) ).

tff(c_8400,plain,
    ! [W0_581] :
      ( aSet0(sdtlpdtrp0(xN,W0_581))
      | ~ aElementOf0(W0_581,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_886]) ).

tff(c_8438,plain,
    aElementOf0(szmzizndt0(sdtlpdtrp0(xN,'#skF_39')),sdtlpdtrp0(xN,'#skF_39')),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_8591,plain,
    ! [W1_631,W0_632] :
      ( aElement0(W1_631)
      | ~ aElementOf0(W1_631,W0_632)
      | ~ aSet0(W0_632) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_8607,plain,
    ( aElement0(szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))
    | ~ aSet0(sdtlpdtrp0(xN,'#skF_39')) ),
    inference(resolution,[status(thm)],[c_8438,c_8591]) ).

tff(c_18361,plain,
    ~ aSet0(sdtlpdtrp0(xN,'#skF_39')),
    inference(splitLeft,[status(thm)],[c_8607]) ).

tff(c_18364,plain,
    ~ aElementOf0('#skF_39',szNzAzT0),
    inference(resolution,[status(thm)],[c_8400,c_18361]) ).

tff(c_18368,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8442,c_18364]) ).

tff(c_18369,plain,
    aElement0(szmzizndt0(sdtlpdtrp0(xN,'#skF_39'))),
    inference(splitRight,[status(thm)],[c_8607]) ).

tff(c_8318,plain,
    szszuzczcdt0(xk) = xK,
    inference(cnfTransformation,[status(thm)],[f_824]) ).

tff(c_33832,plain,
    ! [W0_1535,W1_1536] :
      ( ( szszuzczcdt0(sbrdtbr0(W0_1535)) = sbrdtbr0(sdtpldt0(W0_1535,W1_1536)) )
      | aElementOf0(W1_1536,W0_1535)
      | ~ aElement0(W1_1536)
      | ~ isFinite0(W0_1535)
      | ~ aSet0(W0_1535) ),
    inference(cnfTransformation,[status(thm)],[f_342]) ).

tff(c_8446,plain,
    ( ~ aElementOf0('#skF_41',xS)
    | ( sbrdtbr0(sdtpldt0('#skF_40',szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))) != xK ) ),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_8888,plain,
    sbrdtbr0(sdtpldt0('#skF_40',szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))) != xK,
    inference(splitLeft,[status(thm)],[c_8446]) ).

tff(c_33950,plain,
    ( ( szszuzczcdt0(sbrdtbr0('#skF_40')) != xK )
    | aElementOf0(szmzizndt0(sdtlpdtrp0(xN,'#skF_39')),'#skF_40')
    | ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))
    | ~ isFinite0('#skF_40')
    | ~ aSet0('#skF_40') ),
    inference(superposition,[status(thm),theory(equality)],[c_33832,c_8888]) ).

tff(c_34022,plain,
    aElementOf0(szmzizndt0(sdtlpdtrp0(xN,'#skF_39')),'#skF_40'),
    inference(demodulation,[status(thm),theory(equality)],[c_8440,c_8934,c_18369,c_8318,c_8426,c_33950]) ).

tff(c_34024,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9206,c_34022]) ).

tff(c_34025,plain,
    ~ aElementOf0('#skF_41',xS),
    inference(splitRight,[status(thm)],[c_8446]) ).

tff(c_344,plain,
    aSet0(xS),
    inference(cnfTransformation,[status(thm)],[f_674]) ).

tff(c_110,plain,
    aElementOf0(sz00,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_8322,plain,
    sdtlpdtrp0(xN,sz00) = xS,
    inference(cnfTransformation,[status(thm)],[f_873]) ).

tff(c_66440,plain,
    ! [W0_2575,W1_2576] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_2575),sdtlpdtrp0(xN,W1_2576))
      | ~ sdtlseqdt0(W1_2576,W0_2575)
      | ~ aElementOf0(W1_2576,szNzAzT0)
      | ~ aElementOf0(W0_2575,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_899]) ).

tff(c_66463,plain,
    ! [W0_2575] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_2575),xS)
      | ~ sdtlseqdt0(sz00,W0_2575)
      | ~ aElementOf0(sz00,szNzAzT0)
      | ~ aElementOf0(W0_2575,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_8322,c_66440]) ).

tff(c_67125,plain,
    ! [W0_2593] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_2593),xS)
      | ~ sdtlseqdt0(sz00,W0_2593)
      | ~ aElementOf0(W0_2593,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_66463]) ).

tff(c_54398,plain,
    ! [W0_2236,W1_2237] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_2236),sdtlpdtrp0(xN,W1_2237))
      | ~ sdtlseqdt0(W1_2237,W0_2236)
      | ~ aElementOf0(W1_2237,szNzAzT0)
      | ~ aElementOf0(W0_2236,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_899]) ).

tff(c_54425,plain,
    ! [W0_2236] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_2236),xS)
      | ~ sdtlseqdt0(sz00,W0_2236)
      | ~ aElementOf0(sz00,szNzAzT0)
      | ~ aElementOf0(W0_2236,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_8322,c_54398]) ).

tff(c_57024,plain,
    ! [W0_2284] :
      ( aSubsetOf0(sdtlpdtrp0(xN,W0_2284),xS)
      | ~ sdtlseqdt0(sz00,W0_2284)
      | ~ aElementOf0(W0_2284,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_54425]) ).

tff(c_8434,plain,
    aSet0(sdtmndt0(sdtlpdtrp0(xN,'#skF_39'),szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_8428,plain,
    aSubsetOf0('#skF_40',sdtmndt0(sdtlpdtrp0(xN,'#skF_39'),szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_34026,plain,
    sbrdtbr0(sdtpldt0('#skF_40',szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))) = xK,
    inference(splitRight,[status(thm)],[c_8446]) ).

tff(c_8448,plain,
    ( aElementOf0('#skF_41',sdtpldt0('#skF_40',szmzizndt0(sdtlpdtrp0(xN,'#skF_39'))))
    | ( sbrdtbr0(sdtpldt0('#skF_40',szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))) != xK ) ),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_42720,plain,
    aElementOf0('#skF_41',sdtpldt0('#skF_40',szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))),
    inference(demodulation,[status(thm),theory(equality)],[c_34026,c_8448]) ).

tff(c_8450,plain,
    ! [W2_616] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,'#skF_39')) = W2_616 )
      | aElementOf0(W2_616,'#skF_40')
      | ~ aElementOf0(W2_616,sdtpldt0('#skF_40',szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))) ),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_42730,plain,
    ( ( szmzizndt0(sdtlpdtrp0(xN,'#skF_39')) = '#skF_41' )
    | aElementOf0('#skF_41','#skF_40') ),
    inference(resolution,[status(thm)],[c_42720,c_8450]) ).

tff(c_42736,plain,
    aElementOf0('#skF_41','#skF_40'),
    inference(splitLeft,[status(thm)],[c_42730]) ).

tff(c_43033,plain,
    ! [W2_1906,W0_1907,W1_1908] :
      ( aElementOf0(W2_1906,W0_1907)
      | ~ aElementOf0(W2_1906,W1_1908)
      | ~ aSubsetOf0(W1_1908,W0_1907)
      | ~ aSet0(W0_1907) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_43197,plain,
    ! [W0_1913] :
      ( aElementOf0('#skF_41',W0_1913)
      | ~ aSubsetOf0('#skF_40',W0_1913)
      | ~ aSet0(W0_1913) ),
    inference(resolution,[status(thm)],[c_42736,c_43033]) ).

tff(c_43207,plain,
    ( aElementOf0('#skF_41',sdtmndt0(sdtlpdtrp0(xN,'#skF_39'),szmzizndt0(sdtlpdtrp0(xN,'#skF_39'))))
    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,'#skF_39'),szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))) ),
    inference(resolution,[status(thm)],[c_8428,c_43197]) ).

tff(c_43220,plain,
    aElementOf0('#skF_41',sdtmndt0(sdtlpdtrp0(xN,'#skF_39'),szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))),
    inference(demodulation,[status(thm),theory(equality)],[c_8434,c_43207]) ).

tff(c_8460,plain,
    ! [W2_613] :
      ( aElementOf0(W2_613,sdtlpdtrp0(xN,'#skF_39'))
      | ~ aElementOf0(W2_613,sdtmndt0(sdtlpdtrp0(xN,'#skF_39'),szmzizndt0(sdtlpdtrp0(xN,'#skF_39')))) ),
    inference(cnfTransformation,[status(thm)],[f_988]) ).

tff(c_47960,plain,
    aElementOf0('#skF_41',sdtlpdtrp0(xN,'#skF_39')),
    inference(resolution,[status(thm)],[c_43220,c_8460]) ).

tff(c_24,plain,
    ! [W2_23,W0_14,W1_20] :
      ( aElementOf0(W2_23,W0_14)
      | ~ aElementOf0(W2_23,W1_20)
      | ~ aSubsetOf0(W1_20,W0_14)
      | ~ aSet0(W0_14) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_47979,plain,
    ! [W0_14] :
      ( aElementOf0('#skF_41',W0_14)
      | ~ aSubsetOf0(sdtlpdtrp0(xN,'#skF_39'),W0_14)
      | ~ aSet0(W0_14) ),
    inference(resolution,[status(thm)],[c_47960,c_24]) ).

tff(c_57040,plain,
    ( aElementOf0('#skF_41',xS)
    | ~ aSet0(xS)
    | ~ sdtlseqdt0(sz00,'#skF_39')
    | ~ aElementOf0('#skF_39',szNzAzT0) ),
    inference(resolution,[status(thm)],[c_57024,c_47979]) ).

tff(c_57070,plain,
    ( aElementOf0('#skF_41',xS)
    | ~ sdtlseqdt0(sz00,'#skF_39') ),
    inference(demodulation,[status(thm),theory(equality)],[c_8442,c_344,c_57040]) ).

tff(c_57071,plain,
    ~ sdtlseqdt0(sz00,'#skF_39'),
    inference(negUnitSimplification,[status(thm)],[c_34025,c_57070]) ).

tff(c_57087,plain,
    ~ aElementOf0('#skF_39',szNzAzT0),
    inference(resolution,[status(thm)],[c_126,c_57071]) ).

tff(c_57091,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8442,c_57087]) ).

tff(c_57092,plain,
    szmzizndt0(sdtlpdtrp0(xN,'#skF_39')) = '#skF_41',
    inference(splitRight,[status(thm)],[c_42730]) ).

tff(c_57129,plain,
    aElementOf0('#skF_41',sdtlpdtrp0(xN,'#skF_39')),
    inference(demodulation,[status(thm),theory(equality)],[c_57092,c_8438]) ).

tff(c_58041,plain,
    ! [W2_2343,W0_2344,W1_2345] :
      ( aElementOf0(W2_2343,W0_2344)
      | ~ aElementOf0(W2_2343,W1_2345)
      | ~ aSubsetOf0(W1_2345,W0_2344)
      | ~ aSet0(W0_2344) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_58099,plain,
    ! [W0_2344] :
      ( aElementOf0('#skF_41',W0_2344)
      | ~ aSubsetOf0(sdtlpdtrp0(xN,'#skF_39'),W0_2344)
      | ~ aSet0(W0_2344) ),
    inference(resolution,[status(thm)],[c_57129,c_58041]) ).

tff(c_67139,plain,
    ( aElementOf0('#skF_41',xS)
    | ~ aSet0(xS)
    | ~ sdtlseqdt0(sz00,'#skF_39')
    | ~ aElementOf0('#skF_39',szNzAzT0) ),
    inference(resolution,[status(thm)],[c_67125,c_58099]) ).

tff(c_67167,plain,
    ( aElementOf0('#skF_41',xS)
    | ~ sdtlseqdt0(sz00,'#skF_39') ),
    inference(demodulation,[status(thm),theory(equality)],[c_8442,c_344,c_67139]) ).

tff(c_67168,plain,
    ~ sdtlseqdt0(sz00,'#skF_39'),
    inference(negUnitSimplification,[status(thm)],[c_34025,c_67167]) ).

tff(c_67333,plain,
    ~ aElementOf0('#skF_39',szNzAzT0),
    inference(resolution,[status(thm)],[c_126,c_67168]) ).

tff(c_67337,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8442,c_67333]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM579+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n025.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 15:13:49 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 91.41/69.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 91.41/69.67  
% 91.41/69.67  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 91.41/69.70  
% 91.41/69.70  Inference rules
% 91.41/69.70  ----------------------
% 91.41/69.70  #Ref     : 16
% 91.41/69.70  #Sup     : 10811
% 91.41/69.70  #Fact    : 0
% 91.41/69.70  #Define  : 0
% 91.41/69.70  #Split   : 582
% 91.41/69.70  #Chain   : 0
% 91.41/69.70  #Close   : 0
% 91.41/69.70  
% 91.41/69.70  Ordering : KBO
% 91.41/69.70  
% 91.41/69.70  Simplification rules
% 91.41/69.70  ----------------------
% 91.41/69.70  #Subsume      : 3081
% 91.41/69.70  #Demod        : 9680
% 91.41/69.70  #Tautology    : 2319
% 91.41/69.70  #SimpNegUnit  : 774
% 91.41/69.70  #BackRed      : 359
% 91.41/69.70  
% 91.41/69.70  #Partial instantiations: 0
% 91.41/69.70  #Strategies tried      : 1
% 91.41/69.70  
% 91.41/69.70  Timing (in seconds)
% 91.41/69.70  ----------------------
% 91.41/69.70  Preprocessing        : 2.11
% 91.41/69.70  Parsing              : 0.47
% 91.41/69.71  CNF conversion       : 0.17
% 91.41/69.71  Main loop            : 66.50
% 91.41/69.71  Inferencing          : 2.55
% 91.41/69.71  Reduction            : 47.42
% 91.41/69.71  Demodulation         : 40.51
% 91.41/69.71  BG Simplification    : 0.72
% 91.41/69.71  Subsumption          : 12.79
% 91.41/69.71  Abstraction          : 0.55
% 91.41/69.71  MUC search           : 0.00
% 91.41/69.71  Cooper               : 0.00
% 91.41/69.71  Total                : 68.67
% 91.41/69.71  Index Insertion      : 0.00
% 91.41/69.71  Index Deletion       : 0.00
% 91.41/69.71  Index Matching       : 0.00
% 91.41/69.71  BG Taut test         : 0.00
%------------------------------------------------------------------------------