TSTP Solution File: NUM558+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM558+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 : n005.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 10:52:07 EDT 2023

% Result   : Theorem 7.75s 2.65s
% Output   : CNFRefutation 7.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   52
% Syntax   : Number of formulae    :   74 (  14 unt;  45 typ;   0 def)
%            Number of atoms       :  102 (  15 equ)
%            Maximal formula atoms :   43 (   3 avg)
%            Number of connectives :   95 (  22   ~;  18   |;  36   &)
%                                         (   2 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   59 (  34   >;  25   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   37 (  37 usr;  11 con; 0-3 aty)
%            Number of variables   :   24 (;  23   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xy > xx > xk > xT > xS > xQ > xP > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_16 > #skF_18 > #skF_17 > #skF_6 > #skF_19 > #skF_1 > #skF_4 > #skF_12 > #skF_5 > #skF_10 > #skF_8 > #skF_15 > #skF_13 > #skF_14 > #skF_3 > #skF_2 > #skF_9

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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_683,hypothesis,
    ( ! [W0] :
        ( aElementOf0(W0,xP)
       => aElementOf0(W0,xS) )
    & aSubsetOf0(xP,xS)
    & ( sbrdtbr0(xP) = xk )
    & aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2378) ).

tff(f_624,hypothesis,
    ( aSet0(slbdtsldtrb0(xS,xk))
    & ! [W0] :
        ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
         => ( aSet0(W0)
            & ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xS) )
            & aSubsetOf0(W0,xS)
            & ( sbrdtbr0(W0) = xk ) ) )
        & ( ( ( ( aSet0(W0)
                & ! [W1] :
                    ( aElementOf0(W1,W0)
                   => aElementOf0(W1,xS) ) )
              | aSubsetOf0(W0,xS) )
            & ( sbrdtbr0(W0) = xk ) )
         => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
    & aSet0(slbdtsldtrb0(xT,xk))
    & ! [W0] :
        ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
         => ( aSet0(W0)
            & ! [W1] :
                ( aElementOf0(W1,W0)
               => aElementOf0(W1,xT) )
            & aSubsetOf0(W0,xT)
            & ( sbrdtbr0(W0) = xk ) ) )
        & ( ( ( ( aSet0(W0)
                & ! [W1] :
                    ( aElementOf0(W1,W0)
                   => aElementOf0(W1,xT) ) )
              | aSubsetOf0(W0,xT) )
            & ( sbrdtbr0(W0) = xk ) )
         => aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
    & ! [W0] :
        ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
       => aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
    & ~ ( ! [W0] :
            ( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
             => ( aSet0(W0)
                & ! [W1] :
                    ( aElementOf0(W1,W0)
                   => aElementOf0(W1,xS) )
                & aSubsetOf0(W0,xS)
                & ( sbrdtbr0(W0) = xk ) ) )
            & ( ( ( ( aSet0(W0)
                    & ! [W1] :
                        ( aElementOf0(W1,W0)
                       => aElementOf0(W1,xS) ) )
                  | aSubsetOf0(W0,xS) )
                & ( sbrdtbr0(W0) = xk ) )
             => aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
       => ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
          | ( slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).

tff(f_685,negated_conjecture,
    ~ aElementOf0(xx,xT),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_673,hypothesis,
    ( aSet0(sdtmndt0(xQ,xy))
    & ! [W0] :
        ( aElementOf0(W0,sdtmndt0(xQ,xy))
      <=> ( aElement0(W0)
          & aElementOf0(W0,xQ)
          & ( W0 != xy ) ) )
    & aSet0(xP)
    & ! [W0] :
        ( aElementOf0(W0,xP)
      <=> ( aElement0(W0)
          & ( aElementOf0(W0,sdtmndt0(xQ,xy))
            | ( W0 = xx ) ) ) )
    & ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).

tff(f_526,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & ( xk != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).

tff(f_625,hypothesis,
    aElementOf0(xx,xS),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).

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

tff(c_364,plain,
    sbrdtbr0(xP) = xk,
    inference(cnfTransformation,[status(thm)],[f_683]) ).

tff(c_362,plain,
    aElementOf0(xP,slbdtsldtrb0(xS,xk)),
    inference(cnfTransformation,[status(thm)],[f_683]) ).

tff(c_1632,plain,
    ! [W0_275] :
      ( aElementOf0(W0_275,slbdtsldtrb0(xT,xk))
      | ~ aElementOf0(W0_275,slbdtsldtrb0(xS,xk)) ),
    inference(cnfTransformation,[status(thm)],[f_624]) ).

tff(c_288,plain,
    ! [W0_176] :
      ( aSubsetOf0(W0_176,xT)
      | ~ aElementOf0(W0_176,slbdtsldtrb0(xT,xk)) ),
    inference(cnfTransformation,[status(thm)],[f_624]) ).

tff(c_1696,plain,
    ! [W0_277] :
      ( aSubsetOf0(W0_277,xT)
      | ~ aElementOf0(W0_277,slbdtsldtrb0(xS,xk)) ),
    inference(resolution,[status(thm)],[c_1632,c_288]) ).

tff(c_1722,plain,
    aSubsetOf0(xP,xT),
    inference(resolution,[status(thm)],[c_362,c_1696]) ).

tff(c_294,plain,
    ! [W0_176] :
      ( ~ aSubsetOf0(W0_176,xT)
      | aElementOf0(W0_176,slbdtsldtrb0(xT,xk))
      | ( sbrdtbr0(W0_176) != xk ) ),
    inference(cnfTransformation,[status(thm)],[f_624]) ).

tff(c_370,plain,
    ~ aElementOf0(xx,xT),
    inference(cnfTransformation,[status(thm)],[f_685]) ).

tff(c_352,plain,
    ( aElementOf0(xx,xP)
    | ~ aElement0(xx) ),
    inference(cnfTransformation,[status(thm)],[f_673]) ).

tff(c_413,plain,
    ~ aElement0(xx),
    inference(splitLeft,[status(thm)],[c_352]) ).

tff(c_258,plain,
    aSet0(xS),
    inference(cnfTransformation,[status(thm)],[f_526]) ).

tff(c_314,plain,
    aElementOf0(xx,xS),
    inference(cnfTransformation,[status(thm)],[f_625]) ).

tff(c_588,plain,
    ! [W1_212,W0_213] :
      ( aElement0(W1_212)
      | ~ aElementOf0(W1_212,W0_213)
      | ~ aSet0(W0_213) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_609,plain,
    ( aElement0(xx)
    | ~ aSet0(xS) ),
    inference(resolution,[status(thm)],[c_314,c_588]) ).

tff(c_639,plain,
    aElement0(xx),
    inference(demodulation,[status(thm),theory(equality)],[c_258,c_609]) ).

tff(c_641,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_413,c_639]) ).

tff(c_642,plain,
    aElementOf0(xx,xP),
    inference(splitRight,[status(thm)],[c_352]) ).

tff(c_2271,plain,
    ! [W1_308,W0_309] :
      ( aElementOf0(W1_308,xT)
      | ~ aElementOf0(W1_308,W0_309)
      | ~ aElementOf0(W0_309,slbdtsldtrb0(xT,xk)) ),
    inference(cnfTransformation,[status(thm)],[f_624]) ).

tff(c_2301,plain,
    ( aElementOf0(xx,xT)
    | ~ aElementOf0(xP,slbdtsldtrb0(xT,xk)) ),
    inference(resolution,[status(thm)],[c_642,c_2271]) ).

tff(c_2332,plain,
    ~ aElementOf0(xP,slbdtsldtrb0(xT,xk)),
    inference(negUnitSimplification,[status(thm)],[c_370,c_2301]) ).

tff(c_2344,plain,
    ( ~ aSubsetOf0(xP,xT)
    | ( sbrdtbr0(xP) != xk ) ),
    inference(resolution,[status(thm)],[c_294,c_2332]) ).

tff(c_2351,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_364,c_1722,c_2344]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : NUM558+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % 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
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 15:22:11 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 7.75/2.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.75/2.65  
% 7.75/2.65  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.98/2.68  
% 7.98/2.68  Inference rules
% 7.98/2.68  ----------------------
% 7.98/2.68  #Ref     : 0
% 7.98/2.68  #Sup     : 374
% 7.98/2.68  #Fact    : 0
% 7.98/2.68  #Define  : 0
% 7.98/2.68  #Split   : 26
% 7.98/2.68  #Chain   : 0
% 7.98/2.68  #Close   : 0
% 7.98/2.68  
% 7.98/2.68  Ordering : KBO
% 7.98/2.68  
% 7.98/2.68  Simplification rules
% 7.98/2.68  ----------------------
% 7.98/2.68  #Subsume      : 79
% 7.98/2.68  #Demod        : 391
% 7.98/2.68  #Tautology    : 157
% 7.98/2.68  #SimpNegUnit  : 35
% 7.98/2.68  #BackRed      : 73
% 7.98/2.68  
% 7.98/2.68  #Partial instantiations: 0
% 7.98/2.68  #Strategies tried      : 1
% 7.98/2.68  
% 7.98/2.68  Timing (in seconds)
% 7.98/2.68  ----------------------
% 7.98/2.68  Preprocessing        : 0.83
% 7.98/2.68  Parsing              : 0.40
% 7.98/2.68  CNF conversion       : 0.08
% 7.98/2.68  Main loop            : 0.87
% 7.98/2.68  Inferencing          : 0.27
% 7.98/2.68  Reduction            : 0.31
% 7.98/2.68  Demodulation         : 0.21
% 7.98/2.68  BG Simplification    : 0.07
% 7.98/2.68  Subsumption          : 0.17
% 7.98/2.69  Abstraction          : 0.03
% 7.98/2.69  MUC search           : 0.00
% 7.98/2.69  Cooper               : 0.00
% 7.98/2.69  Total                : 1.75
% 7.98/2.69  Index Insertion      : 0.00
% 7.98/2.69  Index Deletion       : 0.00
% 7.98/2.69  Index Matching       : 0.00
% 7.98/2.69  BG Taut test         : 0.00
%------------------------------------------------------------------------------