TSTP Solution File: NUM421+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM421+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 : n014.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 10:51:37 EDT 2023

% Result   : Theorem 18.04s 7.03s
% Output   : CNFRefutation 18.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   74 (  30 unt;   7 typ;   0 def)
%            Number of atoms       :  135 (  55 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  122 (  54   ~;  47   |;  12   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   46 (;  46   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ aInteger0 > sdtpldt0 > sdtasdt0 > #nlpp > smndt0 > xa > sz10 > sz00

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(aInteger0,type,
    aInteger0: $i > $o ).

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

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

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

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

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

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

tff(f_104,hypothesis,
    aInteger0(xa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__419) ).

tff(f_30,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).

tff(f_87,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

tff(f_108,negated_conjecture,
    ~ ( ( sdtasdt0(xa,sz00) = sz00 )
      & ( sz00 = sdtasdt0(sz00,xa) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(f_35,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => aInteger0(smndt0(W0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).

tff(f_67,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( ( sdtpldt0(W0,sz00) = W0 )
        & ( W0 = sdtpldt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

tff(f_73,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
        & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).

tff(f_55,axiom,
    ! [W0,W1,W2] :
      ( ( aInteger0(W0)
        & aInteger0(W1)
        & aInteger0(W2) )
     => ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).

tff(f_47,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => aInteger0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).

tff(f_61,axiom,
    ! [W0,W1] :
      ( ( aInteger0(W0)
        & aInteger0(W1) )
     => ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

tff(f_93,axiom,
    ! [W0] :
      ( aInteger0(W0)
     => ( ( sdtasdt0(W0,sz10) = W0 )
        & ( W0 = sdtasdt0(sz10,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).

tff(f_31,axiom,
    aInteger0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).

tff(f_103,axiom,
    ! [W0,W1,W2] :
      ( ( aInteger0(W0)
        & aInteger0(W1)
        & aInteger0(W2) )
     => ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
        & ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).

tff(c_38,plain,
    aInteger0(xa),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_4,plain,
    aInteger0(sz00),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_289,plain,
    ! [W1_35,W0_36] :
      ( ( sdtasdt0(W1_35,W0_36) = sdtasdt0(W0_36,W1_35) )
      | ~ aInteger0(W1_35)
      | ~ aInteger0(W0_36) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_371,plain,
    ! [W0_40] :
      ( ( sdtasdt0(sz00,W0_40) = sdtasdt0(W0_40,sz00) )
      | ~ aInteger0(W0_40) ),
    inference(resolution,[status(thm)],[c_4,c_289]) ).

tff(c_397,plain,
    sdtasdt0(xa,sz00) = sdtasdt0(sz00,xa),
    inference(resolution,[status(thm)],[c_38,c_371]) ).

tff(c_40,plain,
    ( ( sdtasdt0(sz00,xa) != sz00 )
    | ( sdtasdt0(xa,sz00) != sz00 ) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_88,plain,
    sdtasdt0(xa,sz00) != sz00,
    inference(splitLeft,[status(thm)],[c_40]) ).

tff(c_398,plain,
    sdtasdt0(sz00,xa) != sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_397,c_88]) ).

tff(c_8,plain,
    ! [W0_2] :
      ( aInteger0(smndt0(W0_2))
      | ~ aInteger0(W0_2) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_59,plain,
    ! [W0_25] :
      ( ( sdtpldt0(W0_25,sz00) = W0_25 )
      | ~ aInteger0(W0_25) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_73,plain,
    sdtpldt0(sz00,sz00) = sz00,
    inference(resolution,[status(thm)],[c_4,c_59]) ).

tff(c_24,plain,
    ! [W0_13] :
      ( ( sdtpldt0(W0_13,smndt0(W0_13)) = sz00 )
      | ~ aInteger0(W0_13) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_101,plain,
    ! [W0_26] :
      ( ( sdtpldt0(sz00,W0_26) = W0_26 )
      | ~ aInteger0(W0_26) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_118,plain,
    sdtpldt0(sz00,xa) = xa,
    inference(resolution,[status(thm)],[c_38,c_101]) ).

tff(c_453,plain,
    ! [W0_42,W1_43,W2_44] :
      ( ( sdtpldt0(sdtpldt0(W0_42,W1_43),W2_44) = sdtpldt0(W0_42,sdtpldt0(W1_43,W2_44)) )
      | ~ aInteger0(W2_44)
      | ~ aInteger0(W1_43)
      | ~ aInteger0(W0_42) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_481,plain,
    ! [W2_44] :
      ( ( sdtpldt0(sz00,sdtpldt0(xa,W2_44)) = sdtpldt0(xa,W2_44) )
      | ~ aInteger0(W2_44)
      | ~ aInteger0(xa)
      | ~ aInteger0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_118,c_453]) ).

tff(c_1616,plain,
    ! [W2_66] :
      ( ( sdtpldt0(sz00,sdtpldt0(xa,W2_66)) = sdtpldt0(xa,W2_66) )
      | ~ aInteger0(W2_66) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_38,c_481]) ).

tff(c_1641,plain,
    ( ( sdtpldt0(xa,smndt0(xa)) = sdtpldt0(sz00,sz00) )
    | ~ aInteger0(smndt0(xa))
    | ~ aInteger0(xa) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_1616]) ).

tff(c_1657,plain,
    ( ( sdtpldt0(xa,smndt0(xa)) = sz00 )
    | ~ aInteger0(smndt0(xa)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_73,c_1641]) ).

tff(c_1660,plain,
    ~ aInteger0(smndt0(xa)),
    inference(splitLeft,[status(thm)],[c_1657]) ).

tff(c_1663,plain,
    ~ aInteger0(xa),
    inference(resolution,[status(thm)],[c_8,c_1660]) ).

tff(c_1667,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_1663]) ).

tff(c_1669,plain,
    aInteger0(smndt0(xa)),
    inference(splitRight,[status(thm)],[c_1657]) ).

tff(c_12,plain,
    ! [W0_5,W1_6] :
      ( aInteger0(sdtasdt0(W0_5,W1_6))
      | ~ aInteger0(W1_6)
      | ~ aInteger0(W0_5) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_402,plain,
    ( aInteger0(sdtasdt0(sz00,xa))
    | ~ aInteger0(sz00)
    | ~ aInteger0(xa) ),
    inference(superposition,[status(thm),theory(equality)],[c_397,c_12]) ).

tff(c_406,plain,
    aInteger0(sdtasdt0(sz00,xa)),
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_4,c_402]) ).

tff(c_18,plain,
    ! [W0_12] :
      ( ( sdtpldt0(sz00,W0_12) = W0_12 )
      | ~ aInteger0(W0_12) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_431,plain,
    sdtpldt0(sz00,sdtasdt0(sz00,xa)) = sdtasdt0(sz00,xa),
    inference(resolution,[status(thm)],[c_406,c_18]) ).

tff(c_1668,plain,
    sdtpldt0(xa,smndt0(xa)) = sz00,
    inference(splitRight,[status(thm)],[c_1657]) ).

tff(c_352,plain,
    ! [W1_38,W0_39] :
      ( ( sdtpldt0(W1_38,W0_39) = sdtpldt0(W0_39,W1_38) )
      | ~ aInteger0(W1_38)
      | ~ aInteger0(W0_39) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_370,plain,
    ! [W0_39] :
      ( ( sdtpldt0(xa,W0_39) = sdtpldt0(W0_39,xa) )
      | ~ aInteger0(W0_39) ),
    inference(resolution,[status(thm)],[c_38,c_352]) ).

tff(c_1816,plain,
    sdtpldt0(smndt0(xa),xa) = sdtpldt0(xa,smndt0(xa)),
    inference(resolution,[status(thm)],[c_1669,c_370]) ).

tff(c_2675,plain,
    sdtpldt0(smndt0(xa),xa) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_1668,c_1816]) ).

tff(c_42,plain,
    ! [W0_24] :
      ( ( sdtasdt0(W0_24,sz10) = W0_24 )
      | ~ aInteger0(W0_24) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_58,plain,
    sdtasdt0(xa,sz10) = xa,
    inference(resolution,[status(thm)],[c_38,c_42]) ).

tff(c_6,plain,
    aInteger0(sz10),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_74,plain,
    sdtpldt0(sz10,sz00) = sz10,
    inference(resolution,[status(thm)],[c_6,c_59]) ).

tff(c_1001,plain,
    ! [W0_57,W1_58,W2_59] :
      ( ( sdtpldt0(sdtasdt0(W0_57,W1_58),sdtasdt0(W0_57,W2_59)) = sdtasdt0(W0_57,sdtpldt0(W1_58,W2_59)) )
      | ~ aInteger0(W2_59)
      | ~ aInteger0(W1_58)
      | ~ aInteger0(W0_57) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_1084,plain,
    ! [W2_59] :
      ( ( sdtpldt0(xa,sdtasdt0(xa,W2_59)) = sdtasdt0(xa,sdtpldt0(sz10,W2_59)) )
      | ~ aInteger0(W2_59)
      | ~ aInteger0(sz10)
      | ~ aInteger0(xa) ),
    inference(superposition,[status(thm),theory(equality)],[c_58,c_1001]) ).

tff(c_36785,plain,
    ! [W2_224] :
      ( ( sdtpldt0(xa,sdtasdt0(xa,W2_224)) = sdtasdt0(xa,sdtpldt0(sz10,W2_224)) )
      | ~ aInteger0(W2_224) ),
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_6,c_1084]) ).

tff(c_36874,plain,
    ( ( sdtpldt0(xa,sdtasdt0(sz00,xa)) = sdtasdt0(xa,sdtpldt0(sz10,sz00)) )
    | ~ aInteger0(sz00) ),
    inference(superposition,[status(thm),theory(equality)],[c_397,c_36785]) ).

tff(c_36921,plain,
    sdtpldt0(xa,sdtasdt0(sz00,xa)) = xa,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_58,c_74,c_36874]) ).

tff(c_22,plain,
    ! [W0_13] :
      ( ( sdtpldt0(smndt0(W0_13),W0_13) = sz00 )
      | ~ aInteger0(W0_13) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_478,plain,
    ! [W0_13,W2_44] :
      ( ( sdtpldt0(smndt0(W0_13),sdtpldt0(W0_13,W2_44)) = sdtpldt0(sz00,W2_44) )
      | ~ aInteger0(W2_44)
      | ~ aInteger0(W0_13)
      | ~ aInteger0(smndt0(W0_13))
      | ~ aInteger0(W0_13) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_453]) ).

tff(c_36948,plain,
    ( ( sdtpldt0(smndt0(xa),xa) = sdtpldt0(sz00,sdtasdt0(sz00,xa)) )
    | ~ aInteger0(sdtasdt0(sz00,xa))
    | ~ aInteger0(xa)
    | ~ aInteger0(smndt0(xa))
    | ~ aInteger0(xa) ),
    inference(superposition,[status(thm),theory(equality)],[c_36921,c_478]) ).

tff(c_37006,plain,
    sdtasdt0(sz00,xa) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_38,c_1669,c_38,c_406,c_431,c_2675,c_36948]) ).

tff(c_37008,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_398,c_37006]) ).

tff(c_37009,plain,
    sdtasdt0(sz00,xa) != sz00,
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_37010,plain,
    sdtasdt0(xa,sz00) = sz00,
    inference(splitRight,[status(thm)],[c_40]) ).

tff(c_37330,plain,
    ! [W1_239,W0_240] :
      ( ( sdtasdt0(W1_239,W0_240) = sdtasdt0(W0_240,W1_239) )
      | ~ aInteger0(W1_239)
      | ~ aInteger0(W0_240) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_37546,plain,
    ! [W0_247] :
      ( ( sdtasdt0(xa,W0_247) = sdtasdt0(W0_247,xa) )
      | ~ aInteger0(W0_247) ),
    inference(resolution,[status(thm)],[c_38,c_37330]) ).

tff(c_37561,plain,
    sdtasdt0(xa,sz00) = sdtasdt0(sz00,xa),
    inference(resolution,[status(thm)],[c_4,c_37546]) ).

tff(c_37573,plain,
    sdtasdt0(sz00,xa) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_37010,c_37561]) ).

tff(c_37575,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_37009,c_37573]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM421+1 : 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
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 15:17:33 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 18.04/7.03  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.04/7.04  
% 18.04/7.04  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.04/7.07  
% 18.04/7.07  Inference rules
% 18.04/7.07  ----------------------
% 18.04/7.07  #Ref     : 0
% 18.04/7.07  #Sup     : 8083
% 18.04/7.07  #Fact    : 0
% 18.04/7.07  #Define  : 0
% 18.04/7.07  #Split   : 4
% 18.04/7.07  #Chain   : 0
% 18.04/7.07  #Close   : 0
% 18.04/7.07  
% 18.04/7.07  Ordering : KBO
% 18.04/7.07  
% 18.04/7.07  Simplification rules
% 18.04/7.07  ----------------------
% 18.04/7.07  #Subsume      : 663
% 18.04/7.07  #Demod        : 13331
% 18.04/7.07  #Tautology    : 2353
% 18.04/7.07  #SimpNegUnit  : 2
% 18.04/7.07  #BackRed      : 9
% 18.04/7.07  
% 18.04/7.07  #Partial instantiations: 0
% 18.04/7.07  #Strategies tried      : 1
% 18.04/7.07  
% 18.04/7.07  Timing (in seconds)
% 18.04/7.07  ----------------------
% 18.04/7.07  Preprocessing        : 0.48
% 18.04/7.07  Parsing              : 0.27
% 18.04/7.07  CNF conversion       : 0.03
% 18.04/7.07  Main loop            : 5.52
% 18.04/7.07  Inferencing          : 1.18
% 18.04/7.07  Reduction            : 2.82
% 18.04/7.07  Demodulation         : 2.48
% 18.04/7.07  BG Simplification    : 0.14
% 18.04/7.07  Subsumption          : 1.10
% 18.04/7.07  Abstraction          : 0.21
% 18.04/7.07  MUC search           : 0.00
% 18.04/7.07  Cooper               : 0.00
% 18.04/7.07  Total                : 6.06
% 18.04/7.07  Index Insertion      : 0.00
% 18.04/7.07  Index Deletion       : 0.00
% 18.04/7.07  Index Matching       : 0.00
% 18.04/7.07  BG Taut test         : 0.00
%------------------------------------------------------------------------------