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Beagle---0.9.52.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.52
% Problem  : NUM631+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n024.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 : Wed Apr  9 07:56:41 PM UTC 2025

% Result   : Theorem 102.89s 79.57s
% Output   : CNFRefutation 102.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   43 (  25 unt;   0 typ;   0 def)
%            Number of atoms       :  116 (  46 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   98 (  25   ~;  25   |;  31   &)
%                                         (   2 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   87 (  87 usr;  20 con; 0-4 aty)
%            Number of variables   :   25 (  24   !;   1   ?;   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 > xp > xn > xk > xe > xd > xc > xT > xS > xQ > xP > xO > xN > xK > xD > xC > szNzAzT0 > sz00 > slcrc0 > #skF_53 > #skF_47 > #skF_7 > #skF_11 > #skF_41 > #skF_17 > #skF_31 > #skF_33 > #skF_44 > #skF_6 > #skF_1 > #skF_18 > #skF_55 > #skF_37 > #skF_54 > #skF_38 > #skF_4 > #skF_29 > #skF_52 > #skF_12 > #skF_30 > #skF_32 > #skF_23 > #skF_35 > #skF_5 > #skF_49 > #skF_19 > #skF_10 > #skF_42 > #skF_8 > #skF_20 > #skF_28 > #skF_26 > #skF_24 > #skF_34 > #skF_15 > #skF_13 > #skF_14 > #skF_50 > #skF_25 > #skF_3 > #skF_2 > #skF_48 > #skF_40 > #skF_27 > #skF_36 > #skF_43 > #skF_46 > #skF_21 > #skF_45 > #skF_9 > #skF_22 > #skF_16 > #skF_51 > #skF_39

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_53',type,
    '#skF_53': $i > $i ).

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

tff('#skF_47',type,
    '#skF_47': ( $i * $i ) > $i ).

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

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

tff('#skF_41',type,
    '#skF_41': ( $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('#skF_44',type,
    '#skF_44': ( $i * $i * $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(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('#skF_55',type,
    '#skF_55': $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('#skF_54',type,
    '#skF_54': $i ).

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

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

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

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

tff('#skF_52',type,
    '#skF_52': $i > $i ).

tff(xP,type,
    xP: $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_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_49',type,
    '#skF_49': ( $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_42',type,
    '#skF_42': ( $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_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(xO,type,
    xO: $i ).

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

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

tff('#skF_50',type,
    '#skF_50': ( $i * $i ) > $i ).

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

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

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

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(xp,type,
    xp: $i ).

tff('#skF_48',type,
    '#skF_48': $i > $i ).

tff('#skF_40',type,
    '#skF_40': ( $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('#skF_43',type,
    '#skF_43': ( $i * $i ) > $i ).

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

tff('#skF_46',type,
    '#skF_46': $i > $i ).

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

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

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

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

tff('#skF_45',type,
    '#skF_45': $i > $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('#skF_51',type,
    '#skF_51': $i > $i ).

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

tff(f_1467,hypothesis,
    ( aElementOf0(xn,szDzozmdt0(xd))
    & ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
    & aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aElementOf0(xn,szNzAzT0)
    & ( sdtlpdtrp0(xe,xn) = xp ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).

tff(f_1439,hypothesis,
    ( aSet0(xP)
    & ! [W0] :
        ( aElementOf0(W0,xQ)
       => sdtlseqdt0(szmzizndt0(xQ),W0) )
    & ! [W0] :
        ( aElementOf0(W0,xP)
      <=> ( aElement0(W0)
          & aElementOf0(W0,xQ)
          & ( W0 != szmzizndt0(xQ) ) ) )
    & ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).

tff(f_1381,hypothesis,
    ( aSet0(xQ)
    & ! [W0] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xO) )
    & aSubsetOf0(xQ,xO)
    & ( sbrdtbr0(xQ) = xK )
    & aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).

tff(f_1440,hypothesis,
    aElementOf0(xp,xQ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5173) ).

tff(f_1421,hypothesis,
    ( aElementOf0(xp,xQ)
    & ! [W0] :
        ( aElementOf0(W0,xQ)
       => sdtlseqdt0(xp,W0) )
    & ( xp = szmzizndt0(xQ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).

tff(f_163,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).

tff(f_1276,hypothesis,
    ( aFunction0(xe)
    & ( szDzozmdt0(xe) = szNzAzT0 )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
          & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).

tff(f_1517,hypothesis,
    ( ! [W0] :
        ( aElementOf0(W0,sdtlpdtrp0(xN,xn))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W0) )
    & aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
    & ! [W0] :
        ( aElementOf0(W0,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
      <=> ( aElement0(W0)
          & ( aElementOf0(W0,xP)
            | ( W0 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) )
    & ( sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5632) ).

tff(f_1457,hypothesis,
    sbrdtbr0(xP) = xk,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5217) ).

tff(f_1474,hypothesis,
    ( ! [W0] :
        ( aElementOf0(W0,xP)
       => aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
    & aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5334) ).

tff(f_1261,hypothesis,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ? [W1] :
          ( aElementOf0(W1,xT)
          & ! [W2] :
              ( ( aSet0(W2)
                & ( ( ( ! [W3] :
                          ( aElementOf0(W3,W2)
                         => aElementOf0(W3,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                      | aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                    & ( sbrdtbr0(W2) = xk ) )
                  | aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
             => ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) = W1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4618) ).

tff(f_1468,hypothesis,
    sdtlpdtrp0(xd,xn) = szDzizrdt0(xd),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5321) ).

tff(f_1519,negated_conjecture,
    sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_1298,hypothesis,
    ( aFunction0(xd)
    & ( szDzozmdt0(xd) = szNzAzT0 )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ! [W1] :
            ( ( aSet0(W1)
              & ( ( ( ! [W2] :
                        ( aElementOf0(W2,W1)
                       => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                    | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                  & ( sbrdtbr0(W1) = xk ) )
                | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
           => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).

tff(c_9858,plain,
    aElementOf0(xn,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_1467]) ).

tff(c_9830,plain,
    aSet0(xP),
    inference(cnfTransformation,[status(thm)],[f_1439]) ).

tff(c_9796,plain,
    aSet0(xQ),
    inference(cnfTransformation,[status(thm)],[f_1381]) ).

tff(c_9838,plain,
    aElementOf0(xp,xQ),
    inference(cnfTransformation,[status(thm)],[f_1440]) ).

tff(c_9818,plain,
    szmzizndt0(xQ) = xp,
    inference(cnfTransformation,[status(thm)],[f_1421]) ).

tff(c_9824,plain,
    sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
    inference(cnfTransformation,[status(thm)],[f_1439]) ).

tff(c_9911,plain,
    sdtmndt0(xQ,xp) = xP,
    inference(demodulation,[status(thm),theory(equality)],[c_9818,c_9824]) ).

tff(c_59624,plain,
    ! [W0_2152,W1_2153] :
      ( ( sdtpldt0(sdtmndt0(W0_2152,W1_2153),W1_2153) = W0_2152 )
      | ~ aElementOf0(W1_2153,W0_2152)
      | ~ aSet0(W0_2152) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_59651,plain,
    ( ( sdtpldt0(xP,xp) = xQ )
    | ~ aElementOf0(xp,xQ)
    | ~ aSet0(xQ) ),
    inference(superposition,[status(thm),theory(equality)],[c_9911,c_59624]) ).

tff(c_59657,plain,
    sdtpldt0(xP,xp) = xQ,
    inference(demodulation,[status(thm),theory(equality)],[c_9796,c_9838,c_59651]) ).

tff(c_9856,plain,
    sdtlpdtrp0(xe,xn) = xp,
    inference(cnfTransformation,[status(thm)],[f_1467]) ).

tff(c_9706,plain,
    ! [W0_780] :
      ( ( szmzizndt0(sdtlpdtrp0(xN,W0_780)) = sdtlpdtrp0(xe,W0_780) )
      | ~ aElementOf0(W0_780,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_1276]) ).

tff(c_9892,plain,
    sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
    inference(cnfTransformation,[status(thm)],[f_1517]) ).

tff(c_62062,plain,
    ( ( sdtlpdtrp0(xc,sdtpldt0(xP,sdtlpdtrp0(xe,xn))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) )
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_9706,c_9892]) ).

tff(c_62066,plain,
    sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,xQ),
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_59657,c_9856,c_62062]) ).

tff(c_9852,plain,
    sbrdtbr0(xP) = xk,
    inference(cnfTransformation,[status(thm)],[f_1457]) ).

tff(c_9868,plain,
    aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(cnfTransformation,[status(thm)],[f_1474]) ).

tff(c_79217,plain,
    ! [W2_2490,W0_2491] :
      ( ~ aSubsetOf0(W2_2490,sdtlpdtrp0(xN,szszuzczcdt0(W0_2491)))
      | ( sbrdtbr0(W2_2490) != xk )
      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0_2491),W2_2490) = '#skF_48'(W0_2491) )
      | ~ aSet0(W2_2490)
      | ~ aElementOf0(W0_2491,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_1261]) ).

tff(c_79241,plain,
    ( ( sbrdtbr0(xP) != xk )
    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = '#skF_48'(xn) )
    | ~ aSet0(xP)
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_9868,c_79217]) ).

tff(c_79256,plain,
    sdtlpdtrp0(xc,xQ) = '#skF_48'(xn),
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_9830,c_62066,c_9852,c_79241]) ).

tff(c_9866,plain,
    sdtlpdtrp0(xd,xn) = szDzizrdt0(xd),
    inference(cnfTransformation,[status(thm)],[f_1468]) ).

tff(c_9906,plain,
    sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xc,xQ),
    inference(cnfTransformation,[status(thm)],[f_1519]) ).

tff(c_9907,plain,
    sdtlpdtrp0(xc,xQ) != szDzizrdt0(xd),
    inference(demodulation,[status(thm),theory(equality)],[c_9866,c_9906]) ).

tff(c_79262,plain,
    szDzizrdt0(xd) != '#skF_48'(xn),
    inference(demodulation,[status(thm),theory(equality)],[c_79256,c_9907]) ).

tff(c_79260,plain,
    sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = '#skF_48'(xn),
    inference(demodulation,[status(thm),theory(equality)],[c_79256,c_62066]) ).

tff(c_81006,plain,
    ! [W1_2500,W0_2501] :
      ( ~ aSubsetOf0(W1_2500,sdtlpdtrp0(xN,szszuzczcdt0(W0_2501)))
      | ( sbrdtbr0(W1_2500) != xk )
      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0_2501),W1_2500) = sdtlpdtrp0(xd,W0_2501) )
      | ~ aSet0(W1_2500)
      | ~ aElementOf0(W0_2501,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_1298]) ).

tff(c_81030,plain,
    ( ( sbrdtbr0(xP) != xk )
    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xd,xn) )
    | ~ aSet0(xP)
    | ~ aElementOf0(xn,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_9868,c_81006]) ).

tff(c_81045,plain,
    szDzizrdt0(xd) = '#skF_48'(xn),
    inference(demodulation,[status(thm),theory(equality)],[c_9858,c_9830,c_79260,c_9866,c_9852,c_81030]) ).

tff(c_81047,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_79262,c_81045]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.24  % Problem  : NUM631+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.25  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.53  % Computer : n024.cluster.edu
% 0.13/0.53  % Model    : x86_64 x86_64
% 0.13/0.53  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.53  % Memory   : 8042.1875MB
% 0.13/0.53  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.53  % CPULimit : 300
% 0.13/0.54  % WCLimit  : 300
% 0.13/0.54  % DateTime : Tue Apr  8 14:16:07 EDT 2025
% 0.13/0.54  % CPUTime  : 
% 102.89/79.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 102.89/79.58  
% 102.89/79.58  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------