TSTP Solution File: NUM598+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM598+1 : 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 : n013.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 10:52:16 EDT 2023

% Result   : Theorem 153.28s 129.02s
% Output   : CNFRefutation 153.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   77
% Syntax   : Number of formulae    :  140 (  27 unt;  66 typ;   0 def)
%            Number of atoms       :  195 (  37 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  218 (  97   ~;  94   |;  14   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  105 (  53   >;  52   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   57 (  57 usr;  13 con; 0-4 aty)
%            Number of variables   :   49 (;  49   !;   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 > xe > xd > xc > xT > xS > xO > xN > xK > xC > szNzAzT0 > sz00 > slcrc0 > #skF_26 > #skF_7 > #skF_11 > #skF_17 > #skF_6 > #skF_27 > #skF_1 > #skF_18 > #skF_4 > #skF_29 > #skF_12 > #skF_23 > #skF_28 > #skF_5 > #skF_19 > #skF_10 > #skF_8 > #skF_20 > #skF_24 > #skF_15 > #skF_13 > #skF_14 > #skF_25 > #skF_3 > #skF_2 > #skF_21 > #skF_9 > #skF_22 > #skF_30 > #skF_16

%Foreground sorts:

%Background operators:

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

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

tff('#skF_27',type,
    '#skF_27': ( $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(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_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(xO,type,
    xO: $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(szmzizndt0,type,
    szmzizndt0: $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_30',type,
    '#skF_30': $i > $i ).

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

tff(f_851,negated_conjecture,
    ~ isCountable0(xO),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_663,hypothesis,
    ( aSet0(xT)
    & isFinite0(xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).

tff(f_846,hypothesis,
    ( aElementOf0(szDzizrdt0(xd),xT)
    & isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).

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

tff(f_842,hypothesis,
    ( aFunction0(xd)
    & ( szDzozmdt0(xd) = szNzAzT0 )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ! [W1] :
            ( ( aSet0(W1)
              & aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) )
           => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).

tff(f_588,axiom,
    ! [W0,W1] :
      ( ( aFunction0(W0)
        & aElement0(W1) )
     => aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPttSet) ).

tff(f_849,hypothesis,
    ( aSet0(xO)
    & ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).

tff(f_829,hypothesis,
    ( aFunction0(xe)
    & ( szDzozmdt0(xe) = szNzAzT0 )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).

tff(f_650,axiom,
    ! [W0] :
      ( aFunction0(W0)
     => ! [W1] :
          ( ( aSubsetOf0(W1,szDzozmdt0(W0))
            & isCountable0(W1) )
         => ( ! [W2,W3] :
                ( ( aElementOf0(W2,szDzozmdt0(W0))
                  & aElementOf0(W3,szDzozmdt0(W0))
                  & ( W2 != W3 ) )
               => ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
           => isCountable0(sdtlcdtrc0(W0,W1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgCount) ).

tff(f_613,axiom,
    ! [W0] :
      ( aFunction0(W0)
     => ! [W1] :
          ( aElementOf0(W1,szDzozmdt0(W0))
         => aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).

tff(f_748,hypothesis,
    ! [W0,W1] :
      ( ( aElementOf0(W0,szNzAzT0)
        & aElementOf0(W1,szNzAzT0)
        & ( W0 != W1 ) )
     => ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3821) ).

tff(c_432,plain,
    ~ isCountable0(xO),
    inference(cnfTransformation,[status(thm)],[f_851]) ).

tff(c_334,plain,
    aSet0(xT),
    inference(cnfTransformation,[status(thm)],[f_663]) ).

tff(c_426,plain,
    aElementOf0(szDzizrdt0(xd),xT),
    inference(cnfTransformation,[status(thm)],[f_846]) ).

tff(c_643,plain,
    ! [W1_442,W0_443] :
      ( aElement0(W1_442)
      | ~ aElementOf0(W1_442,W0_443)
      | ~ aSet0(W0_443) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_649,plain,
    ( aElement0(szDzizrdt0(xd))
    | ~ aSet0(xT) ),
    inference(resolution,[status(thm)],[c_426,c_643]) ).

tff(c_664,plain,
    aElement0(szDzizrdt0(xd)),
    inference(demodulation,[status(thm),theory(equality)],[c_334,c_649]) ).

tff(c_420,plain,
    aFunction0(xd),
    inference(cnfTransformation,[status(thm)],[f_842]) ).

tff(c_418,plain,
    szDzozmdt0(xd) = szNzAzT0,
    inference(cnfTransformation,[status(thm)],[f_842]) ).

tff(c_1402,plain,
    ! [W0_519,W1_520] :
      ( aSubsetOf0(sdtlbdtrb0(W0_519,W1_520),szDzozmdt0(W0_519))
      | ~ aElement0(W1_520)
      | ~ aFunction0(W0_519) ),
    inference(cnfTransformation,[status(thm)],[f_588]) ).

tff(c_1426,plain,
    ! [W1_520] :
      ( aSubsetOf0(sdtlbdtrb0(xd,W1_520),szNzAzT0)
      | ~ aElement0(W1_520)
      | ~ aFunction0(xd) ),
    inference(superposition,[status(thm),theory(equality)],[c_418,c_1402]) ).

tff(c_1438,plain,
    ! [W1_520] :
      ( aSubsetOf0(sdtlbdtrb0(xd,W1_520),szNzAzT0)
      | ~ aElement0(W1_520) ),
    inference(demodulation,[status(thm),theory(equality)],[c_420,c_1426]) ).

tff(c_424,plain,
    isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
    inference(cnfTransformation,[status(thm)],[f_846]) ).

tff(c_428,plain,
    sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) = xO,
    inference(cnfTransformation,[status(thm)],[f_849]) ).

tff(c_414,plain,
    aFunction0(xe),
    inference(cnfTransformation,[status(thm)],[f_829]) ).

tff(c_412,plain,
    szDzozmdt0(xe) = szNzAzT0,
    inference(cnfTransformation,[status(thm)],[f_829]) ).

tff(c_6674,plain,
    ! [W0_744,W1_745] :
      ( ( '#skF_24'(W0_744,W1_745) != '#skF_25'(W0_744,W1_745) )
      | isCountable0(sdtlcdtrc0(W0_744,W1_745))
      | ~ isCountable0(W1_745)
      | ~ aSubsetOf0(W1_745,szDzozmdt0(W0_744))
      | ~ aFunction0(W0_744) ),
    inference(cnfTransformation,[status(thm)],[f_650]) ).

tff(c_6736,plain,
    ! [W1_745] :
      ( ( '#skF_24'(xe,W1_745) != '#skF_25'(xe,W1_745) )
      | isCountable0(sdtlcdtrc0(xe,W1_745))
      | ~ isCountable0(W1_745)
      | ~ aSubsetOf0(W1_745,szNzAzT0)
      | ~ aFunction0(xe) ),
    inference(superposition,[status(thm),theory(equality)],[c_412,c_6674]) ).

tff(c_206450,plain,
    ! [W1_3361] :
      ( ( '#skF_24'(xe,W1_3361) != '#skF_25'(xe,W1_3361) )
      | isCountable0(sdtlcdtrc0(xe,W1_3361))
      | ~ isCountable0(W1_3361)
      | ~ aSubsetOf0(W1_3361,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_6736]) ).

tff(c_206453,plain,
    ( ( '#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) != '#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
    | isCountable0(xO)
    | ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
    | ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_428,c_206450]) ).

tff(c_206455,plain,
    ( ( '#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) != '#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
    | isCountable0(xO)
    | ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_424,c_206453]) ).

tff(c_206456,plain,
    ( ( '#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) != '#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
    | ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
    inference(negUnitSimplification,[status(thm)],[c_432,c_206455]) ).

tff(c_206511,plain,
    ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),
    inference(splitLeft,[status(thm)],[c_206456]) ).

tff(c_206547,plain,
    ~ aElement0(szDzizrdt0(xd)),
    inference(resolution,[status(thm)],[c_1438,c_206511]) ).

tff(c_206552,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_664,c_206547]) ).

tff(c_206554,plain,
    aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),
    inference(splitRight,[status(thm)],[c_206456]) ).

tff(c_8357,plain,
    ! [W0_783,W1_784] :
      ( aElementOf0('#skF_25'(W0_783,W1_784),szDzozmdt0(W0_783))
      | isCountable0(sdtlcdtrc0(W0_783,W1_784))
      | ~ isCountable0(W1_784)
      | ~ aSubsetOf0(W1_784,szDzozmdt0(W0_783))
      | ~ aFunction0(W0_783) ),
    inference(cnfTransformation,[status(thm)],[f_650]) ).

tff(c_8443,plain,
    ! [W1_784] :
      ( aElementOf0('#skF_25'(xe,W1_784),szNzAzT0)
      | isCountable0(sdtlcdtrc0(xe,W1_784))
      | ~ isCountable0(W1_784)
      | ~ aSubsetOf0(W1_784,szDzozmdt0(xe))
      | ~ aFunction0(xe) ),
    inference(superposition,[status(thm),theory(equality)],[c_412,c_8357]) ).

tff(c_8494,plain,
    ! [W1_784] :
      ( aElementOf0('#skF_25'(xe,W1_784),szNzAzT0)
      | isCountable0(sdtlcdtrc0(xe,W1_784))
      | ~ isCountable0(W1_784)
      | ~ aSubsetOf0(W1_784,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_412,c_8443]) ).

tff(c_206553,plain,
    '#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) != '#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
    inference(splitRight,[status(thm)],[c_206456]) ).

tff(c_410,plain,
    ! [W0_420] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W0_420)) = sdtlpdtrp0(xe,W0_420) )
      | ~ aElementOf0(W0_420,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_829]) ).

tff(c_6863,plain,
    ! [W0_748,W1_749] :
      ( aElementOf0('#skF_24'(W0_748,W1_749),szDzozmdt0(W0_748))
      | isCountable0(sdtlcdtrc0(W0_748,W1_749))
      | ~ isCountable0(W1_749)
      | ~ aSubsetOf0(W1_749,szDzozmdt0(W0_748))
      | ~ aFunction0(W0_748) ),
    inference(cnfTransformation,[status(thm)],[f_650]) ).

tff(c_6934,plain,
    ! [W1_749] :
      ( aElementOf0('#skF_24'(xe,W1_749),szNzAzT0)
      | isCountable0(sdtlcdtrc0(xe,W1_749))
      | ~ isCountable0(W1_749)
      | ~ aSubsetOf0(W1_749,szDzozmdt0(xe))
      | ~ aFunction0(xe) ),
    inference(superposition,[status(thm),theory(equality)],[c_412,c_6863]) ).

tff(c_6985,plain,
    ! [W1_749] :
      ( aElementOf0('#skF_24'(xe,W1_749),szNzAzT0)
      | isCountable0(sdtlcdtrc0(xe,W1_749))
      | ~ isCountable0(W1_749)
      | ~ aSubsetOf0(W1_749,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_412,c_6934]) ).

tff(c_118709,plain,
    ! [W0_2216,W1_2217] :
      ( ( sdtlpdtrp0(W0_2216,'#skF_24'(W0_2216,W1_2217)) = sdtlpdtrp0(W0_2216,'#skF_25'(W0_2216,W1_2217)) )
      | isCountable0(sdtlcdtrc0(W0_2216,W1_2217))
      | ~ isCountable0(W1_2217)
      | ~ aSubsetOf0(W1_2217,szDzozmdt0(W0_2216))
      | ~ aFunction0(W0_2216) ),
    inference(cnfTransformation,[status(thm)],[f_650]) ).

tff(c_118764,plain,
    ! [W1_2217] :
      ( ( sdtlpdtrp0(xe,'#skF_24'(xe,W1_2217)) = sdtlpdtrp0(xe,'#skF_25'(xe,W1_2217)) )
      | isCountable0(sdtlcdtrc0(xe,W1_2217))
      | ~ isCountable0(W1_2217)
      | ~ aSubsetOf0(W1_2217,szNzAzT0)
      | ~ aFunction0(xe) ),
    inference(superposition,[status(thm),theory(equality)],[c_412,c_118709]) ).

tff(c_384498,plain,
    ! [W1_5398] :
      ( ( sdtlpdtrp0(xe,'#skF_24'(xe,W1_5398)) = sdtlpdtrp0(xe,'#skF_25'(xe,W1_5398)) )
      | isCountable0(sdtlcdtrc0(xe,W1_5398))
      | ~ isCountable0(W1_5398)
      | ~ aSubsetOf0(W1_5398,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_118764]) ).

tff(c_384501,plain,
    ( ( sdtlpdtrp0(xe,'#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) = sdtlpdtrp0(xe,'#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
    | isCountable0(xO)
    | ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
    | ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_428,c_384498]) ).

tff(c_384503,plain,
    ( ( sdtlpdtrp0(xe,'#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) = sdtlpdtrp0(xe,'#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
    | isCountable0(xO) ),
    inference(demodulation,[status(thm),theory(equality)],[c_206554,c_424,c_384501]) ).

tff(c_384504,plain,
    sdtlpdtrp0(xe,'#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) = sdtlpdtrp0(xe,'#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
    inference(negUnitSimplification,[status(thm)],[c_432,c_384503]) ).

tff(c_3618,plain,
    ! [W0_634,W1_635] :
      ( aElementOf0(sdtlpdtrp0(W0_634,W1_635),sdtlcdtrc0(W0_634,szDzozmdt0(W0_634)))
      | ~ aElementOf0(W1_635,szDzozmdt0(W0_634))
      | ~ aFunction0(W0_634) ),
    inference(cnfTransformation,[status(thm)],[f_613]) ).

tff(c_3662,plain,
    ! [W1_635] :
      ( aElementOf0(sdtlpdtrp0(xe,W1_635),sdtlcdtrc0(xe,szNzAzT0))
      | ~ aElementOf0(W1_635,szDzozmdt0(xe))
      | ~ aFunction0(xe) ),
    inference(superposition,[status(thm),theory(equality)],[c_412,c_3618]) ).

tff(c_3688,plain,
    ! [W1_635] :
      ( aElementOf0(sdtlpdtrp0(xe,W1_635),sdtlcdtrc0(xe,szNzAzT0))
      | ~ aElementOf0(W1_635,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_414,c_412,c_3662]) ).

tff(c_384644,plain,
    ( aElementOf0(sdtlpdtrp0(xe,'#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),sdtlcdtrc0(xe,szNzAzT0))
    | ~ aElementOf0('#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_384504,c_3688]) ).

tff(c_385396,plain,
    ~ aElementOf0('#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0),
    inference(splitLeft,[status(thm)],[c_384644]) ).

tff(c_385399,plain,
    ( isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
    | ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
    | ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
    inference(resolution,[status(thm)],[c_6985,c_385396]) ).

tff(c_385402,plain,
    isCountable0(xO),
    inference(demodulation,[status(thm),theory(equality)],[c_206554,c_424,c_428,c_385399]) ).

tff(c_385404,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_432,c_385402]) ).

tff(c_385406,plain,
    aElementOf0('#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0),
    inference(splitRight,[status(thm)],[c_384644]) ).

tff(c_5184,plain,
    ! [W1_676,W0_677] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W1_676)) != szmzizndt0(sdtlpdtrp0(xN,W0_677)) )
      | ( W1_676 = W0_677 )
      | ~ aElementOf0(W1_676,szNzAzT0)
      | ~ aElementOf0(W0_677,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_748]) ).

tff(c_5190,plain,
    ! [W1_676,W0_420] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W1_676)) != sdtlpdtrp0(xe,W0_420) )
      | ( W1_676 = W0_420 )
      | ~ aElementOf0(W1_676,szNzAzT0)
      | ~ aElementOf0(W0_420,szNzAzT0)
      | ~ aElementOf0(W0_420,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_410,c_5184]) ).

tff(c_384628,plain,
    ! [W1_676] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W1_676)) != sdtlpdtrp0(xe,'#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
      | ( W1_676 = '#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
      | ~ aElementOf0(W1_676,szNzAzT0)
      | ~ aElementOf0('#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
      | ~ aElementOf0('#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_384504,c_5190]) ).

tff(c_387205,plain,
    ! [W1_5409] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W1_5409)) != sdtlpdtrp0(xe,'#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
      | ( W1_5409 = '#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
      | ~ aElementOf0(W1_5409,szNzAzT0) ),
    inference(demodulation,[status(thm),theory(equality)],[c_385406,c_385406,c_384628]) ).

tff(c_387222,plain,
    ! [W0_420] :
      ( ( sdtlpdtrp0(xe,W0_420) != sdtlpdtrp0(xe,'#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
      | ( W0_420 = '#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
      | ~ aElementOf0(W0_420,szNzAzT0)
      | ~ aElementOf0(W0_420,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_410,c_387205]) ).

tff(c_401677,plain,
    ( ( '#skF_24'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) = '#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
    | ~ aElementOf0('#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
    | ~ aElementOf0('#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0) ),
    inference(reflexivity,[status(thm),theory(equality)],[c_387222]) ).

tff(c_401678,plain,
    ( ~ aElementOf0('#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0)
    | ~ aElementOf0('#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0) ),
    inference(negUnitSimplification,[status(thm)],[c_206553,c_401677]) ).

tff(c_402048,plain,
    ~ aElementOf0('#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0),
    inference(splitLeft,[status(thm)],[c_401678]) ).

tff(c_402054,plain,
    ( isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
    | ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
    | ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
    inference(resolution,[status(thm)],[c_8494,c_402048]) ).

tff(c_402060,plain,
    isCountable0(xO),
    inference(demodulation,[status(thm),theory(equality)],[c_206554,c_424,c_428,c_402054]) ).

tff(c_402062,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_432,c_402060]) ).

tff(c_402063,plain,
    ~ aElementOf0('#skF_25'(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szNzAzT0),
    inference(splitRight,[status(thm)],[c_401678]) ).

tff(c_402070,plain,
    ( isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
    | ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
    | ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
    inference(resolution,[status(thm)],[c_8494,c_402063]) ).

tff(c_402076,plain,
    isCountable0(xO),
    inference(demodulation,[status(thm),theory(equality)],[c_206554,c_424,c_428,c_402070]) ).

tff(c_402078,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_432,c_402076]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM598+1 : 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
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 14:45:17 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 153.28/129.02  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 153.28/129.03  
% 153.28/129.03  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 153.28/129.06  
% 153.28/129.06  Inference rules
% 153.28/129.06  ----------------------
% 153.28/129.06  #Ref     : 15
% 153.28/129.06  #Sup     : 78127
% 153.28/129.06  #Fact    : 18
% 153.28/129.06  #Define  : 0
% 153.28/129.06  #Split   : 1219
% 153.28/129.06  #Chain   : 0
% 153.28/129.06  #Close   : 0
% 153.28/129.06  
% 153.28/129.06  Ordering : KBO
% 153.28/129.06  
% 153.28/129.06  Simplification rules
% 153.28/129.06  ----------------------
% 153.28/129.06  #Subsume      : 19206
% 153.28/129.06  #Demod        : 102568
% 153.28/129.06  #Tautology    : 14591
% 153.28/129.06  #SimpNegUnit  : 9493
% 153.28/129.06  #BackRed      : 5220
% 153.28/129.06  
% 153.28/129.06  #Partial instantiations: 0
% 153.28/129.06  #Strategies tried      : 1
% 153.28/129.06  
% 153.28/129.06  Timing (in seconds)
% 153.28/129.06  ----------------------
% 153.28/129.07  Preprocessing        : 0.90
% 153.28/129.07  Parsing              : 0.44
% 153.28/129.07  CNF conversion       : 0.09
% 153.28/129.07  Main loop            : 126.99
% 153.28/129.07  Inferencing          : 21.36
% 153.28/129.07  Reduction            : 66.90
% 153.28/129.07  Demodulation         : 53.37
% 153.28/129.07  BG Simplification    : 0.65
% 153.28/129.07  Subsumption          : 29.02
% 153.28/129.07  Abstraction          : 1.24
% 153.28/129.07  MUC search           : 0.00
% 153.28/129.07  Cooper               : 0.00
% 153.28/129.07  Total                : 127.95
% 153.28/129.07  Index Insertion      : 0.00
% 153.28/129.07  Index Deletion       : 0.00
% 153.28/129.07  Index Matching       : 0.00
% 153.28/129.07  BG Taut test         : 0.00
%------------------------------------------------------------------------------