TSTP Solution File: RNG063+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : RNG063+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% 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 : Thu Aug 31 13:48:50 EDT 2023

% Result   : Theorem 3.64s 3.98s
% Output   : CNFRefutation 3.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   63
% Syntax   : Number of formulae    :  249 ( 102 unt;  33 typ;   0 def)
%            Number of atoms       :  491 ( 167 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  477 ( 202   ~; 196   |;  60   &)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  15   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;  18 con; 0-2 aty)
%            Number of variables   :  150 (   2 sgn;  62   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aNaturalNumber0: $i > $o ).

tff(decl_23,type,
    sz00: $i ).

tff(decl_24,type,
    szszuzczcdt0: $i > $i ).

tff(decl_25,type,
    iLess0: ( $i * $i ) > $o ).

tff(decl_26,type,
    aScalar0: $i > $o ).

tff(decl_27,type,
    sz0z00: $i ).

tff(decl_28,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_29,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_30,type,
    smndt0: $i > $i ).

tff(decl_31,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_32,type,
    aVector0: $i > $o ).

tff(decl_33,type,
    aDimensionOf0: $i > $i ).

tff(decl_34,type,
    sdtlbdtrb0: ( $i * $i ) > $i ).

tff(decl_35,type,
    sziznziztdt0: $i > $i ).

tff(decl_36,type,
    sdtasasdt0: ( $i * $i ) > $i ).

tff(decl_37,type,
    xs: $i ).

tff(decl_38,type,
    xt: $i ).

tff(decl_39,type,
    xp: $i ).

tff(decl_40,type,
    xq: $i ).

tff(decl_41,type,
    xA: $i ).

tff(decl_42,type,
    xB: $i ).

tff(decl_43,type,
    xC: $i ).

tff(decl_44,type,
    xD: $i ).

tff(decl_45,type,
    xE: $i ).

tff(decl_46,type,
    xF: $i ).

tff(decl_47,type,
    xG: $i ).

tff(decl_48,type,
    xH: $i ).

tff(decl_49,type,
    xR: $i ).

tff(decl_50,type,
    xP: $i ).

tff(decl_51,type,
    xS: $i ).

tff(decl_52,type,
    xN: $i ).

tff(decl_53,type,
    esk1_1: $i > $i ).

tff(decl_54,type,
    esk2_2: ( $i * $i ) > $i ).

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(m__2144,hypothesis,
    ( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
    & sdtasdt0(smndt0(xS),xR) = smndt0(xN)
    & sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).

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

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

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__1930,hypothesis,
    ( aScalar0(xS)
    & xS = sdtasdt0(xF,xD) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).

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

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

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

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

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

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

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

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__1766,hypothesis,
    ( aScalar0(xB)
    & xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).

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

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

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

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

fof(m__2180,hypothesis,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2180) ).

fof(m__,conjecture,
    sdtpldt0(sdtpldt0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),xN),xN) = sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(c_0_30,plain,
    ! [X27,X28] :
      ( ( sdtasdt0(X27,smndt0(X28)) = smndt0(sdtasdt0(X27,X28))
        | ~ aScalar0(X27)
        | ~ aScalar0(X28) )
      & ( sdtasdt0(smndt0(X27),X28) = smndt0(sdtasdt0(X27,X28))
        | ~ aScalar0(X27)
        | ~ aScalar0(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])]) ).

cnf(c_0_31,plain,
    ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_32,hypothesis,
    sdtasdt0(smndt0(xS),xR) = smndt0(xN),
    inference(split_conjunct,[status(thm)],[m__2144]) ).

cnf(c_0_33,hypothesis,
    aScalar0(xR),
    inference(split_conjunct,[status(thm)],[m__1892]) ).

fof(c_0_34,plain,
    ! [X29,X30] :
      ( ~ aScalar0(X29)
      | ~ aScalar0(X30)
      | sdtasdt0(smndt0(X29),smndt0(X30)) = sdtasdt0(X29,X30) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMDNeg])]) ).

fof(c_0_35,plain,
    ! [X16] :
      ( ( sdtpldt0(X16,sz0z00) = X16
        | ~ aScalar0(X16) )
      & ( sdtpldt0(sz0z00,X16) = X16
        | ~ aScalar0(X16) )
      & ( sdtasdt0(X16,sz0z00) = sz0z00
        | ~ aScalar0(X16) )
      & ( sdtasdt0(sz0z00,X16) = sz0z00
        | ~ aScalar0(X16) )
      & ( sdtpldt0(X16,smndt0(X16)) = sz0z00
        | ~ aScalar0(X16) )
      & ( sdtpldt0(smndt0(X16),X16) = sz0z00
        | ~ aScalar0(X16) )
      & ( smndt0(smndt0(X16)) = X16
        | ~ aScalar0(X16) )
      & ( smndt0(sz0z00) = sz0z00
        | ~ aScalar0(X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])]) ).

cnf(c_0_36,hypothesis,
    ( sdtasdt0(smndt0(xS),smndt0(xR)) = smndt0(smndt0(xN))
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).

cnf(c_0_37,plain,
    ( sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_38,hypothesis,
    aScalar0(xS),
    inference(split_conjunct,[status(thm)],[m__1930]) ).

fof(c_0_39,plain,
    ! [X13,X14] :
      ( ~ aScalar0(X13)
      | ~ aScalar0(X14)
      | aScalar0(sdtasdt0(X13,X14)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])]) ).

cnf(c_0_40,hypothesis,
    xR = sdtasdt0(xC,xG),
    inference(split_conjunct,[status(thm)],[m__1892]) ).

cnf(c_0_41,hypothesis,
    aScalar0(xG),
    inference(split_conjunct,[status(thm)],[m__1854]) ).

cnf(c_0_42,hypothesis,
    aScalar0(xC),
    inference(split_conjunct,[status(thm)],[m__1783]) ).

cnf(c_0_43,plain,
    ( smndt0(smndt0(X1)) = X1
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_44,hypothesis,
    ( smndt0(smndt0(xN)) = sdtasdt0(xS,xR)
    | ~ aScalar0(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_33]),c_0_38])]) ).

cnf(c_0_45,hypothesis,
    aScalar0(xN),
    inference(split_conjunct,[status(thm)],[m__1949]) ).

fof(c_0_46,plain,
    ! [X15] :
      ( ~ aScalar0(X15)
      | aScalar0(smndt0(X15)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])]) ).

cnf(c_0_47,plain,
    ( aScalar0(sdtasdt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_48,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_31,c_0_40]),c_0_41]),c_0_42])]) ).

cnf(c_0_49,hypothesis,
    ( sdtasdt0(xS,xR) = xN
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).

cnf(c_0_50,plain,
    ( aScalar0(smndt0(X1))
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_51,hypothesis,
    xS = sdtasdt0(xF,xD),
    inference(split_conjunct,[status(thm)],[m__1930]) ).

cnf(c_0_52,hypothesis,
    aScalar0(xD),
    inference(split_conjunct,[status(thm)],[m__1800]) ).

cnf(c_0_53,hypothesis,
    aScalar0(xF),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

fof(c_0_54,plain,
    ! [X20,X21,X22] :
      ( ( sdtasdt0(X20,sdtpldt0(X21,X22)) = sdtpldt0(sdtasdt0(X20,X21),sdtasdt0(X20,X22))
        | ~ aScalar0(X20)
        | ~ aScalar0(X21)
        | ~ aScalar0(X22) )
      & ( sdtasdt0(sdtpldt0(X20,X21),X22) = sdtpldt0(sdtasdt0(X20,X22),sdtasdt0(X21,X22))
        | ~ aScalar0(X20)
        | ~ aScalar0(X21)
        | ~ aScalar0(X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])]) ).

cnf(c_0_55,plain,
    ( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_56,hypothesis,
    xN = sdtasdt0(xR,xS),
    inference(split_conjunct,[status(thm)],[m__1949]) ).

cnf(c_0_57,hypothesis,
    ( aScalar0(smndt0(xR))
    | ~ aScalar0(smndt0(xG)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42])]) ).

cnf(c_0_58,hypothesis,
    sdtasdt0(xS,xR) = xN,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_38])]) ).

cnf(c_0_59,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_31,c_0_51]),c_0_52]),c_0_53])]) ).

cnf(c_0_60,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_54]) ).

cnf(c_0_61,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_55,c_0_56]),c_0_38]),c_0_33])]) ).

cnf(c_0_62,hypothesis,
    aScalar0(smndt0(xR)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_50]),c_0_41])]) ).

cnf(c_0_63,plain,
    ( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_64,hypothesis,
    sdtasdt0(xS,smndt0(xR)) = smndt0(xN),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_58]),c_0_33]),c_0_38])]) ).

fof(c_0_65,plain,
    ! [X17,X18,X19] :
      ( ( sdtpldt0(sdtpldt0(X17,X18),X19) = sdtpldt0(X17,sdtpldt0(X18,X19))
        | ~ aScalar0(X17)
        | ~ aScalar0(X18)
        | ~ aScalar0(X19) )
      & ( sdtpldt0(X17,X18) = sdtpldt0(X18,X17)
        | ~ aScalar0(X17)
        | ~ aScalar0(X18)
        | ~ aScalar0(X19) )
      & ( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
        | ~ aScalar0(X17)
        | ~ aScalar0(X18)
        | ~ aScalar0(X19) )
      & ( sdtasdt0(X17,X18) = sdtasdt0(X18,X17)
        | ~ aScalar0(X17)
        | ~ aScalar0(X18)
        | ~ aScalar0(X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])]) ).

cnf(c_0_66,hypothesis,
    sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
    inference(split_conjunct,[status(thm)],[m__2144]) ).

fof(c_0_67,plain,
    ! [X49] :
      ( ~ aScalar0(X49)
      | sdtlseqdt0(sz0z00,sdtasdt0(X49,X49)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])]) ).

fof(c_0_68,plain,
    ! [X68] :
      ( ~ aVector0(X68)
      | sdtlseqdt0(sz0z00,sdtasasdt0(X68,X68)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])]) ).

cnf(c_0_69,hypothesis,
    ( aScalar0(smndt0(xS))
    | ~ aScalar0(smndt0(xD)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_59]),c_0_53])]) ).

cnf(c_0_70,hypothesis,
    ( sdtpldt0(sdtasdt0(smndt0(xR),X1),smndt0(xN)) = sdtasdt0(smndt0(xR),sdtpldt0(X1,xS))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_38])]),c_0_62])]) ).

cnf(c_0_71,hypothesis,
    ( sdtpldt0(sdtasdt0(X1,smndt0(xR)),smndt0(xN)) = sdtasdt0(sdtpldt0(X1,xS),smndt0(xR))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_38])]),c_0_62])]) ).

cnf(c_0_72,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_73,hypothesis,
    ( sdtasdt0(xR,smndt0(smndt0(xS))) = smndt0(smndt0(xN))
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_66]),c_0_33])]) ).

fof(c_0_74,plain,
    ! [X47,X48] :
      ( ( sdtlseqdt0(sz0z00,sdtpldt0(X47,X48))
        | ~ sdtlseqdt0(sz0z00,X47)
        | ~ sdtlseqdt0(sz0z00,X48)
        | ~ aScalar0(X47)
        | ~ aScalar0(X48) )
      & ( sdtlseqdt0(sz0z00,sdtasdt0(X47,X48))
        | ~ sdtlseqdt0(sz0z00,X47)
        | ~ sdtlseqdt0(sz0z00,X48)
        | ~ aScalar0(X47)
        | ~ aScalar0(X48) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])]) ).

cnf(c_0_75,plain,
    ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_76,hypothesis,
    xG = sdtasdt0(xB,xB),
    inference(split_conjunct,[status(thm)],[m__1854]) ).

cnf(c_0_77,hypothesis,
    aScalar0(xB),
    inference(split_conjunct,[status(thm)],[m__1766]) ).

cnf(c_0_78,plain,
    ( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
    | ~ aVector0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_79,hypothesis,
    xC = sdtasasdt0(xp,xp),
    inference(split_conjunct,[status(thm)],[m__1783]) ).

cnf(c_0_80,hypothesis,
    aVector0(xp),
    inference(split_conjunct,[status(thm)],[m__1709]) ).

cnf(c_0_81,hypothesis,
    xF = sdtasdt0(xA,xA),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_82,hypothesis,
    aScalar0(xA),
    inference(split_conjunct,[status(thm)],[m__1746]) ).

cnf(c_0_83,hypothesis,
    xD = sdtasasdt0(xq,xq),
    inference(split_conjunct,[status(thm)],[m__1800]) ).

cnf(c_0_84,hypothesis,
    aVector0(xq),
    inference(split_conjunct,[status(thm)],[m__1726]) ).

cnf(c_0_85,hypothesis,
    aScalar0(smndt0(xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_50]),c_0_52])]) ).

cnf(c_0_86,hypothesis,
    sdtasdt0(sdtpldt0(smndt0(xR),xS),smndt0(xR)) = sdtasdt0(smndt0(xR),sdtpldt0(smndt0(xR),xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_62])]) ).

cnf(c_0_87,hypothesis,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(spm,[status(thm)],[c_0_72,c_0_45]) ).

fof(c_0_88,plain,
    ! [X37,X38,X39,X40] :
      ( ~ aScalar0(X37)
      | ~ aScalar0(X38)
      | ~ aScalar0(X39)
      | ~ aScalar0(X40)
      | ~ sdtlseqdt0(X37,X38)
      | ~ sdtlseqdt0(X39,X40)
      | sdtlseqdt0(sdtpldt0(X37,X39),sdtpldt0(X38,X40)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])]) ).

cnf(c_0_89,hypothesis,
    ( smndt0(smndt0(xN)) = xN
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_43]),c_0_56]),c_0_38])]) ).

cnf(c_0_90,hypothesis,
    ( aScalar0(smndt0(xN))
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_66]),c_0_33])]) ).

cnf(c_0_91,plain,
    ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
    | ~ sdtlseqdt0(sz0z00,X1)
    | ~ sdtlseqdt0(sz0z00,X2)
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_92,hypothesis,
    sdtlseqdt0(sz0z00,xG),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]) ).

cnf(c_0_93,hypothesis,
    sdtlseqdt0(sz0z00,xC),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).

cnf(c_0_94,hypothesis,
    sdtlseqdt0(sz0z00,xF),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_81]),c_0_82])]) ).

cnf(c_0_95,hypothesis,
    sdtlseqdt0(sz0z00,xD),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_83]),c_0_84])]) ).

cnf(c_0_96,hypothesis,
    ( sdtpldt0(sdtasdt0(smndt0(xS),X1),smndt0(xN)) = sdtasdt0(smndt0(xS),sdtpldt0(X1,xR))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_32]),c_0_33])]),c_0_85])]) ).

cnf(c_0_97,hypothesis,
    sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
    inference(split_conjunct,[status(thm)],[m__2144]) ).

cnf(c_0_98,plain,
    ( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X3,smndt0(X2))) = sdtasdt0(sdtpldt0(smndt0(X1),X3),smndt0(X2))
    | ~ aScalar0(X3)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_37]),c_0_50]),c_0_50]) ).

cnf(c_0_99,hypothesis,
    sdtasdt0(sdtpldt0(xS,smndt0(xR)),smndt0(xR)) = sdtasdt0(smndt0(xR),sdtpldt0(xS,smndt0(xR))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_38]),c_0_62])]) ).

cnf(c_0_100,plain,
    ( sdtpldt0(sdtasdt0(X1,smndt0(X2)),sdtasdt0(X3,X2)) = sdtasdt0(sdtpldt0(X1,smndt0(X3)),smndt0(X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_37]),c_0_50]),c_0_50]) ).

cnf(c_0_101,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_88]) ).

cnf(c_0_102,plain,
    ( sdtpldt0(sz0z00,X1) = X1
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_103,plain,
    aScalar0(sz0z00),
    inference(split_conjunct,[status(thm)],[mSZeroSc]) ).

cnf(c_0_104,plain,
    ( sdtpldt0(smndt0(X1),X1) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_105,hypothesis,
    smndt0(smndt0(xN)) = xN,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_85])]) ).

cnf(c_0_106,hypothesis,
    aScalar0(smndt0(xN)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_85])]) ).

cnf(c_0_107,hypothesis,
    sdtlseqdt0(sz0z00,xR),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_40]),c_0_92]),c_0_41]),c_0_42])]),c_0_93])]) ).

cnf(c_0_108,hypothesis,
    sdtlseqdt0(sz0z00,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_51]),c_0_94]),c_0_52]),c_0_53])]),c_0_95])]) ).

fof(c_0_109,plain,
    ! [X41,X42,X43,X44] :
      ( ~ aScalar0(X41)
      | ~ aScalar0(X42)
      | ~ aScalar0(X43)
      | ~ aScalar0(X44)
      | ~ sdtlseqdt0(X41,X42)
      | ~ sdtlseqdt0(sz0z00,X43)
      | ~ sdtlseqdt0(X43,X44)
      | sdtlseqdt0(sdtasdt0(X41,X43),sdtasdt0(X42,X44)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])]) ).

cnf(c_0_110,hypothesis,
    sdtasdt0(smndt0(xS),sdtpldt0(smndt0(xS),xR)) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_85])]) ).

cnf(c_0_111,hypothesis,
    sdtasdt0(smndt0(xR),sdtpldt0(smndt0(xR),xS)) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),
    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_98]),c_0_64]),c_0_38]),c_0_33])]) ).

cnf(c_0_112,hypothesis,
    sdtasdt0(smndt0(xR),sdtpldt0(xS,smndt0(xR))) = sdtpldt0(smndt0(xN),sdtasdt0(xR,xR)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_64]),c_0_38]),c_0_33])]) ).

cnf(c_0_113,hypothesis,
    ( sdtpldt0(smndt0(xN),sdtasdt0(xR,X1)) = sdtasdt0(xR,sdtpldt0(smndt0(xS),X1))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_66]),c_0_33])]),c_0_85])]) ).

cnf(c_0_114,hypothesis,
    ( sdtpldt0(smndt0(xN),sdtasdt0(X1,xR)) = sdtasdt0(sdtpldt0(smndt0(xS),X1),xR)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_32]),c_0_33])]),c_0_85])]) ).

cnf(c_0_115,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_101,c_0_102]),c_0_103])]) ).

cnf(c_0_116,hypothesis,
    sdtpldt0(xN,smndt0(xN)) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106])]) ).

cnf(c_0_117,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_91,c_0_58]),c_0_33]),c_0_38])]),c_0_107]),c_0_108])]) ).

fof(c_0_118,plain,
    ! [X31] :
      ( ~ aScalar0(X31)
      | sdtlseqdt0(X31,X31) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])]) ).

cnf(c_0_119,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_109]) ).

cnf(c_0_120,plain,
    ( sdtasdt0(sz0z00,X1) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_121,plain,
    ( sdtpldt0(sdtasdt0(smndt0(X1),X2),sdtasdt0(X1,X3)) = sdtasdt0(smndt0(X1),sdtpldt0(X2,smndt0(X3)))
    | ~ aScalar0(X2)
    | ~ aScalar0(X3)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_37]),c_0_50]),c_0_50]) ).

cnf(c_0_122,hypothesis,
    sdtasdt0(smndt0(xS),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_87]),c_0_33]),c_0_85])]) ).

cnf(c_0_123,hypothesis,
    ( sdtasdt0(smndt0(xS),smndt0(smndt0(xS))) = smndt0(sdtasdt0(xS,xS))
    | ~ aScalar0(smndt0(xS)) ),
    inference(spm,[status(thm)],[c_0_31,c_0_97]) ).

cnf(c_0_124,hypothesis,
    sdtpldt0(smndt0(xN),sdtasdt0(xR,xR)) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_87]),c_0_112]),c_0_38]),c_0_62])]) ).

cnf(c_0_125,hypothesis,
    sdtasdt0(sdtpldt0(smndt0(xS),xR),xR) = sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_33])]) ).

cnf(c_0_126,hypothesis,
    ( sdtpldt0(sdtasdt0(xR,X1),smndt0(xN)) = sdtasdt0(xR,sdtpldt0(X1,smndt0(xS)))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_66]),c_0_33])]),c_0_85])]) ).

cnf(c_0_127,hypothesis,
    ( sdtpldt0(sdtasdt0(X1,xR),smndt0(xN)) = sdtasdt0(sdtpldt0(X1,smndt0(xS)),xR)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_32]),c_0_33])]),c_0_85])]) ).

fof(c_0_128,plain,
    ! [X32,X33] :
      ( ~ aScalar0(X32)
      | ~ aScalar0(X33)
      | ~ sdtlseqdt0(X32,X33)
      | ~ sdtlseqdt0(X33,X32)
      | X32 = X33 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])]) ).

cnf(c_0_129,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_115,c_0_116]),c_0_117]),c_0_106]),c_0_45])]) ).

cnf(c_0_130,plain,
    ( sdtlseqdt0(X1,X1)
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_118]) ).

cnf(c_0_131,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_119,c_0_61]),c_0_38])]),c_0_62])]) ).

cnf(c_0_132,plain,
    ( sdtasdt0(X1,sz0z00) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_133,plain,
    sdtlseqdt0(sz0z00,sz0z00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_120]),c_0_103])]) ).

fof(c_0_134,plain,
    ! [X11,X12] :
      ( ~ aScalar0(X11)
      | ~ aScalar0(X12)
      | aScalar0(sdtpldt0(X11,X12)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])]) ).

cnf(c_0_135,hypothesis,
    ( sdtpldt0(smndt0(xN),sdtasdt0(xS,X1)) = sdtasdt0(xS,sdtpldt0(smndt0(xR),X1))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_64]),c_0_38])]),c_0_62])]) ).

cnf(c_0_136,hypothesis,
    sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_32]),c_0_33]),c_0_38])]) ).

cnf(c_0_137,hypothesis,
    ( smndt0(sdtasdt0(xS,xS)) = sdtasdt0(xS,smndt0(xS))
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_123]),c_0_38])]) ).

cnf(c_0_138,hypothesis,
    sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) = sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_124]),c_0_125]),c_0_33])]) ).

cnf(c_0_139,hypothesis,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),xR) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_33])]) ).

cnf(c_0_140,plain,
    ( X1 = X2
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_128]) ).

cnf(c_0_141,hypothesis,
    sdtlseqdt0(smndt0(xN),sz0z00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_106])]) ).

cnf(c_0_142,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_131,c_0_132]),c_0_133]),c_0_108]),c_0_103])]) ).

cnf(c_0_143,plain,
    ( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_31]),c_0_47]) ).

cnf(c_0_144,plain,
    ( aScalar0(sdtpldt0(X1,X2))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_134]) ).

cnf(c_0_145,hypothesis,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
    inference(split_conjunct,[status(thm)],[m__2180]) ).

cnf(c_0_146,hypothesis,
    ( sdtpldt0(sdtasdt0(xS,X1),smndt0(xN)) = sdtasdt0(xS,sdtpldt0(X1,smndt0(xR)))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_64]),c_0_38])]),c_0_62])]) ).

cnf(c_0_147,hypothesis,
    sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)) = sdtasdt0(xS,sdtpldt0(smndt0(xR),xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_38])]) ).

cnf(c_0_148,hypothesis,
    ( sdtasdt0(smndt0(xS),xS) = sdtasdt0(xS,smndt0(xS))
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_137]),c_0_38])]) ).

cnf(c_0_149,hypothesis,
    ( aScalar0(sdtasdt0(xS,xS))
    | ~ aScalar0(smndt0(xS)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_97]) ).

cnf(c_0_150,hypothesis,
    sdtpldt0(smndt0(xN),sdtasdt0(xR,xR)) = sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)),
    inference(rw,[status(thm)],[c_0_124,c_0_138]) ).

cnf(c_0_151,hypothesis,
    sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_138]),c_0_139]),c_0_33])]) ).

cnf(c_0_152,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_140,c_0_141]),c_0_106]),c_0_103])]) ).

cnf(c_0_153,hypothesis,
    sdtlseqdt0(sz0z00,smndt0(xN)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_130]),c_0_62])]) ).

cnf(c_0_154,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aScalar0(X1)
    | ~ aScalar0(X2)
    | ~ aScalar0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_155,plain,
    ( sdtpldt0(X1,smndt0(X1)) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_156,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_143,c_0_48]),c_0_40]),c_0_41]),c_0_42])]) ).

cnf(c_0_157,hypothesis,
    ( aScalar0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))))
    | ~ aScalar0(sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)))
    | ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))) ),
    inference(spm,[status(thm)],[c_0_144,c_0_145]) ).

cnf(c_0_158,hypothesis,
    sdtasdt0(xS,sdtpldt0(smndt0(xR),xS)) = sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_38])]) ).

cnf(c_0_159,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_144,c_0_60]),c_0_47]),c_0_47]) ).

cnf(c_0_160,hypothesis,
    ( smndt0(sdtasdt0(xS,xS)) = sdtasdt0(smndt0(xS),xS)
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_43]),c_0_38])]) ).

cnf(c_0_161,hypothesis,
    sdtasdt0(smndt0(xS),xS) = sdtasdt0(xS,smndt0(xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_85])]) ).

cnf(c_0_162,hypothesis,
    aScalar0(sdtasdt0(xS,xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_50]),c_0_38])]) ).

cnf(c_0_163,hypothesis,
    sdtpldt0(smndt0(xN),sdtasdt0(xR,xR)) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
    inference(rw,[status(thm)],[c_0_150,c_0_151]) ).

cnf(c_0_164,hypothesis,
    smndt0(xN) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153])]) ).

cnf(c_0_165,plain,
    ( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_104]),c_0_50]) ).

cnf(c_0_166,hypothesis,
    sdtpldt0(smndt0(xR),xR) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_62])]) ).

cnf(c_0_167,hypothesis,
    ( aScalar0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))))
    | ~ aScalar0(sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))))
    | ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_136]),c_0_147]),c_0_158]) ).

cnf(c_0_168,hypothesis,
    aScalar0(sdtasdt0(xS,sdtpldt0(xS,smndt0(xR)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_158]),c_0_38]),c_0_62])]) ).

cnf(c_0_169,hypothesis,
    smndt0(sdtasdt0(xS,xS)) = sdtasdt0(xS,smndt0(xS)),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_85])]),c_0_161]) ).

cnf(c_0_170,hypothesis,
    ( smndt0(sdtasdt0(smndt0(xS),xS)) = sdtasdt0(xS,xS)
    | ~ aScalar0(smndt0(xS)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_160]),c_0_162])]) ).

cnf(c_0_171,hypothesis,
    sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
    inference(rw,[status(thm)],[c_0_138,c_0_151]) ).

cnf(c_0_172,hypothesis,
    sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sz0z00,sdtasdt0(xR,xR)),
    inference(rw,[status(thm)],[c_0_163,c_0_164]) ).

cnf(c_0_173,plain,
    ( sdtpldt0(X1,sz0z00) = X1
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_174,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_165,c_0_166]),c_0_156]),c_0_33]),c_0_62])]) ).

fof(c_0_175,negated_conjecture,
    sdtpldt0(sdtpldt0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),xN),xN) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_176,hypothesis,
    ( aScalar0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))))
    | ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_168])]) ).

cnf(c_0_177,plain,
    ( aScalar0(sdtasdt0(sdtpldt0(X1,X2),X3))
    | ~ aScalar0(X3)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_63]),c_0_47]),c_0_47]) ).

cnf(c_0_178,hypothesis,
    sdtpldt0(smndt0(xN),xN) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_105]),c_0_106])]) ).

cnf(c_0_179,hypothesis,
    sdtpldt0(sdtasdt0(xS,smndt0(xS)),sdtasdt0(xS,xS)) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_169]),c_0_162])]) ).

cnf(c_0_180,hypothesis,
    smndt0(sdtasdt0(xS,smndt0(xS))) = sdtasdt0(xS,xS),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_85])]),c_0_161]) ).

cnf(c_0_181,hypothesis,
    aScalar0(sdtasdt0(xS,smndt0(xS))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_161]),c_0_38]),c_0_85])]) ).

cnf(c_0_182,plain,
    ( sdtpldt0(sdtasdt0(X1,X2),sz0z00) = sdtasdt0(X1,sdtpldt0(X2,sz0z00))
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_132]),c_0_103])]) ).

cnf(c_0_183,hypothesis,
    sdtpldt0(sdtasdt0(xR,xR),sz0z00) = sdtpldt0(sz0z00,sdtasdt0(xR,xR)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_164]),c_0_172]) ).

cnf(c_0_184,hypothesis,
    sdtpldt0(sz0z00,xR) = xR,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_33])]) ).

cnf(c_0_185,negated_conjecture,
    sdtpldt0(sdtpldt0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),xN),xN) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
    inference(split_conjunct,[status(thm)],[c_0_175]) ).

cnf(c_0_186,hypothesis,
    ( aScalar0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))))
    | ~ aScalar0(sdtasdt0(xR,sdtpldt0(xR,smndt0(xS)))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_138]),c_0_151]) ).

cnf(c_0_187,hypothesis,
    aScalar0(sdtasdt0(xR,sdtpldt0(xR,smndt0(xS)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_139]),c_0_33]),c_0_85])]) ).

cnf(c_0_188,hypothesis,
    ( sdtpldt0(sdtasdt0(xS,X1),xN) = sdtasdt0(xS,sdtpldt0(X1,xR))
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_58]),c_0_33]),c_0_38])]) ).

cnf(c_0_189,hypothesis,
    ( sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(smndt0(xN),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
    | ~ aScalar0(sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)))
    | ~ aScalar0(sdtasdt0(xR,xR)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_154]),c_0_106])]) ).

cnf(c_0_190,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_165,c_0_178]),c_0_105]),c_0_45]),c_0_106])]) ).

cnf(c_0_191,hypothesis,
    sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) = sdtasdt0(xS,sdtpldt0(smndt0(xR),xS)),
    inference(rw,[status(thm)],[c_0_136,c_0_147]) ).

cnf(c_0_192,hypothesis,
    sdtpldt0(sdtasdt0(xS,xS),sz0z00) = sdtpldt0(sz0z00,sdtasdt0(xS,xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_179]),c_0_180]),c_0_162]),c_0_181])]) ).

cnf(c_0_193,hypothesis,
    sdtpldt0(sz0z00,sdtasdt0(xR,xR)) = sdtasdt0(xR,xR),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_174]),c_0_184]),c_0_33])]) ).

cnf(c_0_194,negated_conjecture,
    ( sdtpldt0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),sdtpldt0(xN,xN)) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))
    | ~ aScalar0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_154]),c_0_45])]) ).

cnf(c_0_195,hypothesis,
    aScalar0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_187])]) ).

cnf(c_0_196,hypothesis,
    sdtasdt0(xS,sdtpldt0(xR,xR)) = sdtpldt0(xN,xN),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_58]),c_0_33])]) ).

cnf(c_0_197,plain,
    ( smndt0(sz0z00) = sz0z00
    | ~ aScalar0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_198,hypothesis,
    ( sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(smndt0(xN),sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
    | ~ aScalar0(sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))))
    | ~ aScalar0(sdtasdt0(xR,xR)) ),
    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_189,c_0_136]),c_0_136]),c_0_147]),c_0_158]),c_0_147]),c_0_158]) ).

cnf(c_0_199,hypothesis,
    sdtpldt0(sz0z00,xN) = xN,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_190]),c_0_45])]) ).

cnf(c_0_200,hypothesis,
    sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) = sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))),
    inference(rw,[status(thm)],[c_0_191,c_0_158]) ).

cnf(c_0_201,hypothesis,
    sdtpldt0(sz0z00,sdtasdt0(xS,xS)) = sdtasdt0(xS,xS),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_192]),c_0_162])]) ).

cnf(c_0_202,hypothesis,
    sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))) = sdtasdt0(xR,xR),
    inference(rw,[status(thm)],[c_0_172,c_0_193]) ).

cnf(c_0_203,negated_conjecture,
    sdtpldt0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),sdtpldt0(xN,xN)) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_194,c_0_195])]) ).

cnf(c_0_204,hypothesis,
    aScalar0(sdtpldt0(xN,xN)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_196]),c_0_33]),c_0_38])]) ).

cnf(c_0_205,hypothesis,
    smndt0(sz0z00) = sz0z00,
    inference(spm,[status(thm)],[c_0_197,c_0_45]) ).

cnf(c_0_206,hypothesis,
    ( sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(smndt0(xN),sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
    | ~ aScalar0(sdtasdt0(xR,xR)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_168])]) ).

cnf(c_0_207,hypothesis,
    xN = sz0z00,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_164]),c_0_190]),c_0_199]) ).

cnf(c_0_208,hypothesis,
    sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))) = sdtasdt0(xS,xS),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_164]),c_0_201]) ).

cnf(c_0_209,hypothesis,
    aScalar0(sdtasdt0(xR,xR)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_202]),c_0_85]),c_0_33])]) ).

cnf(c_0_210,hypothesis,
    sdtpldt0(sdtpldt0(xN,xN),sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_87]),c_0_204]),c_0_195])]) ).

cnf(c_0_211,hypothesis,
    sdtpldt0(sz0z00,sz0z00) = sz0z00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_205]),c_0_103])]) ).

cnf(c_0_212,hypothesis,
    sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
    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_206,c_0_207]),c_0_205]),c_0_208]),c_0_201]),c_0_209])]) ).

cnf(c_0_213,hypothesis,
    sdtpldt0(sz0z00,sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_210,c_0_207]),c_0_207]),c_0_211]),c_0_212]) ).

cnf(c_0_214,plain,
    ( sdtpldt0(sz0z00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2)
    | ~ aScalar0(X2)
    | ~ aScalar0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_102]),c_0_103])]) ).

cnf(c_0_215,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_162]),c_0_209])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.18  % Problem    : RNG063+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.18  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.09/0.39  % Computer : n002.cluster.edu
% 0.09/0.39  % Model    : x86_64 x86_64
% 0.09/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39  % Memory   : 8042.1875MB
% 0.09/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.39  % CPULimit   : 300
% 0.09/0.39  % WCLimit    : 300
% 0.09/0.39  % DateTime   : Sun Aug 27 02:56:33 EDT 2023
% 0.09/0.39  % CPUTime  : 
% 0.13/0.65  start to proof: theBenchmark
% 3.64/3.98  % Version  : CSE_E---1.5
% 3.64/3.98  % Problem  : theBenchmark.p
% 3.64/3.98  % Proof found
% 3.64/3.98  % SZS status Theorem for theBenchmark.p
% 3.64/3.98  % SZS output start Proof
% See solution above
% 3.64/4.00  % Total time : 3.319000 s
% 3.64/4.00  % SZS output end Proof
% 3.64/4.00  % Total time : 3.321000 s
%------------------------------------------------------------------------------