TSTP Solution File: RNG123+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG123+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 : n020.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 10:55:02 EDT 2023

% Result   : Theorem 13.36s 4.96s
% Output   : CNFRefutation 13.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   80
% Syntax   : Number of formulae    :   91 (  10 unt;  75 typ;   0 def)
%            Number of atoms       :   49 (  12 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :   39 (   6   ~;   5   |;  22   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    4 (   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    :   64 (  64 usr;  27 con; 0-4 aty)
%            Number of variables   :   20 (;   8   !;  12   ?;   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_48 > #skF_4 > #skF_37 > #skF_8 > #skF_47 > #skF_14 > #skF_15 > #skF_29 > #skF_26 > #skF_18 > #skF_45 > #skF_23 > #skF_28 > #skF_46 > #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_48',type,
    '#skF_48': $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_47',type,
    '#skF_47': $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_45',type,
    '#skF_45': $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('#skF_46',type,
    '#skF_46': $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_617,negated_conjecture,
    ~ ( ? [W0,W1] :
          ( aElementOf0(W0,slsdtgt0(xa))
          & aElementOf0(W1,slsdtgt0(xb))
          & ( sdtpldt0(W0,W1) = xr ) )
      | aElementOf0(xr,xI) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_592,hypothesis,
    ( ? [W0,W1] :
        ( aElementOf0(W0,slsdtgt0(xa))
        & aElementOf0(W1,slsdtgt0(xb))
        & ( sdtpldt0(W0,W1) = smndt0(sdtasdt0(xq,xu)) ) )
    & aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).

tff(f_607,hypothesis,
    ( ? [W0,W1] :
        ( aElementOf0(W0,slsdtgt0(xa))
        & aElementOf0(W1,slsdtgt0(xb))
        & ( sdtpldt0(W0,W1) = xb ) )
    & ? [W0,W1] :
        ( aElementOf0(W0,slsdtgt0(xa))
        & aElementOf0(W1,slsdtgt0(xb))
        & ( sdtpldt0(W0,W1) = xb ) )
    & aElementOf0(xb,xI) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2699) ).

tff(f_608,hypothesis,
    xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2718) ).

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(c_442,plain,
    ~ aElementOf0(xr,xI),
    inference(cnfTransformation,[status(thm)],[f_617]) ).

tff(c_426,plain,
    smndt0(sdtasdt0(xq,xu)) = sdtpldt0('#skF_45','#skF_46'),
    inference(cnfTransformation,[status(thm)],[f_592]) ).

tff(c_424,plain,
    aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
    inference(cnfTransformation,[status(thm)],[f_592]) ).

tff(c_446,plain,
    aElementOf0(sdtpldt0('#skF_45','#skF_46'),xI),
    inference(demodulation,[status(thm),theory(equality)],[c_426,c_424]) ).

tff(c_432,plain,
    aElementOf0(xb,xI),
    inference(cnfTransformation,[status(thm)],[f_607]) ).

tff(c_440,plain,
    sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = xr,
    inference(cnfTransformation,[status(thm)],[f_608]) ).

tff(c_445,plain,
    sdtpldt0(sdtpldt0('#skF_45','#skF_46'),xb) = xr,
    inference(demodulation,[status(thm),theory(equality)],[c_426,c_440]) ).

tff(c_8855,plain,
    ! [W0_367,W1_368] :
      ( aElementOf0(sdtpldt0(W0_367,W1_368),xI)
      | ~ aElementOf0(W1_368,xI)
      | ~ aElementOf0(W0_367,xI) ),
    inference(cnfTransformation,[status(thm)],[f_452]) ).

tff(c_9041,plain,
    ( aElementOf0(xr,xI)
    | ~ aElementOf0(xb,xI)
    | ~ aElementOf0(sdtpldt0('#skF_45','#skF_46'),xI) ),
    inference(superposition,[status(thm),theory(equality)],[c_445,c_8855]) ).

tff(c_9173,plain,
    aElementOf0(xr,xI),
    inference(demodulation,[status(thm),theory(equality)],[c_446,c_432,c_9041]) ).

tff(c_9175,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_442,c_9173]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : RNG123+4 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14  % 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 : n020.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 17:56:07 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 13.36/4.96  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.36/4.96  
% 13.36/4.96  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.43/4.99  
% 13.43/4.99  Inference rules
% 13.43/4.99  ----------------------
% 13.43/4.99  #Ref     : 0
% 13.43/4.99  #Sup     : 2211
% 13.43/4.99  #Fact    : 0
% 13.43/4.99  #Define  : 0
% 13.43/4.99  #Split   : 35
% 13.43/4.99  #Chain   : 0
% 13.43/4.99  #Close   : 0
% 13.43/4.99  
% 13.43/4.99  Ordering : KBO
% 13.43/4.99  
% 13.43/4.99  Simplification rules
% 13.43/4.99  ----------------------
% 13.43/4.99  #Subsume      : 226
% 13.43/4.99  #Demod        : 1919
% 13.43/4.99  #Tautology    : 1079
% 13.43/4.99  #SimpNegUnit  : 14
% 13.43/4.99  #BackRed      : 3
% 13.43/4.99  
% 13.43/4.99  #Partial instantiations: 0
% 13.43/4.99  #Strategies tried      : 1
% 13.43/4.99  
% 13.43/4.99  Timing (in seconds)
% 13.43/4.99  ----------------------
% 13.43/4.99  Preprocessing        : 0.99
% 13.43/4.99  Parsing              : 0.52
% 13.43/4.99  CNF conversion       : 0.08
% 13.43/4.99  Main loop            : 2.78
% 13.43/4.99  Inferencing          : 0.69
% 13.43/4.99  Reduction            : 1.33
% 13.43/4.99  Demodulation         : 1.02
% 13.43/4.99  BG Simplification    : 0.08
% 13.43/4.99  Subsumption          : 0.52
% 13.43/4.99  Abstraction          : 0.05
% 13.43/4.99  MUC search           : 0.00
% 13.43/4.99  Cooper               : 0.00
% 13.43/4.99  Total                : 3.82
% 13.43/4.99  Index Insertion      : 0.00
% 13.43/4.99  Index Deletion       : 0.00
% 13.43/4.99  Index Matching       : 0.00
% 13.43/4.99  BG Taut test         : 0.00
%------------------------------------------------------------------------------