TSTP Solution File: RNG066+1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : RNG066+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n002.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 May 21 02:36:08 EDT 2024

% Result   : Theorem 12.28s 2.04s
% Output   : CNFRefutation 12.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  197 (  86 unt;   0 def)
%            Number of atoms       :  503 ( 125 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  523 ( 217   ~; 216   |;  67   &)
%                                         (   0 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  17 con; 0-2 aty)
%            Number of variables   :  148 (   1 sgn  72   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mMNeg,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
        & sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).

fof(mMulSc,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => aScalar0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).

fof(m__1930,hypothesis,
    ( aScalar0(xS)
    & xS = sdtasdt0(xF,xD) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).

fof(m__1800,hypothesis,
    ( aScalar0(xD)
    & xD = sdtasasdt0(xq,xq) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).

fof(m__1837,hypothesis,
    ( aScalar0(xF)
    & xF = sdtasdt0(xA,xA) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).

fof(mScZero,axiom,
    ! [X1] :
      ( aScalar0(X1)
     => ( sdtpldt0(X1,sz0z00) = X1
        & sdtpldt0(sz0z00,X1) = X1
        & sdtasdt0(X1,sz0z00) = sz0z00
        & sdtasdt0(sz0z00,X1) = sz0z00
        & sdtpldt0(X1,smndt0(X1)) = sz0z00
        & sdtpldt0(smndt0(X1),X1) = sz0z00
        & smndt0(smndt0(X1)) = X1
        & smndt0(sz0z00) = sz0z00 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).

fof(m__1949,hypothesis,
    ( aScalar0(xN)
    & xN = sdtasdt0(xR,xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).

fof(m__1892,hypothesis,
    ( aScalar0(xR)
    & xR = sdtasdt0(xC,xG) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).

fof(mNegSc,axiom,
    ! [X1] :
      ( aScalar0(X1)
     => aScalar0(smndt0(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).

fof(mScSqPos,axiom,
    ! [X1] :
      ( aVector0(X1)
     => sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).

fof(mSqPos,axiom,
    ! [X1] :
      ( aScalar0(X1)
     => sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).

fof(mPosMon,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => ( ( sdtlseqdt0(sz0z00,X1)
          & sdtlseqdt0(sz0z00,X2) )
       => ( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
          & sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).

fof(m__1726,hypothesis,
    ( aVector0(xq)
    & xq = sziznziztdt0(xt) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).

fof(m__1746,hypothesis,
    ( aScalar0(xA)
    & xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).

fof(m__1854,hypothesis,
    ( aScalar0(xG)
    & xG = sdtasdt0(xB,xB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).

fof(m__1766,hypothesis,
    ( aScalar0(xB)
    & xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).

fof(m__1783,hypothesis,
    ( aScalar0(xC)
    & xC = sdtasasdt0(xp,xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).

fof(m__1709,hypothesis,
    ( aVector0(xp)
    & xp = sziznziztdt0(xs) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).

fof(mLEMon,axiom,
    ! [X1,X2,X3,X4] :
      ( ( aScalar0(X1)
        & aScalar0(X2)
        & aScalar0(X3)
        & aScalar0(X4) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X3,X4) )
       => sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMon) ).

fof(mSZeroSc,axiom,
    aScalar0(sz0z00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).

fof(mLEMonM,axiom,
    ! [X1,X2,X3,X4] :
      ( ( aScalar0(X1)
        & aScalar0(X2)
        & aScalar0(X3)
        & aScalar0(X4) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(sz0z00,X3)
          & sdtlseqdt0(X3,X4) )
       => sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMonM) ).

fof(mLETot,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | sdtlseqdt0(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).

fof(mArith,axiom,
    ! [X1,X2,X3] :
      ( ( aScalar0(X1)
        & aScalar0(X2)
        & aScalar0(X3) )
     => ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
        & sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
        & sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
        & sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).

fof(mLERef,axiom,
    ! [X1] :
      ( aScalar0(X1)
     => sdtlseqdt0(X1,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).

fof(mLEASm,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).

fof(mLETrn,axiom,
    ! [X1,X2,X3] :
      ( ( aScalar0(X1)
        & aScalar0(X2)
        & aScalar0(X3) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X3) )
       => sdtlseqdt0(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).

fof(m__1911,hypothesis,
    ( aScalar0(xP)
    & xP = sdtasdt0(xE,xH) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).

fof(m__1873,hypothesis,
    ( aScalar0(xH)
    & xH = sdtasdt0(xA,xB) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1873) ).

fof(m__1820,hypothesis,
    ( aScalar0(xE)
    & xE = sdtasasdt0(xp,xq) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).

fof(m__2004,hypothesis,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2004) ).

fof(m__,conjecture,
    sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mDistr,axiom,
    ! [X1,X2,X3] :
      ( ( aScalar0(X1)
        & aScalar0(X2)
        & aScalar0(X3) )
     => ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
        & sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).

fof(mSumSc,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => aScalar0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).

fof(mSqrt,axiom,
    ! [X1,X2] :
      ( ( aScalar0(X1)
        & aScalar0(X2) )
     => ( ( sdtlseqdt0(sz0z00,X1)
          & sdtlseqdt0(sz0z00,X2)
          & sdtasdt0(X1,X1) = sdtasdt0(X2,X2) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).

fof(c_0_34,plain,
    ! [X31,X32] :
      ( ( sdtasdt0(X31,smndt0(X32)) = smndt0(sdtasdt0(X31,X32))
        | ~ aScalar0(X31)
        | ~ aScalar0(X32) )
      & ( sdtasdt0(smndt0(X31),X32) = smndt0(sdtasdt0(X31,X32))
        | ~ aScalar0(X31)
        | ~ aScalar0(X32) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])])]) ).

fof(c_0_35,plain,
    ! [X17,X18] :
      ( ~ aScalar0(X17)
      | ~ aScalar0(X18)
      | aScalar0(sdtasdt0(X17,X18)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])])]) ).

cnf(c_0_36,plain,
    ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_37,hypothesis,
    xS = sdtasdt0(xF,xD),
    inference(split_conjunct,[status(thm)],[m__1930]) ).

cnf(c_0_38,hypothesis,
    aScalar0(xD),
    inference(split_conjunct,[status(thm)],[m__1800]) ).

cnf(c_0_39,hypothesis,
    aScalar0(xF),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

fof(c_0_40,plain,
    ! [X20] :
      ( ( sdtpldt0(X20,sz0z00) = X20
        | ~ aScalar0(X20) )
      & ( sdtpldt0(sz0z00,X20) = X20
        | ~ aScalar0(X20) )
      & ( sdtasdt0(X20,sz0z00) = sz0z00
        | ~ aScalar0(X20) )
      & ( sdtasdt0(sz0z00,X20) = sz0z00
        | ~ aScalar0(X20) )
      & ( sdtpldt0(X20,smndt0(X20)) = sz0z00
        | ~ aScalar0(X20) )
      & ( sdtpldt0(smndt0(X20),X20) = sz0z00
        | ~ aScalar0(X20) )
      & ( smndt0(smndt0(X20)) = X20
        | ~ aScalar0(X20) )
      & ( smndt0(sz0z00) = sz0z00
        | ~ aScalar0(X20) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])])]) ).

cnf(c_0_41,hypothesis,
    xN = sdtasdt0(xR,xS),
    inference(split_conjunct,[status(thm)],[m__1949]) ).

cnf(c_0_42,hypothesis,
    aScalar0(xS),
    inference(split_conjunct,[status(thm)],[m__1930]) ).

cnf(c_0_43,hypothesis,
    aScalar0(xR),
    inference(split_conjunct,[status(thm)],[m__1892]) ).

cnf(c_0_44,plain,
    ( aScalar0(sdtasdt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_45,hypothesis,
    sdtasdt0(xF,smndt0(xD)) = smndt0(xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]) ).

fof(c_0_46,plain,
    ! [X19] :
      ( ~ aScalar0(X19)
      | aScalar0(smndt0(X19)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])])]) ).

fof(c_0_47,plain,
    ! [X75] :
      ( ~ aVector0(X75)
      | sdtlseqdt0(sz0z00,sdtasasdt0(X75,X75)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])])]) ).

fof(c_0_48,plain,
    ! [X55] :
      ( ~ aScalar0(X55)
      | sdtlseqdt0(sz0z00,sdtasdt0(X55,X55)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])])]) ).

cnf(c_0_49,plain,
    ( smndt0(smndt0(X1)) = X1
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_50,hypothesis,
    sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_41]),c_0_42]),c_0_43])]) ).

cnf(c_0_51,hypothesis,
    ( aScalar0(smndt0(xS))
    | ~ aScalar0(smndt0(xD)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_39])]) ).

cnf(c_0_52,plain,
    ( aScalar0(smndt0(X1))
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

fof(c_0_53,plain,
    ! [X53,X54] :
      ( ( sdtlseqdt0(sz0z00,sdtpldt0(X53,X54))
        | ~ sdtlseqdt0(sz0z00,X53)
        | ~ sdtlseqdt0(sz0z00,X54)
        | ~ aScalar0(X53)
        | ~ aScalar0(X54) )
      & ( sdtlseqdt0(sz0z00,sdtasdt0(X53,X54))
        | ~ sdtlseqdt0(sz0z00,X53)
        | ~ sdtlseqdt0(sz0z00,X54)
        | ~ aScalar0(X53)
        | ~ aScalar0(X54) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])])]) ).

cnf(c_0_54,plain,
    ( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
    | ~ aVector0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_55,hypothesis,
    xD = sdtasasdt0(xq,xq),
    inference(split_conjunct,[status(thm)],[m__1800]) ).

cnf(c_0_56,hypothesis,
    aVector0(xq),
    inference(split_conjunct,[status(thm)],[m__1726]) ).

cnf(c_0_57,plain,
    ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_58,hypothesis,
    xF = sdtasdt0(xA,xA),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_59,hypothesis,
    aScalar0(xA),
    inference(split_conjunct,[status(thm)],[m__1746]) ).

cnf(c_0_60,hypothesis,
    xG = sdtasdt0(xB,xB),
    inference(split_conjunct,[status(thm)],[m__1854]) ).

cnf(c_0_61,hypothesis,
    aScalar0(xB),
    inference(split_conjunct,[status(thm)],[m__1766]) ).

cnf(c_0_62,hypothesis,
    xC = sdtasasdt0(xp,xp),
    inference(split_conjunct,[status(thm)],[m__1783]) ).

cnf(c_0_63,hypothesis,
    aVector0(xp),
    inference(split_conjunct,[status(thm)],[m__1709]) ).

cnf(c_0_64,hypothesis,
    xR = sdtasdt0(xC,xG),
    inference(split_conjunct,[status(thm)],[m__1892]) ).

cnf(c_0_65,hypothesis,
    aScalar0(xG),
    inference(split_conjunct,[status(thm)],[m__1854]) ).

cnf(c_0_66,hypothesis,
    aScalar0(xC),
    inference(split_conjunct,[status(thm)],[m__1783]) ).

fof(c_0_67,plain,
    ! [X43,X44,X45,X46] :
      ( ~ aScalar0(X43)
      | ~ aScalar0(X44)
      | ~ aScalar0(X45)
      | ~ aScalar0(X46)
      | ~ sdtlseqdt0(X43,X44)
      | ~ sdtlseqdt0(X45,X46)
      | sdtlseqdt0(sdtpldt0(X43,X45),sdtpldt0(X44,X46)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])])]) ).

cnf(c_0_68,plain,
    ( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_36]),c_0_44]) ).

cnf(c_0_69,hypothesis,
    ( aScalar0(smndt0(xN))
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_50]),c_0_43])]) ).

cnf(c_0_70,hypothesis,
    aScalar0(smndt0(xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_38])]) ).

cnf(c_0_71,plain,
    ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
    | ~ sdtlseqdt0(sz0z00,X1)
    | ~ sdtlseqdt0(sz0z00,X2)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_72,hypothesis,
    sdtlseqdt0(sz0z00,xD),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).

cnf(c_0_73,hypothesis,
    sdtlseqdt0(sz0z00,xF),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).

cnf(c_0_74,hypothesis,
    sdtlseqdt0(sz0z00,xG),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_60]),c_0_61])]) ).

cnf(c_0_75,hypothesis,
    sdtlseqdt0(sz0z00,xC),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_62]),c_0_63])]) ).

cnf(c_0_76,hypothesis,
    sdtasdt0(xC,smndt0(xG)) = smndt0(xR),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_64]),c_0_65]),c_0_66])]) ).

cnf(c_0_77,plain,
    ( sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3)
    | ~ aScalar0(X4)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_78,plain,
    ( sdtpldt0(sz0z00,X1) = X1
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_79,plain,
    aScalar0(sz0z00),
    inference(split_conjunct,[status(thm)],[mSZeroSc]) ).

cnf(c_0_80,plain,
    ( sdtpldt0(smndt0(X1),X1) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_81,hypothesis,
    smndt0(smndt0(xN)) = xN,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_50]),c_0_41]),c_0_42]),c_0_43])]) ).

cnf(c_0_82,hypothesis,
    aScalar0(smndt0(xN)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).

cnf(c_0_83,hypothesis,
    sdtlseqdt0(sz0z00,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_37]),c_0_72]),c_0_73]),c_0_38]),c_0_39])]) ).

cnf(c_0_84,hypothesis,
    sdtlseqdt0(sz0z00,xR),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_64]),c_0_74]),c_0_75]),c_0_65]),c_0_66])]) ).

fof(c_0_85,plain,
    ! [X47,X48,X49,X50] :
      ( ~ aScalar0(X47)
      | ~ aScalar0(X48)
      | ~ aScalar0(X49)
      | ~ aScalar0(X50)
      | ~ sdtlseqdt0(X47,X48)
      | ~ sdtlseqdt0(sz0z00,X49)
      | ~ sdtlseqdt0(X49,X50)
      | sdtlseqdt0(sdtasdt0(X47,X49),sdtasdt0(X48,X50)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])])]) ).

cnf(c_0_86,plain,
    ( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_87,hypothesis,
    ( aScalar0(smndt0(xR))
    | ~ aScalar0(smndt0(xG)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_76]),c_0_66])]) ).

fof(c_0_88,plain,
    ! [X51,X52] :
      ( ~ aScalar0(X51)
      | ~ aScalar0(X52)
      | sdtlseqdt0(X51,X52)
      | sdtlseqdt0(X52,X51) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])])]) ).

fof(c_0_89,plain,
    ! [X21,X22,X23] :
      ( ( sdtpldt0(sdtpldt0(X21,X22),X23) = sdtpldt0(X21,sdtpldt0(X22,X23))
        | ~ aScalar0(X21)
        | ~ aScalar0(X22)
        | ~ aScalar0(X23) )
      & ( sdtpldt0(X21,X22) = sdtpldt0(X22,X21)
        | ~ aScalar0(X21)
        | ~ aScalar0(X22)
        | ~ aScalar0(X23) )
      & ( sdtasdt0(sdtasdt0(X21,X22),X23) = sdtasdt0(X21,sdtasdt0(X22,X23))
        | ~ aScalar0(X21)
        | ~ aScalar0(X22)
        | ~ aScalar0(X23) )
      & ( sdtasdt0(X21,X22) = sdtasdt0(X22,X21)
        | ~ aScalar0(X21)
        | ~ aScalar0(X22)
        | ~ aScalar0(X23) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])])]) ).

cnf(c_0_90,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X2,X3))
    | ~ sdtlseqdt0(sz0z00,X2)
    | ~ sdtlseqdt0(X1,X3)
    | ~ aScalar0(X3)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79])]) ).

cnf(c_0_91,hypothesis,
    sdtpldt0(xN,smndt0(xN)) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).

cnf(c_0_92,hypothesis,
    sdtlseqdt0(sz0z00,xN),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_41]),c_0_42]),c_0_43])]),c_0_83]),c_0_84])]) ).

cnf(c_0_93,hypothesis,
    aScalar0(xN),
    inference(split_conjunct,[status(thm)],[m__1949]) ).

fof(c_0_94,plain,
    ! [X37] :
      ( ~ aScalar0(X37)
      | sdtlseqdt0(X37,X37) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])])]) ).

cnf(c_0_95,plain,
    ( sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3)
    | ~ aScalar0(X4)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(sz0z00,X3)
    | ~ sdtlseqdt0(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_85]) ).

cnf(c_0_96,hypothesis,
    sdtasdt0(smndt0(xR),xS) = smndt0(xN),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_41]),c_0_42]),c_0_43])]) ).

cnf(c_0_97,hypothesis,
    aScalar0(smndt0(xR)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_52]),c_0_65])]) ).

cnf(c_0_98,plain,
    ( sdtasdt0(sz0z00,X1) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_99,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_88]) ).

cnf(c_0_100,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_89]) ).

cnf(c_0_101,plain,
    ( sdtpldt0(X1,smndt0(X1)) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

fof(c_0_102,plain,
    ! [X38,X39] :
      ( ~ aScalar0(X38)
      | ~ aScalar0(X39)
      | ~ sdtlseqdt0(X38,X39)
      | ~ sdtlseqdt0(X39,X38)
      | X38 = X39 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])])]) ).

cnf(c_0_103,hypothesis,
    ( sdtlseqdt0(X1,sz0z00)
    | ~ sdtlseqdt0(X1,smndt0(xN))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_82]),c_0_93])]) ).

cnf(c_0_104,plain,
    ( sdtlseqdt0(X1,X1)
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_105,hypothesis,
    ( sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xN))
    | ~ sdtlseqdt0(X1,smndt0(xR))
    | ~ sdtlseqdt0(sz0z00,X2)
    | ~ sdtlseqdt0(X2,xS)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_42])]),c_0_97])]) ).

cnf(c_0_106,plain,
    ( sdtasdt0(X1,sz0z00) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_107,plain,
    sdtlseqdt0(sz0z00,sz0z00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_98]),c_0_79])]) ).

cnf(c_0_108,hypothesis,
    ( sdtlseqdt0(X1,smndt0(xR))
    | sdtlseqdt0(smndt0(xR),X1)
    | ~ aScalar0(X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_97]) ).

cnf(c_0_109,plain,
    ( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_80]),c_0_52]) ).

cnf(c_0_110,hypothesis,
    sdtpldt0(smndt0(xN),xN) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_81]),c_0_82])]) ).

fof(c_0_111,plain,
    ! [X40,X41,X42] :
      ( ~ aScalar0(X40)
      | ~ aScalar0(X41)
      | ~ aScalar0(X42)
      | ~ sdtlseqdt0(X40,X41)
      | ~ sdtlseqdt0(X41,X42)
      | sdtlseqdt0(X40,X42) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])])]) ).

cnf(c_0_112,plain,
    ( X1 = X2
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_102]) ).

cnf(c_0_113,hypothesis,
    sdtlseqdt0(smndt0(xN),sz0z00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_82])]) ).

cnf(c_0_114,hypothesis,
    ( sdtlseqdt0(sz0z00,smndt0(xN))
    | ~ sdtlseqdt0(X1,smndt0(xR))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_83]),c_0_79])]) ).

cnf(c_0_115,hypothesis,
    sdtlseqdt0(smndt0(xR),smndt0(xR)),
    inference(spm,[status(thm)],[c_0_108,c_0_97]) ).

cnf(c_0_116,plain,
    ( sdtpldt0(X1,sz0z00) = X1
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_117,hypothesis,
    sdtpldt0(xN,sz0z00) = sdtpldt0(sz0z00,xN),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_81]),c_0_93]),c_0_82])]) ).

cnf(c_0_118,hypothesis,
    xP = sdtasdt0(xE,xH),
    inference(split_conjunct,[status(thm)],[m__1911]) ).

cnf(c_0_119,hypothesis,
    aScalar0(xH),
    inference(split_conjunct,[status(thm)],[m__1873]) ).

cnf(c_0_120,hypothesis,
    aScalar0(xE),
    inference(split_conjunct,[status(thm)],[m__1820]) ).

cnf(c_0_121,hypothesis,
    sdtlseqdt0(sdtasdt0(xP,xP),xN),
    inference(split_conjunct,[status(thm)],[m__2004]) ).

cnf(c_0_122,plain,
    ( sdtlseqdt0(X1,X3)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_111]) ).

cnf(c_0_123,hypothesis,
    ( smndt0(xN) = sz0z00
    | ~ sdtlseqdt0(sz0z00,smndt0(xN)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_82]),c_0_79])]) ).

cnf(c_0_124,hypothesis,
    sdtlseqdt0(sz0z00,smndt0(xN)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_97])]) ).

cnf(c_0_125,hypothesis,
    sdtpldt0(sz0z00,xN) = xN,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_93])]) ).

cnf(c_0_126,hypothesis,
    sdtasdt0(xE,smndt0(xH)) = smndt0(xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_118]),c_0_119]),c_0_120])]) ).

cnf(c_0_127,hypothesis,
    ( sdtasdt0(xP,xP) = xN
    | ~ sdtlseqdt0(xN,sdtasdt0(xP,xP))
    | ~ aScalar0(sdtasdt0(xP,xP)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_121]),c_0_93])]) ).

cnf(c_0_128,plain,
    ( sdtlseqdt0(X1,sdtasdt0(X2,X2))
    | ~ sdtlseqdt0(X1,sz0z00)
    | ~ aScalar0(sdtasdt0(X2,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_57]),c_0_79])]) ).

cnf(c_0_129,hypothesis,
    aScalar0(xP),
    inference(split_conjunct,[status(thm)],[m__1911]) ).

cnf(c_0_130,hypothesis,
    smndt0(xN) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).

cnf(c_0_131,hypothesis,
    sdtpldt0(xN,sz0z00) = xN,
    inference(rw,[status(thm)],[c_0_117,c_0_125]) ).

cnf(c_0_132,hypothesis,
    smndt0(smndt0(xS)) = xS,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_45]),c_0_37]),c_0_38]),c_0_39])]) ).

cnf(c_0_133,plain,
    ( aScalar0(sdtasdt0(X1,smndt0(X2)))
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_36]),c_0_44]) ).

cnf(c_0_134,hypothesis,
    sdtasdt0(xA,smndt0(xA)) = smndt0(xF),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_58]),c_0_59])]) ).

cnf(c_0_135,plain,
    ( smndt0(sz0z00) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_136,hypothesis,
    ( aScalar0(smndt0(xP))
    | ~ aScalar0(smndt0(xH)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_126]),c_0_120])]) ).

cnf(c_0_137,hypothesis,
    ( sdtasdt0(xP,xP) = xN
    | ~ sdtlseqdt0(xN,sz0z00)
    | ~ aScalar0(sdtasdt0(xP,xP)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_93]),c_0_129])]) ).

cnf(c_0_138,hypothesis,
    xN = sz0z00,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_130]),c_0_131]) ).

fof(c_0_139,negated_conjecture,
    ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

fof(c_0_140,plain,
    ! [X24,X25,X26] :
      ( ( sdtasdt0(X24,sdtpldt0(X25,X26)) = sdtpldt0(sdtasdt0(X24,X25),sdtasdt0(X24,X26))
        | ~ aScalar0(X24)
        | ~ aScalar0(X25)
        | ~ aScalar0(X26) )
      & ( sdtasdt0(sdtpldt0(X24,X25),X26) = sdtpldt0(sdtasdt0(X24,X26),sdtasdt0(X25,X26))
        | ~ aScalar0(X24)
        | ~ aScalar0(X25)
        | ~ aScalar0(X26) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])])]) ).

cnf(c_0_141,hypothesis,
    sdtpldt0(xS,smndt0(xS)) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_132]),c_0_70])]) ).

cnf(c_0_142,hypothesis,
    sdtasdt0(smndt0(xF),xD) = smndt0(xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_37]),c_0_38]),c_0_39])]) ).

cnf(c_0_143,hypothesis,
    aScalar0(smndt0(xF)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_59])]) ).

cnf(c_0_144,hypothesis,
    smndt0(sz0z00) = sz0z00,
    inference(spm,[status(thm)],[c_0_135,c_0_93]) ).

cnf(c_0_145,hypothesis,
    smndt0(smndt0(xP)) = xP,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_126]),c_0_118]),c_0_119]),c_0_120])]) ).

cnf(c_0_146,hypothesis,
    aScalar0(smndt0(xP)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_52]),c_0_119])]) ).

cnf(c_0_147,hypothesis,
    ( sdtasdt0(xP,xP) = sz0z00
    | ~ aScalar0(sdtasdt0(xP,xP)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138]),c_0_138]),c_0_107])]) ).

fof(c_0_148,negated_conjecture,
    ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
    inference(fof_nnf,[status(thm)],[c_0_139]) ).

fof(c_0_149,plain,
    ! [X15,X16] :
      ( ~ aScalar0(X15)
      | ~ aScalar0(X16)
      | aScalar0(sdtpldt0(X15,X16)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])])]) ).

cnf(c_0_150,plain,
    ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_140]) ).

cnf(c_0_151,hypothesis,
    ( sdtlseqdt0(X1,sz0z00)
    | ~ sdtlseqdt0(X1,smndt0(xS))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_141]),c_0_83]),c_0_70]),c_0_42])]) ).

cnf(c_0_152,hypothesis,
    ( sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xS))
    | ~ sdtlseqdt0(X1,smndt0(xF))
    | ~ sdtlseqdt0(sz0z00,X2)
    | ~ sdtlseqdt0(X2,xD)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_142]),c_0_38])]),c_0_143])]) ).

fof(c_0_153,plain,
    ! [X56,X57] :
      ( ~ aScalar0(X56)
      | ~ aScalar0(X57)
      | ~ sdtlseqdt0(sz0z00,X56)
      | ~ sdtlseqdt0(sz0z00,X57)
      | sdtasdt0(X56,X56) != sdtasdt0(X57,X57)
      | X56 = X57 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqrt])])]) ).

cnf(c_0_154,plain,
    ( sdtasdt0(sz0z00,smndt0(X1)) = sz0z00
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_98]),c_0_144]),c_0_79])]) ).

cnf(c_0_155,plain,
    ( sdtlseqdt0(sdtpldt0(X1,X2),X3)
    | ~ sdtlseqdt0(X1,sz0z00)
    | ~ sdtlseqdt0(X2,X3)
    | ~ aScalar0(X3)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79])]) ).

cnf(c_0_156,hypothesis,
    sdtpldt0(xP,smndt0(xP)) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_145]),c_0_146])]) ).

cnf(c_0_157,hypothesis,
    sdtasdt0(xP,xP) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_44]),c_0_129])]) ).

cnf(c_0_158,negated_conjecture,
    ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
    inference(split_conjunct,[status(thm)],[c_0_148]) ).

cnf(c_0_159,plain,
    ( aScalar0(sdtpldt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_149]) ).

cnf(c_0_160,hypothesis,
    ( sdtpldt0(sdtasdt0(xE,X1),xP) = sdtasdt0(xE,sdtpldt0(X1,xH))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_118]),c_0_119]),c_0_120])]) ).

cnf(c_0_161,hypothesis,
    sdtlseqdt0(smndt0(xS),sz0z00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_104]),c_0_70])]) ).

cnf(c_0_162,hypothesis,
    ( sdtlseqdt0(sz0z00,smndt0(xS))
    | ~ sdtlseqdt0(X1,smndt0(xF))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_106]),c_0_107]),c_0_72]),c_0_79])]) ).

cnf(c_0_163,hypothesis,
    sdtpldt0(smndt0(xS),xS) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_132]),c_0_70])]) ).

cnf(c_0_164,hypothesis,
    smndt0(smndt0(xR)) = xR,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_76]),c_0_64]),c_0_65]),c_0_66])]) ).

cnf(c_0_165,plain,
    ( X1 = X2
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ sdtlseqdt0(sz0z00,X1)
    | ~ sdtlseqdt0(sz0z00,X2)
    | sdtasdt0(X1,X1) != sdtasdt0(X2,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_153]) ).

cnf(c_0_166,hypothesis,
    sdtasdt0(sz0z00,sz0z00) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_144]),c_0_79])]) ).

cnf(c_0_167,hypothesis,
    ( sdtlseqdt0(sz0z00,X1)
    | ~ sdtlseqdt0(smndt0(xP),X1)
    | ~ sdtlseqdt0(xP,sz0z00)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_146]),c_0_129])]) ).

cnf(c_0_168,hypothesis,
    sdtasdt0(xP,smndt0(xP)) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_157]),c_0_144]),c_0_129])]) ).

cnf(c_0_169,negated_conjecture,
    ( ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS))
    | ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
    | ~ aScalar0(sdtpldt0(xR,xS))
    | ~ aScalar0(sdtpldt0(xP,xP)) ),
    inference(spm,[status(thm)],[c_0_158,c_0_95]) ).

cnf(c_0_170,plain,
    ( aScalar0(sdtasdt0(X1,sdtpldt0(X2,X3)))
    | ~ aScalar0(X3)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_150]),c_0_44]),c_0_44]) ).

cnf(c_0_171,hypothesis,
    sdtasdt0(xE,sdtpldt0(xH,xH)) = sdtpldt0(xP,xP),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_118]),c_0_119])]) ).

cnf(c_0_172,hypothesis,
    ( smndt0(xS) = sz0z00
    | ~ sdtlseqdt0(sz0z00,smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_161]),c_0_70]),c_0_79])]) ).

cnf(c_0_173,hypothesis,
    sdtlseqdt0(sz0z00,smndt0(xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_104]),c_0_143])]) ).

cnf(c_0_174,hypothesis,
    sdtpldt0(xS,sz0z00) = sdtpldt0(sz0z00,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_163]),c_0_132]),c_0_42]),c_0_70])]) ).

cnf(c_0_175,hypothesis,
    sdtpldt0(smndt0(xR),xR) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_164]),c_0_97])]) ).

cnf(c_0_176,plain,
    ( X1 = sz0z00
    | sdtasdt0(X1,X1) != sz0z00
    | ~ sdtlseqdt0(sz0z00,X1)
    | ~ aScalar0(X1) ),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_104]),c_0_79])]),c_0_166]) ).

cnf(c_0_177,hypothesis,
    ( sdtlseqdt0(sz0z00,smndt0(xP))
    | ~ sdtlseqdt0(xP,sz0z00) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_104]),c_0_146])]) ).

cnf(c_0_178,hypothesis,
    sdtasdt0(smndt0(xP),smndt0(xP)) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_168]),c_0_144]),c_0_146]),c_0_129])]) ).

cnf(c_0_179,negated_conjecture,
    ( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
    | ~ sdtlseqdt0(sdtpldt0(xP,xP),xS)
    | ~ aScalar0(sdtpldt0(xR,xS))
    | ~ aScalar0(sdtpldt0(xP,xP)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_90]),c_0_84]),c_0_42]),c_0_43])]) ).

cnf(c_0_180,hypothesis,
    aScalar0(sdtpldt0(xP,xP)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_119]),c_0_120])]) ).

cnf(c_0_181,hypothesis,
    smndt0(xS) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_173])]) ).

cnf(c_0_182,hypothesis,
    sdtpldt0(sz0z00,xS) = xS,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_174]),c_0_42])]) ).

cnf(c_0_183,hypothesis,
    sdtpldt0(xR,sz0z00) = sdtpldt0(sz0z00,xR),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_175]),c_0_164]),c_0_43]),c_0_97])]) ).

cnf(c_0_184,hypothesis,
    ( smndt0(xP) = sz0z00
    | ~ sdtlseqdt0(xP,sz0z00) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_178]),c_0_146])]) ).

cnf(c_0_185,hypothesis,
    ( sdtlseqdt0(X1,xP)
    | sdtlseqdt0(xP,X1)
    | ~ aScalar0(X1) ),
    inference(spm,[status(thm)],[c_0_99,c_0_129]) ).

cnf(c_0_186,negated_conjecture,
    ( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
    | ~ sdtlseqdt0(sdtpldt0(xP,xP),xS)
    | ~ aScalar0(sdtpldt0(xR,xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_180])]) ).

cnf(c_0_187,hypothesis,
    xS = sz0z00,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_181]),c_0_174]),c_0_182]) ).

cnf(c_0_188,hypothesis,
    sdtpldt0(sz0z00,xR) = xR,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_183]),c_0_43])]) ).

cnf(c_0_189,hypothesis,
    ( xP = sz0z00
    | ~ sdtlseqdt0(xP,sz0z00) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_184]),c_0_144]),c_0_129])]) ).

cnf(c_0_190,hypothesis,
    ( sdtlseqdt0(xP,sz0z00)
    | sdtlseqdt0(sz0z00,xP) ),
    inference(spm,[status(thm)],[c_0_185,c_0_79]) ).

cnf(c_0_191,negated_conjecture,
    ( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
    | ~ sdtlseqdt0(sdtpldt0(xP,xP),sz0z00) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_187]),c_0_187]),c_0_183]),c_0_188]),c_0_43])]) ).

cnf(c_0_192,hypothesis,
    ( xP = sz0z00
    | sdtlseqdt0(sz0z00,xP) ),
    inference(spm,[status(thm)],[c_0_189,c_0_190]) ).

cnf(c_0_193,negated_conjecture,
    ( ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
    | ~ sdtlseqdt0(xP,sz0z00) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_155]),c_0_79]),c_0_129])]) ).

cnf(c_0_194,hypothesis,
    xP = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_192]),c_0_157]),c_0_129])]) ).

cnf(c_0_195,hypothesis,
    sdtpldt0(sz0z00,sz0z00) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_144]),c_0_79])]) ).

cnf(c_0_196,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_194]),c_0_194]),c_0_195]),c_0_107]),c_0_194]),c_0_107])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : RNG066+1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13  % Command    : run_E %s %d THM
% 0.13/0.32  % Computer : n002.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Sat May 18 12:26:08 EDT 2024
% 0.13/0.33  % CPUTime    : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.28/2.04  # Version: 3.1.0
% 12.28/2.04  # Preprocessing class: FSLSSMSMSSSNFFN.
% 12.28/2.04  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.28/2.04  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 12.28/2.04  # Starting new_bool_3 with 300s (1) cores
% 12.28/2.04  # Starting new_bool_1 with 300s (1) cores
% 12.28/2.04  # Starting sh5l with 300s (1) cores
% 12.28/2.04  # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 26321 completed with status 0
% 12.28/2.04  # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 12.28/2.04  # Preprocessing class: FSLSSMSMSSSNFFN.
% 12.28/2.04  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.28/2.04  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 12.28/2.04  # No SInE strategy applied
% 12.28/2.04  # Search class: FGHSF-FFMM21-MFFFFFNN
% 12.28/2.04  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 12.28/2.04  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 12.28/2.04  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 12.28/2.04  # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 12.28/2.04  # Starting new_bool_3 with 136s (1) cores
% 12.28/2.04  # Starting new_bool_1 with 136s (1) cores
% 12.28/2.04  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 26327 completed with status 0
% 12.28/2.04  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 12.28/2.04  # Preprocessing class: FSLSSMSMSSSNFFN.
% 12.28/2.04  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.28/2.04  # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 12.28/2.04  # No SInE strategy applied
% 12.28/2.04  # Search class: FGHSF-FFMM21-MFFFFFNN
% 12.28/2.04  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 12.28/2.04  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 12.28/2.04  # Preprocessing time       : 0.002 s
% 12.28/2.04  # Presaturation interreduction done
% 12.28/2.04  
% 12.28/2.04  # Proof found!
% 12.28/2.04  # SZS status Theorem
% 12.28/2.04  # SZS output start CNFRefutation
% See solution above
% 12.28/2.04  # Parsed axioms                        : 59
% 12.28/2.04  # Removed by relevancy pruning/SinE    : 0
% 12.28/2.04  # Initial clauses                      : 93
% 12.28/2.04  # Removed in clause preprocessing      : 5
% 12.28/2.04  # Initial clauses in saturation        : 88
% 12.28/2.04  # Processed clauses                    : 6223
% 12.28/2.04  # ...of these trivial                  : 400
% 12.28/2.04  # ...subsumed                          : 3278
% 12.28/2.04  # ...remaining for further processing  : 2545
% 12.28/2.04  # Other redundant clauses eliminated   : 3
% 12.28/2.04  # Clauses deleted for lack of memory   : 0
% 12.28/2.04  # Backward-subsumed                    : 104
% 12.28/2.04  # Backward-rewritten                   : 1242
% 12.28/2.04  # Generated clauses                    : 111087
% 12.28/2.04  # ...of the previous two non-redundant : 102420
% 12.28/2.04  # ...aggressively subsumed             : 0
% 12.28/2.04  # Contextual simplify-reflections      : 129
% 12.28/2.04  # Paramodulations                      : 111073
% 12.28/2.04  # Factorizations                       : 0
% 12.28/2.04  # NegExts                              : 0
% 12.28/2.04  # Equation resolutions                 : 14
% 12.28/2.04  # Disequality decompositions           : 0
% 12.28/2.04  # Total rewrite steps                  : 210858
% 12.28/2.04  # ...of those cached                   : 210346
% 12.28/2.04  # Propositional unsat checks           : 0
% 12.28/2.04  #    Propositional check models        : 0
% 12.28/2.04  #    Propositional check unsatisfiable : 0
% 12.28/2.04  #    Propositional clauses             : 0
% 12.28/2.04  #    Propositional clauses after purity: 0
% 12.28/2.04  #    Propositional unsat core size     : 0
% 12.28/2.04  #    Propositional preprocessing time  : 0.000
% 12.28/2.04  #    Propositional encoding time       : 0.000
% 12.28/2.04  #    Propositional solver time         : 0.000
% 12.28/2.04  #    Success case prop preproc time    : 0.000
% 12.28/2.04  #    Success case prop encoding time   : 0.000
% 12.28/2.04  #    Success case prop solver time     : 0.000
% 12.28/2.04  # Current number of processed clauses  : 1108
% 12.28/2.04  #    Positive orientable unit clauses  : 366
% 12.28/2.04  #    Positive unorientable unit clauses: 0
% 12.28/2.04  #    Negative unit clauses             : 3
% 12.28/2.04  #    Non-unit-clauses                  : 739
% 12.28/2.04  # Current number of unprocessed clauses: 96115
% 12.28/2.04  # ...number of literals in the above   : 409687
% 12.28/2.04  # Current number of archived formulas  : 0
% 12.28/2.04  # Current number of archived clauses   : 1434
% 12.28/2.04  # Clause-clause subsumption calls (NU) : 453088
% 12.28/2.04  # Rec. Clause-clause subsumption calls : 215810
% 12.28/2.04  # Non-unit clause-clause subsumptions  : 3470
% 12.28/2.04  # Unit Clause-clause subsumption calls : 19698
% 12.28/2.04  # Rewrite failures with RHS unbound    : 0
% 12.28/2.04  # BW rewrite match attempts            : 82
% 12.28/2.04  # BW rewrite match successes           : 50
% 12.28/2.04  # Condensation attempts                : 0
% 12.28/2.04  # Condensation successes               : 0
% 12.28/2.04  # Termbank termtop insertions          : 3146510
% 12.28/2.04  # Search garbage collected termcells   : 885
% 12.28/2.04  
% 12.28/2.04  # -------------------------------------------------
% 12.28/2.04  # User time                : 1.439 s
% 12.28/2.04  # System time              : 0.067 s
% 12.28/2.04  # Total time               : 1.506 s
% 12.28/2.04  # Maximum resident set size: 1980 pages
% 12.28/2.04  
% 12.28/2.04  # -------------------------------------------------
% 12.28/2.04  # User time                : 7.444 s
% 12.28/2.04  # System time              : 0.220 s
% 12.28/2.04  # Total time               : 7.664 s
% 12.28/2.04  # Maximum resident set size: 1760 pages
% 12.28/2.04  % E---3.1 exiting
% 12.28/2.04  % E exiting
%------------------------------------------------------------------------------