TSTP Solution File: NUM473+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM473+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 : n025.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 10:51:48 EDT 2023

% Result   : Theorem 105.44s 88.05s
% Output   : CNFRefutation 105.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  139 (  56 unt;  17 typ;   2 def)
%            Number of atoms       :  310 ( 101 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  315 ( 127   ~; 140   |;  28   &)
%                                         (   2 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  10   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :   62 (;  62   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xq > xp > xn > xm > xl > sz10 > sz00 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

tff(sdtmndt0,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(sdtlseqdt0,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

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

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

tff(aNaturalNumber0,type,
    aNaturalNumber0: $i > $o ).

tff(doDivides0,type,
    doDivides0: ( $i * $i ) > $o ).

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

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

tff(iLess0,type,
    iLess0: ( $i * $i ) > $o ).

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

tff(sdtsldt0,type,
    sdtsldt0: ( $i * $i ) > $i ).

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

tff('#skF_1',type,
    '#skF_1': ( $i * $i ) > $i ).

tff(f_362,negated_conjecture,
    ~ sdtlseqdt0(xp,xq),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

tff(f_357,hypothesis,
    xl != sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).

tff(f_352,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).

tff(f_355,hypothesis,
    ( doDivides0(xl,xm)
    & doDivides0(xl,sdtpldt0(xm,xn)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).

tff(f_358,hypothesis,
    xp = sdtsldt0(xm,xl),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).

tff(f_323,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( ( W0 != sz00 )
          & doDivides0(W0,W1) )
       => ! [W2] :
            ( ( W2 = sdtsldt0(W1,W0) )
          <=> ( aNaturalNumber0(W2)
              & ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).

tff(f_41,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtpldt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).

tff(f_359,hypothesis,
    xq = sdtsldt0(sdtpldt0(xm,xn),xl),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).

tff(f_212,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
        | ( ( W1 != W0 )
          & sdtlseqdt0(W1,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).

tff(f_67,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtpldt0(W0,sz00) = W0 )
        & ( W0 = sdtpldt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).

tff(f_35,axiom,
    ( aNaturalNumber0(sz10)
    & ( sz10 != sz00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).

tff(f_87,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( ( sdtasdt0(W0,sz10) = W0 )
        & ( W0 = sdtasdt0(sz10,W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).

tff(f_278,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( W0 != sz00 )
       => sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).

tff(f_31,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).

tff(f_175,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
       => ! [W2] :
            ( ( W2 = sdtmndt0(W1,W0) )
          <=> ( aNaturalNumber0(W2)
              & ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

tff(f_296,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( ( W0 != W1 )
          & sdtlseqdt0(W0,W1) )
       => iLess0(W0,W1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).

tff(f_360,hypothesis,
    sdtlseqdt0(xm,sdtpldt0(xm,xn)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).

tff(f_258,axiom,
    ! [W0,W1,W2] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1)
        & aNaturalNumber0(W2) )
     => ( ( ( W0 != sz00 )
          & ( W1 != W2 )
          & sdtlseqdt0(W1,W2) )
       => ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
          & sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
          & ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
          & sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).

tff(f_73,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).

tff(f_47,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => aNaturalNumber0(sdtasdt0(W0,W1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).

tff(f_189,axiom,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W0) )
       => ( W0 = W1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).

tff(c_135,plain,
    ~ sdtlseqdt0(xp,xq),
    inference(cnfTransformation,[status(thm)],[f_362]) ).

tff(c_127,plain,
    xl != sz00,
    inference(cnfTransformation,[status(thm)],[f_357]) ).

tff(c_121,plain,
    aNaturalNumber0(xl),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

tff(c_119,plain,
    aNaturalNumber0(xm),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

tff(c_125,plain,
    doDivides0(xl,xm),
    inference(cnfTransformation,[status(thm)],[f_355]) ).

tff(c_129,plain,
    sdtsldt0(xm,xl) = xp,
    inference(cnfTransformation,[status(thm)],[f_358]) ).

tff(c_37322,plain,
    ! [W1_473,W0_474] :
      ( aNaturalNumber0(sdtsldt0(W1_473,W0_474))
      | ~ doDivides0(W0_474,W1_473)
      | ( sz00 = W0_474 )
      | ~ aNaturalNumber0(W1_473)
      | ~ aNaturalNumber0(W0_474) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_37362,plain,
    ( aNaturalNumber0(xp)
    | ~ doDivides0(xl,xm)
    | ( xl = sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_129,c_37322]) ).

tff(c_37379,plain,
    ( aNaturalNumber0(xp)
    | ( xl = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_37362]) ).

tff(c_37380,plain,
    aNaturalNumber0(xp),
    inference(negUnitSimplification,[status(thm)],[c_127,c_37379]) ).

tff(c_117,plain,
    aNaturalNumber0(xn),
    inference(cnfTransformation,[status(thm)],[f_352]) ).

tff(c_10,plain,
    ! [W0_2,W1_3] :
      ( aNaturalNumber0(sdtpldt0(W0_2,W1_3))
      | ~ aNaturalNumber0(W1_3)
      | ~ aNaturalNumber0(W0_2) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_123,plain,
    doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnfTransformation,[status(thm)],[f_355]) ).

tff(c_131,plain,
    sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
    inference(cnfTransformation,[status(thm)],[f_359]) ).

tff(c_37359,plain,
    ( aNaturalNumber0(xq)
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ( xl = sz00 )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_131,c_37322]) ).

tff(c_37376,plain,
    ( aNaturalNumber0(xq)
    | ( xl = sz00 )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_123,c_37359]) ).

tff(c_37377,plain,
    ( aNaturalNumber0(xq)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(negUnitSimplification,[status(thm)],[c_127,c_37376]) ).

tff(c_42022,plain,
    ~ aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(splitLeft,[status(thm)],[c_37377]) ).

tff(c_42025,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(resolution,[status(thm)],[c_10,c_42022]) ).

tff(c_42029,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_117,c_42025]) ).

tff(c_42030,plain,
    aNaturalNumber0(xq),
    inference(splitRight,[status(thm)],[c_37377]) ).

tff(c_70,plain,
    ! [W1_50,W0_49] :
      ( sdtlseqdt0(W1_50,W0_49)
      | sdtlseqdt0(W0_49,W1_50)
      | ~ aNaturalNumber0(W1_50)
      | ~ aNaturalNumber0(W0_49) ),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_72,plain,
    ! [W1_50] :
      ( sdtlseqdt0(W1_50,W1_50)
      | ~ aNaturalNumber0(W1_50) ),
    inference(cnfTransformation,[status(thm)],[f_212]) ).

tff(c_330,plain,
    ! [W0_86] :
      ( ( sdtpldt0(W0_86,sz00) = W0_86 )
      | ~ aNaturalNumber0(W0_86) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_350,plain,
    sdtpldt0(xm,sz00) = xm,
    inference(resolution,[status(thm)],[c_119,c_330]) ).

tff(c_8,plain,
    aNaturalNumber0(sz10),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_199,plain,
    ! [W0_83] :
      ( ( sdtasdt0(sz10,W0_83) = W0_83 )
      | ~ aNaturalNumber0(W0_83) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_218,plain,
    sdtasdt0(sz10,xn) = xn,
    inference(resolution,[status(thm)],[c_117,c_199]) ).

tff(c_1371,plain,
    ! [W1_110,W0_111] :
      ( sdtlseqdt0(W1_110,sdtasdt0(W1_110,W0_111))
      | ( sz00 = W0_111 )
      | ~ aNaturalNumber0(W1_110)
      | ~ aNaturalNumber0(W0_111) ),
    inference(cnfTransformation,[status(thm)],[f_278]) ).

tff(c_1437,plain,
    ( sdtlseqdt0(sz10,xn)
    | ( xn = sz00 )
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xn) ),
    inference(superposition,[status(thm),theory(equality)],[c_218,c_1371]) ).

tff(c_1518,plain,
    ( sdtlseqdt0(sz10,xn)
    | ( xn = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_117,c_8,c_1437]) ).

tff(c_3426,plain,
    xn = sz00,
    inference(splitLeft,[status(thm)],[c_1518]) ).

tff(c_3444,plain,
    sdtsldt0(sdtpldt0(xm,sz00),xl) = xq,
    inference(demodulation,[status(thm),theory(equality)],[c_3426,c_131]) ).

tff(c_3466,plain,
    xq = xp,
    inference(demodulation,[status(thm),theory(equality)],[c_129,c_350,c_3444]) ).

tff(c_3595,plain,
    ~ sdtlseqdt0(xp,xp),
    inference(demodulation,[status(thm),theory(equality)],[c_3466,c_135]) ).

tff(c_3605,plain,
    ~ aNaturalNumber0(xp),
    inference(resolution,[status(thm)],[c_72,c_3595]) ).

tff(c_4102,plain,
    ! [W1_178,W0_179] :
      ( aNaturalNumber0(sdtsldt0(W1_178,W0_179))
      | ~ doDivides0(W0_179,W1_178)
      | ( sz00 = W0_179 )
      | ~ aNaturalNumber0(W1_178)
      | ~ aNaturalNumber0(W0_179) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_4136,plain,
    ( aNaturalNumber0(xp)
    | ~ doDivides0(xl,xm)
    | ( xl = sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_129,c_4102]) ).

tff(c_4149,plain,
    ( aNaturalNumber0(xp)
    | ( xl = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_4136]) ).

tff(c_4151,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_127,c_3605,c_4149]) ).

tff(c_4153,plain,
    xn != sz00,
    inference(splitRight,[status(thm)],[c_1518]) ).

tff(c_6,plain,
    sz10 != sz00,
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_299,plain,
    ! [W0_85] :
      ( ( sdtasdt0(W0_85,sz10) = W0_85 )
      | ~ aNaturalNumber0(W0_85) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_319,plain,
    sdtasdt0(xm,sz10) = xm,
    inference(resolution,[status(thm)],[c_119,c_299]) ).

tff(c_1416,plain,
    ( sdtlseqdt0(xm,xm)
    | ( sz10 = sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sz10) ),
    inference(superposition,[status(thm),theory(equality)],[c_319,c_1371]) ).

tff(c_1499,plain,
    ( sdtlseqdt0(xm,xm)
    | ( sz10 = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_119,c_1416]) ).

tff(c_1500,plain,
    sdtlseqdt0(xm,xm),
    inference(negUnitSimplification,[status(thm)],[c_6,c_1499]) ).

tff(c_4,plain,
    aNaturalNumber0(sz00),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_42124,plain,
    ! [W0_528,W2_529] :
      ( ( sdtmndt0(sdtpldt0(W0_528,W2_529),W0_528) = W2_529 )
      | ~ aNaturalNumber0(W2_529)
      | ~ sdtlseqdt0(W0_528,sdtpldt0(W0_528,W2_529))
      | ~ aNaturalNumber0(sdtpldt0(W0_528,W2_529))
      | ~ aNaturalNumber0(W0_528) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_42175,plain,
    ( ( sdtmndt0(sdtpldt0(xm,sz00),xm) = sz00 )
    | ~ aNaturalNumber0(sz00)
    | ~ sdtlseqdt0(xm,xm)
    | ~ aNaturalNumber0(sdtpldt0(xm,sz00))
    | ~ aNaturalNumber0(xm) ),
    inference(superposition,[status(thm),theory(equality)],[c_350,c_42124]) ).

tff(c_42218,plain,
    sdtmndt0(xm,xm) = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_119,c_350,c_1500,c_4,c_350,c_42175]) ).

tff(c_37650,plain,
    ! [W0_481,W1_482] :
      ( ( sdtasdt0(W0_481,sdtsldt0(W1_482,W0_481)) = W1_482 )
      | ~ doDivides0(W0_481,W1_482)
      | ( sz00 = W0_481 )
      | ~ aNaturalNumber0(W1_482)
      | ~ aNaturalNumber0(W0_481) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_37673,plain,
    ( ( sdtasdt0(xl,xp) = xm )
    | ~ doDivides0(xl,xm)
    | ( xl = sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_129,c_37650]) ).

tff(c_37680,plain,
    ( ( sdtasdt0(xl,xp) = xm )
    | ( xl = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_37673]) ).

tff(c_37681,plain,
    sdtasdt0(xl,xp) = xm,
    inference(negUnitSimplification,[status(thm)],[c_127,c_37680]) ).

tff(c_3348,plain,
    ! [W0_158,W1_159] :
      ( iLess0(W0_158,W1_159)
      | ~ sdtlseqdt0(W0_158,W1_159)
      | ( W1_159 = W0_158 )
      | ~ aNaturalNumber0(W1_159)
      | ~ aNaturalNumber0(W0_158) ),
    inference(cnfTransformation,[status(thm)],[f_296]) ).

tff(c_58796,plain,
    ! [W1_576,W0_577] :
      ( iLess0(W1_576,W0_577)
      | ( W1_576 = W0_577 )
      | sdtlseqdt0(W0_577,W1_576)
      | ~ aNaturalNumber0(W1_576)
      | ~ aNaturalNumber0(W0_577) ),
    inference(resolution,[status(thm)],[c_70,c_3348]) ).

tff(c_58853,plain,
    ( iLess0(xq,xp)
    | ( xq = xp )
    | ~ aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xp) ),
    inference(resolution,[status(thm)],[c_58796,c_135]) ).

tff(c_58915,plain,
    ( iLess0(xq,xp)
    | ( xq = xp ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_37380,c_42030,c_58853]) ).

tff(c_58916,plain,
    xq = xp,
    inference(splitLeft,[status(thm)],[c_58915]) ).

tff(c_42031,plain,
    aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(splitRight,[status(thm)],[c_37377]) ).

tff(c_37670,plain,
    ( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ( xl = sz00 )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[status(thm),theory(equality)],[c_131,c_37650]) ).

tff(c_37677,plain,
    ( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
    | ( xl = sz00 )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_123,c_37670]) ).

tff(c_37678,plain,
    ( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(negUnitSimplification,[status(thm)],[c_127,c_37677]) ).

tff(c_56608,plain,
    sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
    inference(demodulation,[status(thm),theory(equality)],[c_42031,c_37678]) ).

tff(c_133,plain,
    sdtlseqdt0(xm,sdtpldt0(xm,xn)),
    inference(cnfTransformation,[status(thm)],[f_360]) ).

tff(c_42199,plain,
    ( ( sdtmndt0(sdtpldt0(xm,xn),xm) = xn )
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xm) ),
    inference(resolution,[status(thm)],[c_133,c_42124]) ).

tff(c_42235,plain,
    sdtmndt0(sdtpldt0(xm,xn),xm) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_42031,c_117,c_42199]) ).

tff(c_56615,plain,
    sdtmndt0(sdtasdt0(xl,xq),xm) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_56608,c_42235]) ).

tff(c_58928,plain,
    sdtmndt0(sdtasdt0(xl,xp),xm) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_58916,c_56615]) ).

tff(c_58989,plain,
    xn = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_42218,c_37681,c_58928]) ).

tff(c_58991,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4153,c_58989]) ).

tff(c_58993,plain,
    xq != xp,
    inference(splitRight,[status(thm)],[c_58915]) ).

tff(c_109,plain,
    ! [W0_70,W1_71] :
      ( ( sdtasdt0(W0_70,sdtsldt0(W1_71,W0_70)) = W1_71 )
      | ~ doDivides0(W0_70,W1_71)
      | ( sz00 = W0_70 )
      | ~ aNaturalNumber0(W1_71)
      | ~ aNaturalNumber0(W0_70) ),
    inference(cnfTransformation,[status(thm)],[f_323]) ).

tff(c_42402,plain,
    ! [W0_530,W1_531,W2_532] :
      ( sdtlseqdt0(sdtasdt0(W0_530,W1_531),sdtasdt0(W0_530,W2_532))
      | ~ sdtlseqdt0(W1_531,W2_532)
      | ( W2_532 = W1_531 )
      | ( sz00 = W0_530 )
      | ~ aNaturalNumber0(W2_532)
      | ~ aNaturalNumber0(W1_531)
      | ~ aNaturalNumber0(W0_530) ),
    inference(cnfTransformation,[status(thm)],[f_258]) ).

tff(c_193751,plain,
    ! [W0_1085,W1_1086,W1_1087] :
      ( sdtlseqdt0(sdtasdt0(W0_1085,W1_1086),W1_1087)
      | ~ sdtlseqdt0(W1_1086,sdtsldt0(W1_1087,W0_1085))
      | ( sdtsldt0(W1_1087,W0_1085) = W1_1086 )
      | ( sz00 = W0_1085 )
      | ~ aNaturalNumber0(sdtsldt0(W1_1087,W0_1085))
      | ~ aNaturalNumber0(W1_1086)
      | ~ aNaturalNumber0(W0_1085)
      | ~ doDivides0(W0_1085,W1_1087)
      | ( sz00 = W0_1085 )
      | ~ aNaturalNumber0(W1_1087)
      | ~ aNaturalNumber0(W0_1085) ),
    inference(superposition,[status(thm),theory(equality)],[c_109,c_42402]) ).

tff(c_692,plain,
    ! [W1_96,W0_97] :
      ( ( sdtasdt0(W1_96,W0_97) = sdtasdt0(W0_97,W1_96) )
      | ~ aNaturalNumber0(W1_96)
      | ~ aNaturalNumber0(W0_97) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_44128,plain,
    ! [W0_538] :
      ( ( sdtasdt0(xl,W0_538) = sdtasdt0(W0_538,xl) )
      | ~ aNaturalNumber0(W0_538) ),
    inference(resolution,[status(thm)],[c_121,c_692]) ).

tff(c_44190,plain,
    sdtasdt0(xq,xl) = sdtasdt0(xl,xq),
    inference(resolution,[status(thm)],[c_42030,c_44128]) ).

tff(c_12,plain,
    ! [W0_4,W1_5] :
      ( aNaturalNumber0(sdtasdt0(W0_4,W1_5))
      | ~ aNaturalNumber0(W1_5)
      | ~ aNaturalNumber0(W0_4) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_53997,plain,
    ( aNaturalNumber0(sdtasdt0(xl,xq))
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xq) ),
    inference(superposition,[status(thm),theory(equality)],[c_44190,c_12]) ).

tff(c_54046,plain,
    aNaturalNumber0(sdtasdt0(xl,xq)),
    inference(demodulation,[status(thm),theory(equality)],[c_42030,c_121,c_53997]) ).

tff(c_3387,plain,
    ( iLess0(xm,sdtpldt0(xm,xn))
    | ( sdtpldt0(xm,xn) = xm )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xm) ),
    inference(resolution,[status(thm)],[c_133,c_3348]) ).

tff(c_3424,plain,
    ( iLess0(xm,sdtpldt0(xm,xn))
    | ( sdtpldt0(xm,xn) = xm )
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_3387]) ).

tff(c_66211,plain,
    ( iLess0(xm,sdtasdt0(xl,xq))
    | ( sdtasdt0(xl,xq) = xm ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54046,c_56608,c_56608,c_56608,c_3424]) ).

tff(c_66212,plain,
    sdtasdt0(xl,xq) = xm,
    inference(splitLeft,[status(thm)],[c_66211]) ).

tff(c_66223,plain,
    sdtmndt0(xm,xm) = xn,
    inference(demodulation,[status(thm),theory(equality)],[c_66212,c_56615]) ).

tff(c_66243,plain,
    xn = sz00,
    inference(demodulation,[status(thm),theory(equality)],[c_42218,c_66223]) ).

tff(c_66245,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4153,c_66243]) ).

tff(c_66247,plain,
    sdtasdt0(xl,xq) != xm,
    inference(splitRight,[status(thm)],[c_66211]) ).

tff(c_1588,plain,
    ! [W1_114,W0_115] :
      ( ( W1_114 = W0_115 )
      | ~ sdtlseqdt0(W1_114,W0_115)
      | ~ sdtlseqdt0(W0_115,W1_114)
      | ~ aNaturalNumber0(W1_114)
      | ~ aNaturalNumber0(W0_115) ),
    inference(cnfTransformation,[status(thm)],[f_189]) ).

tff(c_1612,plain,
    ( ( sdtpldt0(xm,xn) = xm )
    | ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(resolution,[status(thm)],[c_133,c_1588]) ).

tff(c_1646,plain,
    ( ( sdtpldt0(xm,xn) = xm )
    | ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_119,c_1612]) ).

tff(c_67509,plain,
    ( ( sdtasdt0(xl,xq) = xm )
    | ~ sdtlseqdt0(sdtasdt0(xl,xq),xm) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54046,c_56608,c_56608,c_56608,c_1646]) ).

tff(c_67510,plain,
    ~ sdtlseqdt0(sdtasdt0(xl,xq),xm),
    inference(negUnitSimplification,[status(thm)],[c_66247,c_67509]) ).

tff(c_193860,plain,
    ( ~ sdtlseqdt0(xq,sdtsldt0(xm,xl))
    | ( sdtsldt0(xm,xl) = xq )
    | ~ aNaturalNumber0(sdtsldt0(xm,xl))
    | ~ aNaturalNumber0(xq)
    | ~ doDivides0(xl,xm)
    | ( xl = sz00 )
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(resolution,[status(thm)],[c_193751,c_67510]) ).

tff(c_194531,plain,
    ( ~ sdtlseqdt0(xq,xp)
    | ( xq = xp )
    | ( xl = sz00 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_42030,c_37380,c_129,c_129,c_129,c_193860]) ).

tff(c_194532,plain,
    ~ sdtlseqdt0(xq,xp),
    inference(negUnitSimplification,[status(thm)],[c_127,c_58993,c_194531]) ).

tff(c_194979,plain,
    ( sdtlseqdt0(xp,xq)
    | ~ aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xp) ),
    inference(resolution,[status(thm)],[c_70,c_194532]) ).

tff(c_194992,plain,
    sdtlseqdt0(xp,xq),
    inference(demodulation,[status(thm),theory(equality)],[c_37380,c_42030,c_194979]) ).

tff(c_194994,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_135,c_194992]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM473+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/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 : n025.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 14:36:34 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 105.44/88.05  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 105.55/88.06  
% 105.55/88.06  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 105.73/88.11  
% 105.73/88.11  Inference rules
% 105.73/88.11  ----------------------
% 105.73/88.11  #Ref     : 20
% 105.73/88.11  #Sup     : 41706
% 105.73/88.11  #Fact    : 16
% 105.73/88.11  #Define  : 0
% 105.73/88.11  #Split   : 39
% 105.73/88.11  #Chain   : 0
% 105.73/88.11  #Close   : 0
% 105.73/88.11  
% 105.73/88.11  Ordering : KBO
% 105.73/88.11  
% 105.73/88.11  Simplification rules
% 105.73/88.11  ----------------------
% 105.73/88.11  #Subsume      : 4323
% 105.73/88.11  #Demod        : 89053
% 105.73/88.11  #Tautology    : 10538
% 105.73/88.11  #SimpNegUnit  : 7054
% 105.73/88.11  #BackRed      : 951
% 105.73/88.11  
% 105.73/88.11  #Partial instantiations: 0
% 105.73/88.11  #Strategies tried      : 1
% 105.73/88.11  
% 105.73/88.11  Timing (in seconds)
% 105.73/88.11  ----------------------
% 105.73/88.11  Preprocessing        : 0.68
% 105.73/88.11  Parsing              : 0.35
% 105.73/88.11  CNF conversion       : 0.05
% 105.73/88.11  Main loop            : 86.22
% 105.73/88.11  Inferencing          : 6.56
% 105.73/88.11  Reduction            : 59.05
% 105.73/88.11  Demodulation         : 50.54
% 105.73/88.11  BG Simplification    : 0.48
% 105.73/88.11  Subsumption          : 17.61
% 105.73/88.11  Abstraction          : 0.75
% 105.73/88.11  MUC search           : 0.00
% 105.73/88.11  Cooper               : 0.00
% 105.73/88.12  Total                : 86.98
% 105.73/88.12  Index Insertion      : 0.00
% 105.73/88.12  Index Deletion       : 0.00
% 105.73/88.12  Index Matching       : 0.00
% 105.73/88.12  BG Taut test         : 0.00
%------------------------------------------------------------------------------