TSTP Solution File: NUM545+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM545+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/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 : n015.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 10:52:04 EDT 2023

% Result   : Theorem 11.62s 3.72s
% Output   : CNFRefutation 11.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   86 (  28 unt;  31 typ;   3 def)
%            Number of atoms       :  107 (  25 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   97 (  45   ~;  29   |;  10   &)
%                                         (   4 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   47 (  27   >;  20   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;   4 con; 0-3 aty)
%            Number of variables   :   26 (;  24   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xS > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_6 > #skF_1 > #skF_4 > #skF_12 > #skF_5 > #skF_10 > #skF_8 > #skF_3 > #skF_2 > #skF_9

%Foreground sorts:

%Background operators:

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

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

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

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

tff(szszuzczcdt0,type,
    szszuzczcdt0: $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(aElement0,type,
    aElement0: $i > $o ).

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

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

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

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

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

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

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

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

tff('#skF_5',type,
    '#skF_5': ( $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(aElementOf0,type,
    aElementOf0: ( $i * $i ) > $o ).

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

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

tff('#skF_3',type,
    '#skF_3': ( $i * $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_9',type,
    '#skF_9': ( $i * $i ) > $i ).

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

tff(f_52,definition,
    ! [W0] :
      ( ( W0 = slcrc0 )
    <=> ( aSet0(W0)
        & ~ ? [W1] : aElementOf0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).

tff(f_97,axiom,
    ! [W0] :
      ( aSet0(W0)
     => aSubsetOf0(W0,W0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).

tff(f_330,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( ( sbrdtbr0(W0) = sz00 )
      <=> ( W0 = slcrc0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).

tff(f_465,hypothesis,
    ( ( xS != slcrc0 )
   => aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2035) ).

tff(f_461,hypothesis,
    ( aSubsetOf0(xS,szNzAzT0)
    & isFinite0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1986) ).

tff(f_65,axiom,
    ! [W0] :
      ( ( aSet0(W0)
        & isCountable0(W0) )
     => ~ isFinite0(W0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).

tff(f_211,axiom,
    ( aSet0(szNzAzT0)
    & isCountable0(szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).

tff(f_84,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
               => aElementOf0(W2,W0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).

tff(f_405,definition,
    ! [W0] :
      ( ( aSubsetOf0(W0,szNzAzT0)
        & isFinite0(W0)
        & ( W0 != slcrc0 ) )
     => ! [W1] :
          ( ( W1 = szmzazxdt0(W0) )
        <=> ( aElementOf0(W1,W0)
            & ! [W2] :
                ( aElementOf0(W2,W0)
               => sdtlseqdt0(W2,W1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).

tff(f_219,axiom,
    ! [W0] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
        & ( szszuzczcdt0(W0) != sz00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).

tff(f_470,negated_conjecture,
    ~ ? [W0] :
        ( aElementOf0(W0,szNzAzT0)
        & aSubsetOf0(xS,slbdtrb0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_212,axiom,
    aElementOf0(sz00,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).

tff(f_440,axiom,
    slbdtrb0(sz00) = slcrc0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).

tff(c_14,plain,
    aSet0(slcrc0),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_34,plain,
    ! [W0_27] :
      ( aSubsetOf0(W0_27,W0_27)
      | ~ aSet0(W0_27) ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_154,plain,
    ( ( sbrdtbr0(slcrc0) = sz00 )
    | ~ aSet0(slcrc0) ),
    inference(cnfTransformation,[status(thm)],[f_330]) ).

tff(c_228,plain,
    sbrdtbr0(slcrc0) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_154]) ).

tff(c_224,plain,
    ( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
    | ( xS = slcrc0 ) ),
    inference(cnfTransformation,[status(thm)],[f_465]) ).

tff(c_443,plain,
    xS = slcrc0,
    inference(splitLeft,[status(thm)],[c_224]) ).

tff(c_220,plain,
    isFinite0(xS),
    inference(cnfTransformation,[status(thm)],[f_461]) ).

tff(c_253,plain,
    ! [W0_153] :
      ( ~ isFinite0(W0_153)
      | ~ isCountable0(W0_153)
      | ~ aSet0(W0_153) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_263,plain,
    ( ~ isCountable0(xS)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_220,c_253]) ).

tff(c_264,plain,
    ~ aSet0(xS),
    inference(splitLeft,[status(thm)],[c_263]) ).

tff(c_108,plain,
    aSet0(szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_211]) ).

tff(c_222,plain,
    aSubsetOf0(xS,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_461]) ).

tff(c_335,plain,
    ! [W1_167,W0_168] :
      ( aSet0(W1_167)
      | ~ aSubsetOf0(W1_167,W0_168)
      | ~ aSet0(W0_168) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_341,plain,
    ( aSet0(xS)
    | ~ aSet0(szNzAzT0) ),
    inference(resolution,[status(thm)],[c_222,c_335]) ).

tff(c_345,plain,
    aSet0(xS),
    inference(demodulation,[status(thm),theory(equality)],[c_108,c_341]) ).

tff(c_347,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_264,c_345]) ).

tff(c_349,plain,
    aSet0(xS),
    inference(splitRight,[status(thm)],[c_263]) ).

tff(c_378,plain,
    ! [W0_175] :
      ( ( slcrc0 = W0_175 )
      | ( sbrdtbr0(W0_175) != sz00 )
      | ~ aSet0(W0_175) ),
    inference(cnfTransformation,[status(thm)],[f_330]) ).

tff(c_392,plain,
    ( ( xS = slcrc0 )
    | ( sbrdtbr0(xS) != sz00 ) ),
    inference(resolution,[status(thm)],[c_349,c_378]) ).

tff(c_400,plain,
    sbrdtbr0(xS) != sz00,
    inference(splitLeft,[status(thm)],[c_392]) ).

tff(c_449,plain,
    sbrdtbr0(slcrc0) != sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_443,c_400]) ).

tff(c_458,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_228,c_449]) ).

tff(c_460,plain,
    xS != slcrc0,
    inference(splitRight,[status(thm)],[c_224]) ).

tff(c_178,plain,
    ! [W0_121] :
      ( aElementOf0(szmzazxdt0(W0_121),W0_121)
      | ( slcrc0 = W0_121 )
      | ~ isFinite0(W0_121)
      | ~ aSubsetOf0(W0_121,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_405]) ).

tff(c_959,plain,
    ! [W2_242,W0_243,W1_244] :
      ( aElementOf0(W2_242,W0_243)
      | ~ aElementOf0(W2_242,W1_244)
      | ~ aSubsetOf0(W1_244,W0_243)
      | ~ aSet0(W0_243) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_10121,plain,
    ! [W0_582,W0_583] :
      ( aElementOf0(szmzazxdt0(W0_582),W0_583)
      | ~ aSubsetOf0(W0_582,W0_583)
      | ~ aSet0(W0_583)
      | ( slcrc0 = W0_582 )
      | ~ isFinite0(W0_582)
      | ~ aSubsetOf0(W0_582,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_178,c_959]) ).

tff(c_114,plain,
    ! [W0_72] :
      ( aElementOf0(szszuzczcdt0(W0_72),szNzAzT0)
      | ~ aElementOf0(W0_72,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_219]) ).

tff(c_459,plain,
    aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))),
    inference(splitRight,[status(thm)],[c_224]) ).

tff(c_226,plain,
    ! [W0_148] :
      ( ~ aSubsetOf0(xS,slbdtrb0(W0_148))
      | ~ aElementOf0(W0_148,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_470]) ).

tff(c_469,plain,
    ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
    inference(resolution,[status(thm)],[c_459,c_226]) ).

tff(c_473,plain,
    ~ aElementOf0(szmzazxdt0(xS),szNzAzT0),
    inference(resolution,[status(thm)],[c_114,c_469]) ).

tff(c_10169,plain,
    ( ~ aSet0(szNzAzT0)
    | ( xS = slcrc0 )
    | ~ isFinite0(xS)
    | ~ aSubsetOf0(xS,szNzAzT0) ),
    inference(resolution,[status(thm)],[c_10121,c_473]) ).

tff(c_10205,plain,
    xS = slcrc0,
    inference(demodulation,[status(thm),theory(equality)],[c_222,c_220,c_108,c_10169]) ).

tff(c_10207,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_460,c_10205]) ).

tff(c_10208,plain,
    xS = slcrc0,
    inference(splitRight,[status(thm)],[c_392]) ).

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

tff(c_208,plain,
    slbdtrb0(sz00) = slcrc0,
    inference(cnfTransformation,[status(thm)],[f_440]) ).

tff(c_240,plain,
    ( ~ aSubsetOf0(xS,slcrc0)
    | ~ aElementOf0(sz00,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_208,c_226]) ).

tff(c_244,plain,
    ~ aSubsetOf0(xS,slcrc0),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_240]) ).

tff(c_10212,plain,
    ~ aSubsetOf0(slcrc0,slcrc0),
    inference(demodulation,[status(thm),theory(equality)],[c_10208,c_244]) ).

tff(c_10225,plain,
    ~ aSet0(slcrc0),
    inference(resolution,[status(thm)],[c_34,c_10212]) ).

tff(c_10229,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_10225]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM545+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/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
% 0.14/0.35  % Computer : n015.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
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 15:18:29 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 11.62/3.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.62/3.73  
% 11.62/3.73  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.91/3.76  
% 11.91/3.76  Inference rules
% 11.91/3.76  ----------------------
% 11.91/3.76  #Ref     : 1
% 11.91/3.76  #Sup     : 1978
% 11.91/3.76  #Fact    : 0
% 11.91/3.76  #Define  : 0
% 11.91/3.76  #Split   : 45
% 11.91/3.76  #Chain   : 0
% 11.91/3.76  #Close   : 0
% 11.91/3.76  
% 11.91/3.76  Ordering : KBO
% 11.91/3.76  
% 11.91/3.76  Simplification rules
% 11.91/3.76  ----------------------
% 11.91/3.76  #Subsume      : 654
% 11.91/3.76  #Demod        : 1795
% 11.91/3.76  #Tautology    : 446
% 11.91/3.76  #SimpNegUnit  : 210
% 11.91/3.76  #BackRed      : 113
% 11.91/3.76  
% 11.91/3.76  #Partial instantiations: 0
% 11.91/3.76  #Strategies tried      : 1
% 11.91/3.76  
% 11.91/3.76  Timing (in seconds)
% 11.91/3.76  ----------------------
% 11.91/3.76  Preprocessing        : 0.72
% 11.91/3.76  Parsing              : 0.36
% 11.91/3.76  CNF conversion       : 0.06
% 11.91/3.76  Main loop            : 1.98
% 11.91/3.76  Inferencing          : 0.72
% 11.91/3.76  Reduction            : 0.57
% 11.91/3.76  Demodulation         : 0.38
% 11.91/3.76  BG Simplification    : 0.08
% 11.91/3.76  Subsumption          : 0.48
% 11.91/3.76  Abstraction          : 0.07
% 11.91/3.76  MUC search           : 0.00
% 11.91/3.76  Cooper               : 0.00
% 11.91/3.76  Total                : 2.75
% 11.91/3.76  Index Insertion      : 0.00
% 11.91/3.76  Index Deletion       : 0.00
% 11.91/3.76  Index Matching       : 0.00
% 11.91/3.76  BG Taut test         : 0.00
%------------------------------------------------------------------------------