TSTP Solution File: NUM586+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM586+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/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 : n004.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 10:52:13 EDT 2023

% Result   : Theorem 93.73s 71.46s
% Output   : CNFRefutation 93.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   82
% Syntax   : Number of formulae    :   91 (   6 unt;  78 typ;   0 def)
%            Number of atoms       :   80 (  19 equ)
%            Maximal formula atoms :   47 (   6 avg)
%            Number of connectives :   80 (  13   ~;  11   |;  36   &)
%                                         (   4 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  136 (  65   >;  71   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :   69 (  69 usr;  13 con; 0-4 aty)
%            Number of variables   :   21 (;  19   !;   2   ?;   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 > xx > xk > xi > xc > xT > xS > xN > xK > xC > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_41 > #skF_17 > #skF_31 > #skF_33 > #skF_6 > #skF_1 > #skF_18 > #skF_37 > #skF_38 > #skF_4 > #skF_29 > #skF_12 > #skF_30 > #skF_32 > #skF_23 > #skF_35 > #skF_5 > #skF_19 > #skF_43 > #skF_10 > #skF_8 > #skF_20 > #skF_28 > #skF_26 > #skF_24 > #skF_34 > #skF_15 > #skF_13 > #skF_14 > #skF_42 > #skF_25 > #skF_3 > #skF_2 > #skF_40 > #skF_27 > #skF_36 > #skF_21 > #skF_9 > #skF_22 > #skF_16 > #skF_39

%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_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(sdtlbdtrb0,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(szDzozmdt0,type,
    szDzozmdt0: $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('#skF_18',type,
    '#skF_18': ( $i * $i * $i ) > $i ).

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

tff(sdtexdt0,type,
    sdtexdt0: ( $i * $i ) > $i ).

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

tff(xi,type,
    xi: $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_38',type,
    '#skF_38': ( $i * $i ) > $i ).

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

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

tff('#skF_29',type,
    '#skF_29': ( $i * $i * $i ) > $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(xx,type,
    xx: $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_19',type,
    '#skF_19': ( $i * $i * $i ) > $i ).

tff(isCountable0,type,
    isCountable0: $i > $o ).

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

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

tff('#skF_42',type,
    '#skF_42': $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('#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(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_16',type,
    '#skF_16': ( $i * $i * $i ) > $i ).

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

tff(f_1101,hypothesis,
    ( ? [W0] :
        ( aElementOf0(W0,szDzozmdt0(sdtlpdtrp0(xC,xi)))
        & ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) = xx ) )
    & aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4200_02) ).

tff(f_1095,hypothesis,
    aElementOf0(xi,szNzAzT0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4200) ).

tff(f_1094,hypothesis,
    ( aFunction0(xC)
    & ( szDzozmdt0(xC) = szNzAzT0 )
    & ! [W0] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aFunction0(sdtlpdtrp0(xC,W0))
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & ! [W1] :
              ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
               => ( aSet0(W1)
                  & ! [W2] :
                      ( aElementOf0(W2,W1)
                     => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( sbrdtbr0(W1) = xk ) ) )
              & ( ( ( ( aSet0(W1)
                      & ! [W2] :
                          ( aElementOf0(W2,W1)
                         => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & ( sbrdtbr0(W1) = xk ) )
               => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1] :
              ( ( aSet0(W1)
                & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2] :
                        ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                 => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W2] :
                          ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                   => ( ( ( ! [W2] :
                              ( aElementOf0(W2,W1)
                             => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & ( sbrdtbr0(W1) = xk ) )
                      | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
             => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2] :
                    ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ! [W2] :
                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).

tff(f_1136,negated_conjecture,
    ~ ? [W0] :
        ( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
            & ! [W1] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,xi))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),W1) ) )
         => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
              & ! [W1] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,xi))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
           => ( ( ( ( aSet0(W0)
                    & ! [W1] :
                        ( aElementOf0(W1,W0)
                       => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
                  | aSubsetOf0(W0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
                & ( sbrdtbr0(W0) = xk ) )
              | aElementOf0(W0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ) ) )
        & ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0) = xx ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(c_8852,plain,
    sdtlpdtrp0(sdtlpdtrp0(xC,xi),'#skF_42') = xx,
    inference(cnfTransformation,[status(thm)],[f_1101]) ).

tff(c_8854,plain,
    aElementOf0('#skF_42',szDzozmdt0(sdtlpdtrp0(xC,xi))),
    inference(cnfTransformation,[status(thm)],[f_1101]) ).

tff(c_8848,plain,
    aElementOf0(xi,szNzAzT0),
    inference(cnfTransformation,[status(thm)],[f_1095]) ).

tff(c_62076,plain,
    ! [W0_2300] :
      ( ( slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0_2300),szmzizndt0(sdtlpdtrp0(xN,W0_2300))),xk) = szDzozmdt0(sdtlpdtrp0(xC,W0_2300)) )
      | ~ aElementOf0(W0_2300,szNzAzT0) ),
    inference(cnfTransformation,[status(thm)],[f_1094]) ).

tff(c_8856,plain,
    ! [W0_654] :
      ( ~ aElementOf0(W0_654,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
      | ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0_654) != xx ) ),
    inference(cnfTransformation,[status(thm)],[f_1136]) ).

tff(c_62123,plain,
    ! [W0_654] :
      ( ~ aElementOf0(W0_654,szDzozmdt0(sdtlpdtrp0(xC,xi)))
      | ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0_654) != xx )
      | ~ aElementOf0(xi,szNzAzT0) ),
    inference(superposition,[status(thm),theory(equality)],[c_62076,c_8856]) ).

tff(c_62174,plain,
    ! [W0_2301] :
      ( ~ aElementOf0(W0_2301,szDzozmdt0(sdtlpdtrp0(xC,xi)))
      | ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W0_2301) != xx ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8848,c_62123]) ).

tff(c_62245,plain,
    sdtlpdtrp0(sdtlpdtrp0(xC,xi),'#skF_42') != xx,
    inference(resolution,[status(thm)],[c_8854,c_62174]) ).

tff(c_62299,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8852,c_62245]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM586+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % 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
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 15:03:26 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 93.73/71.46  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 93.73/71.47  
% 93.73/71.47  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 93.82/71.49  
% 93.82/71.49  Inference rules
% 93.82/71.49  ----------------------
% 93.82/71.49  #Ref     : 9
% 93.82/71.49  #Sup     : 10322
% 93.82/71.49  #Fact    : 0
% 93.82/71.49  #Define  : 0
% 93.82/71.49  #Split   : 541
% 93.82/71.49  #Chain   : 0
% 93.82/71.49  #Close   : 0
% 93.82/71.49  
% 93.82/71.49  Ordering : KBO
% 93.82/71.49  
% 93.82/71.49  Simplification rules
% 93.82/71.49  ----------------------
% 93.82/71.49  #Subsume      : 2586
% 93.82/71.49  #Demod        : 8812
% 93.82/71.49  #Tautology    : 2026
% 93.82/71.49  #SimpNegUnit  : 548
% 93.82/71.49  #BackRed      : 155
% 93.82/71.49  
% 93.82/71.49  #Partial instantiations: 0
% 93.82/71.49  #Strategies tried      : 1
% 93.82/71.49  
% 93.82/71.49  Timing (in seconds)
% 93.82/71.49  ----------------------
% 93.82/71.50  Preprocessing        : 2.28
% 93.82/71.50  Parsing              : 0.49
% 93.82/71.50  CNF conversion       : 0.20
% 93.82/71.50  Main loop            : 68.14
% 93.82/71.50  Inferencing          : 2.69
% 93.82/71.50  Reduction            : 48.14
% 93.82/71.50  Demodulation         : 41.01
% 93.82/71.50  BG Simplification    : 0.75
% 93.82/71.50  Subsumption          : 12.80
% 93.82/71.50  Abstraction          : 0.55
% 93.82/71.50  MUC search           : 0.00
% 93.82/71.50  Cooper               : 0.00
% 93.82/71.50  Total                : 70.47
% 93.82/71.50  Index Insertion      : 0.00
% 93.82/71.50  Index Deletion       : 0.00
% 93.82/71.50  Index Matching       : 0.00
% 93.82/71.50  BG Taut test         : 0.00
%------------------------------------------------------------------------------