TSTP Solution File: RNG119+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG119+4 : 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 10:55:01 EDT 2023

% Result   : Theorem 84.98s 67.67s
% Output   : CNFRefutation 85.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   87
% Syntax   : Number of formulae    :  190 (  65 unt;  71 typ;   0 def)
%            Number of atoms       :  256 ( 115 equ)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives :  215 (  78   ~;  70   |;  50   &)
%                                         (   5 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   95 (  48   >;  47   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   60 (  60 usr;  23 con; 0-4 aty)
%            Number of variables   :   76 (;  57   !;  19   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aGcdOfAnd0 > misRelativelyPrime0 > iLess0 > doDivides0 > aElementOf0 > aDivisorOf0 > aSet0 > aNaturalNumber0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > slsdtgt0 > sbrdtbr0 > xu > xr > xq > xc > xb > xa > xI > sz10 > sz00 > #skF_33 > #skF_41 > #skF_22 > #skF_24 > #skF_6 > #skF_31 > #skF_17 > #skF_25 > #skF_20 > #skF_36 > #skF_43 > #skF_40 > #skF_4 > #skF_37 > #skF_8 > #skF_14 > #skF_15 > #skF_29 > #skF_26 > #skF_18 > #skF_23 > #skF_28 > #skF_5 > #skF_19 > #skF_38 > #skF_7 > #skF_32 > #skF_39 > #skF_9 > #skF_13 > #skF_42 > #skF_11 > #skF_3 > #skF_2 > #skF_35 > #skF_27 > #skF_44 > #skF_12 > #skF_1 > #skF_16 > #skF_21 > #skF_30 > #skF_10 > #skF_34

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_33',type,
    '#skF_33': $i ).

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

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

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

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

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

tff(sdtasdt0,type,
    sdtasdt0: ( $i * $i ) > $i ).

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

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

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

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

tff(sz10,type,
    sz10: $i ).

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

tff(sdtpldt1,type,
    sdtpldt1: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

tff(misRelativelyPrime0,type,
    misRelativelyPrime0: ( $i * $i ) > $o ).

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

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

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

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

tff(aIdeal0,type,
    aIdeal0: $i > $o ).

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

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

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

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

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

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

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

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

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

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

tff(aNaturalNumber0,type,
    aNaturalNumber0: $i > $o ).

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

tff(slsdtgt0,type,
    slsdtgt0: $i > $i ).

tff(smndt0,type,
    smndt0: $i > $i ).

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

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

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

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

tff(doDivides0,type,
    doDivides0: ( $i * $i ) > $o ).

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

tff(aGcdOfAnd0,type,
    aGcdOfAnd0: ( $i * $i * $i ) > $o ).

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

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

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

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

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

tff('#skF_42',type,
    '#skF_42': $i ).

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

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

tff(aDivisorOf0,type,
    aDivisorOf0: ( $i * $i ) > $o ).

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

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

tff(sdtasasdt0,type,
    sdtasasdt0: ( $i * $i ) > $i ).

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

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

tff('#skF_44',type,
    '#skF_44': $i ).

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

tff(sdteqdtlpzmzozddtrp0,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

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

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

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

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

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

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

tff(f_452,hypothesis,
    ( aSet0(xI)
    & ! [W0] :
        ( aElementOf0(W0,xI)
       => ( ! [W1] :
              ( aElementOf0(W1,xI)
             => aElementOf0(sdtpldt0(W0,W1),xI) )
          & ! [W1] :
              ( aElement0(W1)
             => aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
    & aIdeal0(xI)
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xa))
      <=> ? [W1] :
            ( aElement0(W1)
            & ( sdtasdt0(xa,W1) = W0 ) ) )
    & ! [W0] :
        ( aElementOf0(W0,slsdtgt0(xb))
      <=> ? [W1] :
            ( aElement0(W1)
            & ( sdtasdt0(xb,W1) = W0 ) ) )
    & ! [W0] :
        ( aElementOf0(W0,xI)
      <=> ? [W1,W2] :
            ( aElementOf0(W1,slsdtgt0(xa))
            & aElementOf0(W2,slsdtgt0(xb))
            & ( sdtpldt0(W1,W2) = W0 ) ) )
    & ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).

tff(f_534,hypothesis,
    ( ? [W0,W1] :
        ( aElementOf0(W0,slsdtgt0(xa))
        & aElementOf0(W1,slsdtgt0(xb))
        & ( sdtpldt0(W0,W1) = xu ) )
    & aElementOf0(xu,xI)
    & ( xu != sz00 )
    & ! [W0] :
        ( ( ( ? [W1,W2] :
                ( aElementOf0(W1,slsdtgt0(xa))
                & aElementOf0(W2,slsdtgt0(xb))
                & ( sdtpldt0(W1,W2) = W0 ) )
            | aElementOf0(W0,xI) )
          & ( W0 != sz00 ) )
       => ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2273) ).

tff(f_137,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).

tff(f_582,hypothesis,
    ( aElement0(xq)
    & aElement0(xr)
    & ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) )
    & ( ( xr = sz00 )
      | iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).

tff(f_79,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).

tff(f_573,hypothesis,
    ~ ( ? [W0] :
          ( aElement0(W0)
          & ( sdtasdt0(xu,W0) = xb ) )
      | doDivides0(xu,xb) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2612) ).

tff(f_357,hypothesis,
    ( ( xa != sz00 )
    | ( xb != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2110) ).

tff(f_352,hypothesis,
    ( aElement0(xa)
    & aElement0(xb) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).

tff(f_479,hypothesis,
    ( ? [W0] :
        ( aElement0(W0)
        & ( sdtasdt0(xa,W0) = sz00 ) )
    & aElementOf0(sz00,slsdtgt0(xa))
    & ? [W0] :
        ( aElement0(W0)
        & ( sdtasdt0(xa,W0) = xa ) )
    & aElementOf0(xa,slsdtgt0(xa))
    & ? [W0] :
        ( aElement0(W0)
        & ( sdtasdt0(xb,W0) = sz00 ) )
    & aElementOf0(sz00,slsdtgt0(xb))
    & ? [W0] :
        ( aElement0(W0)
        & ( sdtasdt0(xb,W0) = xb ) )
    & aElementOf0(xb,slsdtgt0(xb)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).

tff(f_125,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => ( ( sdtasdt0(W0,W1) = sz00 )
       => ( ( W0 = sz00 )
          | ( W1 = sz00 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCancel) ).

tff(f_115,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).

tff(f_585,negated_conjecture,
    xr != sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_47,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).

tff(f_67,axiom,
    ! [W0] :
      ( aElement0(W0)
     => ( ( sdtpldt0(W0,sz00) = W0 )
        & ( W0 = sdtpldt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).

tff(f_507,hypothesis,
    ? [W0] :
      ( ! [W1] :
          ( aElementOf0(W1,slsdtgt0(xa))
        <=> ? [W2] :
              ( aElement0(W2)
              & ( sdtasdt0(xa,W2) = W1 ) ) )
      & ! [W1] :
          ( aElementOf0(W1,slsdtgt0(xb))
        <=> ? [W2] :
              ( aElement0(W2)
              & ( sdtasdt0(xb,W2) = W1 ) ) )
      & ? [W1,W2] :
          ( aElementOf0(W1,slsdtgt0(xa))
          & aElementOf0(W2,slsdtgt0(xb))
          & ( sdtpldt0(W1,W2) = W0 ) )
      & aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
      & ( W0 != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2228) ).

tff(f_566,hypothesis,
    ~ ~ ( ? [W0] :
            ( aElement0(W0)
            & ( sdtasdt0(xu,W0) = xa ) )
        & doDivides0(xu,xa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2479) ).

tff(c_300,plain,
    aSet0(xI),
    inference(cnfTransformation,[status(thm)],[f_452]) ).

tff(c_368,plain,
    aElementOf0(xu,xI),
    inference(cnfTransformation,[status(thm)],[f_534]) ).

tff(c_1498,plain,
    ! [W1_294,W0_295] :
      ( aElement0(W1_294)
      | ~ aElementOf0(W1_294,W0_295)
      | ~ aSet0(W0_295) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_1528,plain,
    ( aElement0(xu)
    | ~ aSet0(xI) ),
    inference(resolution,[status(thm)],[c_368,c_1498]) ).

tff(c_1546,plain,
    aElement0(xu),
    inference(demodulation,[status(thm),theory(equality)],[c_300,c_1528]) ).

tff(c_420,plain,
    aElement0(xq),
    inference(cnfTransformation,[status(thm)],[f_582]) ).

tff(c_4575,plain,
    ! [W1_341,W0_342] :
      ( ( sdtasdt0(W1_341,W0_342) = sdtasdt0(W0_342,W1_341) )
      | ~ aElement0(W1_341)
      | ~ aElement0(W0_342) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_71341,plain,
    ! [W0_627] :
      ( ( sdtasdt0(xq,W0_627) = sdtasdt0(W0_627,xq) )
      | ~ aElement0(W0_627) ),
    inference(resolution,[status(thm)],[c_420,c_4575]) ).

tff(c_72093,plain,
    sdtasdt0(xu,xq) = sdtasdt0(xq,xu),
    inference(resolution,[status(thm)],[c_1546,c_71341]) ).

tff(c_480,plain,
    ! [W0_280] :
      ( ( sdtasdt0(xu,W0_280) != xb )
      | ~ aElement0(W0_280) ),
    inference(cnfTransformation,[status(thm)],[f_573]) ).

tff(c_545,plain,
    sdtasdt0(xu,xq) != xb,
    inference(resolution,[status(thm)],[c_420,c_480]) ).

tff(c_104636,plain,
    sdtasdt0(xq,xu) != xb,
    inference(demodulation,[status(thm),theory(equality)],[c_72093,c_545]) ).

tff(c_212,plain,
    ( ( xb != sz00 )
    | ( xa != sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_357]) ).

tff(c_455,plain,
    xa != sz00,
    inference(splitLeft,[status(thm)],[c_212]) ).

tff(c_210,plain,
    aElement0(xa),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

tff(c_342,plain,
    aElement0('#skF_34'),
    inference(cnfTransformation,[status(thm)],[f_479]) ).

tff(c_340,plain,
    sdtasdt0(xa,'#skF_34') = sz00,
    inference(cnfTransformation,[status(thm)],[f_479]) ).

tff(c_5834,plain,
    ! [W1_366,W0_367] :
      ( ( sz00 = W1_366 )
      | ( sz00 = W0_367 )
      | ( sdtasdt0(W0_367,W1_366) != sz00 )
      | ~ aElement0(W1_366)
      | ~ aElement0(W0_367) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_6018,plain,
    ( ( sz00 = '#skF_34' )
    | ( xa = sz00 )
    | ~ aElement0('#skF_34')
    | ~ aElement0(xa) ),
    inference(superposition,[status(thm),theory(equality)],[c_340,c_5834]) ).

tff(c_6330,plain,
    ( ( sz00 = '#skF_34' )
    | ( xa = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_210,c_342,c_6018]) ).

tff(c_6331,plain,
    sz00 = '#skF_34',
    inference(negUnitSimplification,[status(thm)],[c_455,c_6330]) ).

tff(c_44,plain,
    ! [W0_24] :
      ( ( sdtasdt0(W0_24,sz00) = sz00 )
      | ~ aElement0(W0_24) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_1601,plain,
    sdtasdt0(xu,sz00) = sz00,
    inference(resolution,[status(thm)],[c_1546,c_44]) ).

tff(c_422,plain,
    xr = sz00,
    inference(cnfTransformation,[status(thm)],[f_585]) ).

tff(c_418,plain,
    aElement0(xr),
    inference(cnfTransformation,[status(thm)],[f_582]) ).

tff(c_423,plain,
    aElement0(sz00),
    inference(demodulation,[status(thm),theory(equality)],[c_422,c_418]) ).

tff(c_532,plain,
    sdtasdt0(xu,sz00) != xb,
    inference(resolution,[status(thm)],[c_423,c_480]) ).

tff(c_2755,plain,
    xb != sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_1601,c_532]) ).

tff(c_208,plain,
    aElement0(xb),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

tff(c_330,plain,
    aElement0('#skF_32'),
    inference(cnfTransformation,[status(thm)],[f_479]) ).

tff(c_328,plain,
    sdtasdt0(xb,'#skF_32') = sz00,
    inference(cnfTransformation,[status(thm)],[f_479]) ).

tff(c_6014,plain,
    ( ( sz00 = '#skF_32' )
    | ( xb = sz00 )
    | ~ aElement0('#skF_32')
    | ~ aElement0(xb) ),
    inference(superposition,[status(thm),theory(equality)],[c_328,c_5834]) ).

tff(c_6323,plain,
    ( ( sz00 = '#skF_32' )
    | ( xb = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_330,c_6014]) ).

tff(c_6324,plain,
    sz00 = '#skF_32',
    inference(negUnitSimplification,[status(thm)],[c_2755,c_6323]) ).

tff(c_6672,plain,
    '#skF_32' = '#skF_34',
    inference(demodulation,[status(thm),theory(equality)],[c_6331,c_6324]) ).

tff(c_416,plain,
    sdtpldt0(sdtasdt0(xq,xu),xr) = xb,
    inference(cnfTransformation,[status(thm)],[f_582]) ).

tff(c_424,plain,
    sdtpldt0(sdtasdt0(xq,xu),sz00) = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_422,c_416]) ).

tff(c_6426,plain,
    sdtpldt0(sdtasdt0(xq,xu),'#skF_32') = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_6324,c_424]) ).

tff(c_28918,plain,
    sdtpldt0(sdtasdt0(xq,xu),'#skF_34') = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_6672,c_6426]) ).

tff(c_12,plain,
    ! [W0_5,W1_6] :
      ( aElement0(sdtasdt0(W0_5,W1_6))
      | ~ aElement0(W1_6)
      | ~ aElement0(W0_5) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_104713,plain,
    ( aElement0(sdtasdt0(xq,xu))
    | ~ aElement0(xq)
    | ~ aElement0(xu) ),
    inference(superposition,[status(thm),theory(equality)],[c_72093,c_12]) ).

tff(c_104777,plain,
    aElement0(sdtasdt0(xq,xu)),
    inference(demodulation,[status(thm),theory(equality)],[c_1546,c_420,c_104713]) ).

tff(c_20,plain,
    ! [W0_12] :
      ( ( sdtpldt0(W0_12,sz00) = W0_12 )
      | ~ aElement0(W0_12) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_6440,plain,
    ! [W0_12] :
      ( ( sdtpldt0(W0_12,'#skF_32') = W0_12 )
      | ~ aElement0(W0_12) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6324,c_20]) ).

tff(c_24794,plain,
    ! [W0_12] :
      ( ( sdtpldt0(W0_12,'#skF_34') = W0_12 )
      | ~ aElement0(W0_12) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6672,c_6440]) ).

tff(c_105010,plain,
    sdtpldt0(sdtasdt0(xq,xu),'#skF_34') = sdtasdt0(xq,xu),
    inference(resolution,[status(thm)],[c_104777,c_24794]) ).

tff(c_105058,plain,
    sdtasdt0(xq,xu) = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_28918,c_105010]) ).

tff(c_105060,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_104636,c_105058]) ).

tff(c_105062,plain,
    xa = sz00,
    inference(splitRight,[status(thm)],[c_212]) ).

tff(c_374,plain,
    aElementOf0('#skF_40',slsdtgt0(xa)),
    inference(cnfTransformation,[status(thm)],[f_534]) ).

tff(c_105067,plain,
    aElementOf0('#skF_40',slsdtgt0(sz00)),
    inference(demodulation,[status(thm),theory(equality)],[c_105062,c_374]) ).

tff(c_362,plain,
    ! [W1_264] :
      ( ( sdtasdt0(xa,'#skF_39'(W1_264)) = W1_264 )
      | ~ aElementOf0(W1_264,slsdtgt0(xa)) ),
    inference(cnfTransformation,[status(thm)],[f_507]) ).

tff(c_107634,plain,
    ! [W1_718] :
      ( ( sdtasdt0(sz00,'#skF_39'(W1_718)) = W1_718 )
      | ~ aElementOf0(W1_718,slsdtgt0(sz00)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_105062,c_105062,c_362]) ).

tff(c_107660,plain,
    sdtasdt0(sz00,'#skF_39'('#skF_40')) = '#skF_40',
    inference(resolution,[status(thm)],[c_105067,c_107634]) ).

tff(c_364,plain,
    ! [W1_264] :
      ( aElement0('#skF_39'(W1_264))
      | ~ aElementOf0(W1_264,slsdtgt0(xa)) ),
    inference(cnfTransformation,[status(thm)],[f_507]) ).

tff(c_105846,plain,
    ! [W1_686] :
      ( aElement0('#skF_39'(W1_686))
      | ~ aElementOf0(W1_686,slsdtgt0(sz00)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_105062,c_364]) ).

tff(c_105857,plain,
    aElement0('#skF_39'('#skF_40')),
    inference(resolution,[status(thm)],[c_105067,c_105846]) ).

tff(c_42,plain,
    ! [W0_24] :
      ( ( sdtasdt0(sz00,W0_24) = sz00 )
      | ~ aElement0(W0_24) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_105912,plain,
    sdtasdt0(sz00,'#skF_39'('#skF_40')) = sz00,
    inference(resolution,[status(thm)],[c_105857,c_42]) ).

tff(c_108860,plain,
    sz00 = '#skF_40',
    inference(demodulation,[status(thm),theory(equality)],[c_107660,c_105912]) ).

tff(c_366,plain,
    xu != sz00,
    inference(cnfTransformation,[status(thm)],[f_534]) ).

tff(c_108991,plain,
    xu != '#skF_40',
    inference(demodulation,[status(thm),theory(equality)],[c_108860,c_366]) ).

tff(c_106146,plain,
    ! [W1_689,W0_690] :
      ( aElement0(W1_689)
      | ~ aElementOf0(W1_689,W0_690)
      | ~ aSet0(W0_690) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_106173,plain,
    ( aElement0(xu)
    | ~ aSet0(xI) ),
    inference(resolution,[status(thm)],[c_368,c_106146]) ).

tff(c_106189,plain,
    aElement0(xu),
    inference(demodulation,[status(thm),theory(equality)],[c_300,c_106173]) ).

tff(c_408,plain,
    aElement0('#skF_44'),
    inference(cnfTransformation,[status(thm)],[f_566]) ).

tff(c_406,plain,
    sdtasdt0(xu,'#skF_44') = xa,
    inference(cnfTransformation,[status(thm)],[f_566]) ).

tff(c_105097,plain,
    sdtasdt0(xu,'#skF_44') = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_105062,c_406]) ).

tff(c_108978,plain,
    sdtasdt0(xu,'#skF_44') = '#skF_40',
    inference(demodulation,[status(thm),theory(equality)],[c_108860,c_105097]) ).

tff(c_46,plain,
    ! [W1_26,W0_25] :
      ( ( sz00 = W1_26 )
      | ( sz00 = W0_25 )
      | ( sdtasdt0(W0_25,W1_26) != sz00 )
      | ~ aElement0(W1_26)
      | ~ aElement0(W0_25) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_111350,plain,
    ! [W1_771,W0_772] :
      ( ( W1_771 = '#skF_40' )
      | ( W0_772 = '#skF_40' )
      | ( sdtasdt0(W0_772,W1_771) != '#skF_40' )
      | ~ aElement0(W1_771)
      | ~ aElement0(W0_772) ),
    inference(demodulation,[status(thm),theory(equality)],[c_108860,c_108860,c_108860,c_46]) ).

tff(c_111386,plain,
    ( ( '#skF_40' = '#skF_44' )
    | ( xu = '#skF_40' )
    | ~ aElement0('#skF_44')
    | ~ aElement0(xu) ),
    inference(superposition,[status(thm),theory(equality)],[c_108978,c_111350]) ).

tff(c_111564,plain,
    ( ( '#skF_40' = '#skF_44' )
    | ( xu = '#skF_40' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106189,c_408,c_111386]) ).

tff(c_111565,plain,
    '#skF_40' = '#skF_44',
    inference(negUnitSimplification,[status(thm)],[c_108991,c_111564]) ).

tff(c_370,plain,
    sdtpldt0('#skF_40','#skF_41') = xu,
    inference(cnfTransformation,[status(thm)],[f_534]) ).

tff(c_111843,plain,
    sdtpldt0('#skF_44','#skF_41') = xu,
    inference(demodulation,[status(thm),theory(equality)],[c_111565,c_370]) ).

tff(c_372,plain,
    aElementOf0('#skF_41',slsdtgt0(xb)),
    inference(cnfTransformation,[status(thm)],[f_534]) ).

tff(c_106045,plain,
    ! [W1_688] :
      ( aElement0('#skF_38'(W1_688))
      | ~ aElementOf0(W1_688,slsdtgt0(xb)) ),
    inference(cnfTransformation,[status(thm)],[f_507]) ).

tff(c_106061,plain,
    aElement0('#skF_38'('#skF_41')),
    inference(resolution,[status(thm)],[c_372,c_106045]) ).

tff(c_107523,plain,
    ! [W1_716] :
      ( ( sdtasdt0(xb,'#skF_38'(W1_716)) = W1_716 )
      | ~ aElementOf0(W1_716,slsdtgt0(xb)) ),
    inference(cnfTransformation,[status(thm)],[f_507]) ).

tff(c_107552,plain,
    sdtasdt0(xb,'#skF_38'('#skF_41')) = '#skF_41',
    inference(resolution,[status(thm)],[c_372,c_107523]) ).

tff(c_107802,plain,
    ( aElement0('#skF_41')
    | ~ aElement0('#skF_38'('#skF_41'))
    | ~ aElement0(xb) ),
    inference(superposition,[status(thm),theory(equality)],[c_107552,c_12]) ).

tff(c_107808,plain,
    aElement0('#skF_41'),
    inference(demodulation,[status(thm),theory(equality)],[c_208,c_106061,c_107802]) ).

tff(c_18,plain,
    ! [W0_12] :
      ( ( sdtpldt0(sz00,W0_12) = W0_12 )
      | ~ aElement0(W0_12) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_107831,plain,
    sdtpldt0(sz00,'#skF_41') = '#skF_41',
    inference(resolution,[status(thm)],[c_107808,c_18]) ).

tff(c_108874,plain,
    sdtpldt0('#skF_40','#skF_41') = '#skF_41',
    inference(demodulation,[status(thm),theory(equality)],[c_108860,c_107831]) ).

tff(c_126601,plain,
    xu = '#skF_41',
    inference(demodulation,[status(thm),theory(equality)],[c_111843,c_111565,c_108874]) ).

tff(c_105114,plain,
    ! [W0_674] :
      ( ( sdtasdt0(xu,W0_674) != xb )
      | ~ aElement0(W0_674) ),
    inference(cnfTransformation,[status(thm)],[f_573]) ).

tff(c_105175,plain,
    sdtasdt0(xu,xq) != xb,
    inference(resolution,[status(thm)],[c_420,c_105114]) ).

tff(c_126633,plain,
    sdtasdt0('#skF_41',xq) != xb,
    inference(demodulation,[status(thm),theory(equality)],[c_126601,c_105175]) ).

tff(c_108372,plain,
    ! [W1_724,W0_725] :
      ( ( sdtasdt0(W1_724,W0_725) = sdtasdt0(W0_725,W1_724) )
      | ~ aElement0(W1_724)
      | ~ aElement0(W0_725) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_137304,plain,
    ! [W0_1095] :
      ( ( sdtasdt0(xq,W0_1095) = sdtasdt0(W0_1095,xq) )
      | ~ aElement0(W0_1095) ),
    inference(resolution,[status(thm)],[c_420,c_108372]) ).

tff(c_137473,plain,
    sdtasdt0(xq,'#skF_41') = sdtasdt0('#skF_41',xq),
    inference(resolution,[status(thm)],[c_107808,c_137304]) ).

tff(c_108955,plain,
    sdtpldt0(sdtasdt0(xq,xu),'#skF_40') = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_108860,c_424]) ).

tff(c_177362,plain,
    sdtpldt0(sdtasdt0(xq,'#skF_41'),'#skF_44') = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_111565,c_126601,c_108955]) ).

tff(c_183893,plain,
    sdtpldt0(sdtasdt0('#skF_41',xq),'#skF_44') = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_137473,c_177362]) ).

tff(c_111837,plain,
    sz00 = '#skF_44',
    inference(demodulation,[status(thm),theory(equality)],[c_111565,c_108860]) ).

tff(c_106576,plain,
    ! [W0_704,W1_705] :
      ( aElement0(sdtasdt0(W0_704,W1_705))
      | ~ aElement0(W1_705)
      | ~ aElement0(W0_704) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_106766,plain,
    ! [W0_704,W1_705] :
      ( ( sdtpldt0(sdtasdt0(W0_704,W1_705),sz00) = sdtasdt0(W0_704,W1_705) )
      | ~ aElement0(W1_705)
      | ~ aElement0(W0_704) ),
    inference(resolution,[status(thm)],[c_106576,c_20]) ).

tff(c_187546,plain,
    ! [W0_704,W1_705] :
      ( ( sdtpldt0(sdtasdt0(W0_704,W1_705),'#skF_44') = sdtasdt0(W0_704,W1_705) )
      | ~ aElement0(W1_705)
      | ~ aElement0(W0_704) ),
    inference(demodulation,[status(thm),theory(equality)],[c_111837,c_106766]) ).

tff(c_188894,plain,
    ( ( sdtasdt0('#skF_41',xq) = xb )
    | ~ aElement0(xq)
    | ~ aElement0('#skF_41') ),
    inference(superposition,[status(thm),theory(equality)],[c_183893,c_187546]) ).

tff(c_188937,plain,
    sdtasdt0('#skF_41',xq) = xb,
    inference(demodulation,[status(thm),theory(equality)],[c_107808,c_420,c_188894]) ).

tff(c_188939,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_126633,c_188937]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG119+4 : 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 18:09:19 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 84.98/67.67  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 85.00/67.68  
% 85.00/67.68  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 85.18/67.72  
% 85.18/67.72  Inference rules
% 85.18/67.72  ----------------------
% 85.18/67.72  #Ref     : 0
% 85.18/67.72  #Sup     : 44782
% 85.18/67.72  #Fact    : 0
% 85.18/67.72  #Define  : 0
% 85.18/67.72  #Split   : 24
% 85.18/67.72  #Chain   : 0
% 85.18/67.72  #Close   : 0
% 85.18/67.72  
% 85.18/67.72  Ordering : KBO
% 85.18/67.72  
% 85.18/67.72  Simplification rules
% 85.18/67.72  ----------------------
% 85.18/67.72  #Subsume      : 4207
% 85.18/67.72  #Demod        : 50639
% 85.18/67.72  #Tautology    : 10147
% 85.18/67.72  #SimpNegUnit  : 150
% 85.18/67.72  #BackRed      : 597
% 85.18/67.72  
% 85.18/67.72  #Partial instantiations: 0
% 85.18/67.72  #Strategies tried      : 1
% 85.18/67.72  
% 85.18/67.72  Timing (in seconds)
% 85.18/67.72  ----------------------
% 85.18/67.73  Preprocessing        : 0.81
% 85.18/67.73  Parsing              : 0.39
% 85.18/67.73  CNF conversion       : 0.08
% 85.18/67.73  Main loop            : 65.78
% 85.18/67.73  Inferencing          : 6.54
% 85.18/67.73  Reduction            : 41.68
% 85.18/67.73  Demodulation         : 37.04
% 85.18/67.73  BG Simplification    : 0.32
% 85.18/67.73  Subsumption          : 13.97
% 85.18/67.73  Abstraction          : 0.48
% 85.18/67.73  MUC search           : 0.00
% 85.18/67.73  Cooper               : 0.00
% 85.18/67.73  Total                : 66.67
% 85.18/67.73  Index Insertion      : 0.00
% 85.18/67.73  Index Deletion       : 0.00
% 85.18/67.73  Index Matching       : 0.00
% 85.18/67.73  BG Taut test         : 0.00
%------------------------------------------------------------------------------