TSTP Solution File: RNG099+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG099+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/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 : n019.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 10:54:57 EDT 2023

% Result   : Theorem 7.56s 2.88s
% Output   : CNFRefutation 7.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   45
% Syntax   : Number of formulae    :   94 (  33 unt;  32 typ;   2 def)
%            Number of atoms       :  120 (  11 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :  100 (  42   ~;  34   |;  13   &)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   50 (  23   >;  27   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   27 (  27 usr;   9 con; 0-4 aty)
%            Number of variables   :   31 (;  30   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aElementOf0 > aSet0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > xy > xx > xw > xb > xa > xJ > xI > sz10 > sz00 > #skF_6 > #skF_4 > #skF_8 > #skF_5 > #skF_7 > #skF_9 > #skF_13 > #skF_11 > #skF_3 > #skF_2 > #skF_12 > #skF_1 > #skF_10

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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_11',type,
    '#skF_11': $i > $i ).

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

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

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

tff(sdtasasdt0,type,
    sdtasasdt0: ( $i * $i ) > $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_10',type,
    '#skF_10': ( $i * $i * $i ) > $i ).

tff(f_237,hypothesis,
    ( aElement0(xx)
    & aElement0(xy) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).

tff(f_230,hypothesis,
    ( aIdeal0(xI)
    & aIdeal0(xJ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).

tff(f_244,hypothesis,
    aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1332) ).

tff(f_227,definition,
    ! [W0,W1,W2] :
      ( ( aElement0(W0)
        & aElement0(W1)
        & aIdeal0(W2) )
     => ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
      <=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMod) ).

tff(f_205,definition,
    ! [W0] :
      ( aIdeal0(W0)
    <=> ( aSet0(W0)
        & ! [W1] :
            ( aElementOf0(W1,W0)
           => ( ! [W2] :
                  ( aElementOf0(W2,W0)
                 => aElementOf0(sdtpldt0(W1,W2),W0) )
              & ! [W2] :
                  ( aElement0(W2)
                 => aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).

tff(f_242,hypothesis,
    ( aElementOf0(xa,xI)
    & aElementOf0(xb,xJ)
    & ( sdtpldt0(xa,xb) = sz10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).

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

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_47,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).

tff(f_243,hypothesis,
    xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).

tff(f_41,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => aElement0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).

tff(f_245,hypothesis,
    aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).

tff(f_252,negated_conjecture,
    ~ ? [W0] :
        ( aElement0(W0)
        & sdteqdtlpzmzozddtrp0(W0,xx,xI)
        & sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(c_140,plain,
    aElement0(xx),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_134,plain,
    aIdeal0(xI),
    inference(cnfTransformation,[status(thm)],[f_230]) ).

tff(c_150,plain,
    aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
    inference(cnfTransformation,[status(thm)],[f_244]) ).

tff(c_2750,plain,
    ! [W0_208,W1_209,W2_210] :
      ( sdteqdtlpzmzozddtrp0(W0_208,W1_209,W2_210)
      | ~ aElementOf0(sdtpldt0(W0_208,smndt0(W1_209)),W2_210)
      | ~ aIdeal0(W2_210)
      | ~ aElement0(W1_209)
      | ~ aElement0(W0_208) ),
    inference(cnfTransformation,[status(thm)],[f_227]) ).

tff(c_2778,plain,
    ( sdteqdtlpzmzozddtrp0(xw,xx,xI)
    | ~ aIdeal0(xI)
    | ~ aElement0(xx)
    | ~ aElement0(xw) ),
    inference(resolution,[status(thm)],[c_150,c_2750]) ).

tff(c_2791,plain,
    ( sdteqdtlpzmzozddtrp0(xw,xx,xI)
    | ~ aElement0(xw) ),
    inference(demodulation,[status(thm),theory(equality)],[c_140,c_134,c_2778]) ).

tff(c_2795,plain,
    ~ aElement0(xw),
    inference(splitLeft,[status(thm)],[c_2791]) ).

tff(c_138,plain,
    aElement0(xy),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_108,plain,
    ! [W0_117] :
      ( aSet0(W0_117)
      | ~ aIdeal0(W0_117) ),
    inference(cnfTransformation,[status(thm)],[f_205]) ).

tff(c_146,plain,
    aElementOf0(xa,xI),
    inference(cnfTransformation,[status(thm)],[f_242]) ).

tff(c_365,plain,
    ! [W1_153,W0_154] :
      ( aElement0(W1_153)
      | ~ aElementOf0(W1_153,W0_154)
      | ~ aSet0(W0_154) ),
    inference(cnfTransformation,[status(thm)],[f_137]) ).

tff(c_380,plain,
    ( aElement0(xa)
    | ~ aSet0(xI) ),
    inference(resolution,[status(thm)],[c_146,c_365]) ).

tff(c_429,plain,
    ~ aSet0(xI),
    inference(splitLeft,[status(thm)],[c_380]) ).

tff(c_432,plain,
    ~ aIdeal0(xI),
    inference(resolution,[status(thm)],[c_108,c_429]) ).

tff(c_436,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_134,c_432]) ).

tff(c_437,plain,
    aElement0(xa),
    inference(splitRight,[status(thm)],[c_380]) ).

tff(c_988,plain,
    ! [W1_176,W0_177] :
      ( ( sdtasdt0(W1_176,W0_177) = sdtasdt0(W0_177,W1_176) )
      | ~ aElement0(W1_176)
      | ~ aElement0(W0_177) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_1639,plain,
    ! [W0_192] :
      ( ( sdtasdt0(xy,W0_192) = sdtasdt0(W0_192,xy) )
      | ~ aElement0(W0_192) ),
    inference(resolution,[status(thm)],[c_138,c_988]) ).

tff(c_1693,plain,
    sdtasdt0(xy,xa) = sdtasdt0(xa,xy),
    inference(resolution,[status(thm)],[c_437,c_1639]) ).

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_1710,plain,
    ( aElement0(sdtasdt0(xa,xy))
    | ~ aElement0(xa)
    | ~ aElement0(xy) ),
    inference(superposition,[status(thm),theory(equality)],[c_1693,c_12]) ).

tff(c_1716,plain,
    aElement0(sdtasdt0(xa,xy)),
    inference(demodulation,[status(thm),theory(equality)],[c_138,c_437,c_1710]) ).

tff(c_132,plain,
    aIdeal0(xJ),
    inference(cnfTransformation,[status(thm)],[f_230]) ).

tff(c_144,plain,
    aElementOf0(xb,xJ),
    inference(cnfTransformation,[status(thm)],[f_242]) ).

tff(c_381,plain,
    ( aElement0(xb)
    | ~ aSet0(xJ) ),
    inference(resolution,[status(thm)],[c_144,c_365]) ).

tff(c_386,plain,
    ~ aSet0(xJ),
    inference(splitLeft,[status(thm)],[c_381]) ).

tff(c_389,plain,
    ~ aIdeal0(xJ),
    inference(resolution,[status(thm)],[c_108,c_386]) ).

tff(c_393,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_132,c_389]) ).

tff(c_394,plain,
    aElement0(xb),
    inference(splitRight,[status(thm)],[c_381]) ).

tff(c_1190,plain,
    ! [W0_184] :
      ( ( sdtasdt0(xx,W0_184) = sdtasdt0(W0_184,xx) )
      | ~ aElement0(W0_184) ),
    inference(resolution,[status(thm)],[c_140,c_988]) ).

tff(c_1233,plain,
    sdtasdt0(xx,xb) = sdtasdt0(xb,xx),
    inference(resolution,[status(thm)],[c_394,c_1190]) ).

tff(c_1289,plain,
    ( aElement0(sdtasdt0(xb,xx))
    | ~ aElement0(xb)
    | ~ aElement0(xx) ),
    inference(superposition,[status(thm),theory(equality)],[c_1233,c_12]) ).

tff(c_1293,plain,
    aElement0(sdtasdt0(xb,xx)),
    inference(demodulation,[status(thm),theory(equality)],[c_140,c_394,c_1289]) ).

tff(c_148,plain,
    sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) = xw,
    inference(cnfTransformation,[status(thm)],[f_243]) ).

tff(c_1285,plain,
    sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xb,xx)) = xw,
    inference(demodulation,[status(thm),theory(equality)],[c_1233,c_148]) ).

tff(c_4674,plain,
    sdtpldt0(sdtasdt0(xa,xy),sdtasdt0(xb,xx)) = xw,
    inference(demodulation,[status(thm),theory(equality)],[c_1693,c_1285]) ).

tff(c_10,plain,
    ! [W0_3,W1_4] :
      ( aElement0(sdtpldt0(W0_3,W1_4))
      | ~ aElement0(W1_4)
      | ~ aElement0(W0_3) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_4687,plain,
    ( aElement0(xw)
    | ~ aElement0(sdtasdt0(xb,xx))
    | ~ aElement0(sdtasdt0(xa,xy)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4674,c_10]) ).

tff(c_4693,plain,
    aElement0(xw),
    inference(demodulation,[status(thm),theory(equality)],[c_1716,c_1293,c_4687]) ).

tff(c_4695,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2795,c_4693]) ).

tff(c_4697,plain,
    aElement0(xw),
    inference(splitRight,[status(thm)],[c_2791]) ).

tff(c_4696,plain,
    sdteqdtlpzmzozddtrp0(xw,xx,xI),
    inference(splitRight,[status(thm)],[c_2791]) ).

tff(c_152,plain,
    aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
    inference(cnfTransformation,[status(thm)],[f_245]) ).

tff(c_2781,plain,
    ( sdteqdtlpzmzozddtrp0(xw,xy,xJ)
    | ~ aIdeal0(xJ)
    | ~ aElement0(xy)
    | ~ aElement0(xw) ),
    inference(resolution,[status(thm)],[c_152,c_2750]) ).

tff(c_2794,plain,
    ( sdteqdtlpzmzozddtrp0(xw,xy,xJ)
    | ~ aElement0(xw) ),
    inference(demodulation,[status(thm),theory(equality)],[c_138,c_132,c_2781]) ).

tff(c_4871,plain,
    sdteqdtlpzmzozddtrp0(xw,xy,xJ),
    inference(demodulation,[status(thm),theory(equality)],[c_4697,c_2794]) ).

tff(c_154,plain,
    ! [W0_143] :
      ( ~ sdteqdtlpzmzozddtrp0(W0_143,xy,xJ)
      | ~ sdteqdtlpzmzozddtrp0(W0_143,xx,xI)
      | ~ aElement0(W0_143) ),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_4874,plain,
    ( ~ sdteqdtlpzmzozddtrp0(xw,xx,xI)
    | ~ aElement0(xw) ),
    inference(resolution,[status(thm)],[c_4871,c_154]) ).

tff(c_4878,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4697,c_4696,c_4874]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : RNG099+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % 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
% 0.15/0.36  % Computer : n019.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 17:57:01 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 7.56/2.88  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.56/2.89  
% 7.56/2.89  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.56/2.92  
% 7.56/2.92  Inference rules
% 7.56/2.92  ----------------------
% 7.56/2.92  #Ref     : 0
% 7.56/2.92  #Sup     : 1153
% 7.56/2.92  #Fact    : 0
% 7.56/2.92  #Define  : 0
% 7.56/2.92  #Split   : 3
% 7.56/2.92  #Chain   : 0
% 7.56/2.92  #Close   : 0
% 7.56/2.92  
% 7.56/2.92  Ordering : KBO
% 7.56/2.92  
% 7.56/2.92  Simplification rules
% 7.56/2.92  ----------------------
% 7.56/2.92  #Subsume      : 18
% 7.56/2.92  #Demod        : 826
% 7.56/2.92  #Tautology    : 481
% 7.56/2.92  #SimpNegUnit  : 16
% 7.56/2.92  #BackRed      : 1
% 7.56/2.92  
% 7.56/2.92  #Partial instantiations: 0
% 7.56/2.92  #Strategies tried      : 1
% 7.56/2.92  
% 7.56/2.92  Timing (in seconds)
% 7.56/2.92  ----------------------
% 7.95/2.92  Preprocessing        : 0.65
% 7.95/2.92  Parsing              : 0.32
% 7.95/2.93  CNF conversion       : 0.06
% 7.95/2.93  Main loop            : 1.12
% 7.95/2.93  Inferencing          : 0.36
% 7.95/2.93  Reduction            : 0.38
% 7.95/2.93  Demodulation         : 0.29
% 7.95/2.93  BG Simplification    : 0.06
% 7.95/2.93  Subsumption          : 0.23
% 7.95/2.93  Abstraction          : 0.05
% 7.95/2.93  MUC search           : 0.00
% 7.95/2.93  Cooper               : 0.00
% 7.95/2.93  Total                : 1.82
% 7.95/2.93  Index Insertion      : 0.00
% 7.95/2.93  Index Deletion       : 0.00
% 7.95/2.93  Index Matching       : 0.00
% 7.95/2.93  BG Taut test         : 0.00
%------------------------------------------------------------------------------