%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG066+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:05:42 PM UTC 2026
% Result : Theorem 15.19s 2.72s
% Output : CNFRefutation 15.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 40
% Syntax : Number of formulae : 258 ( 109 unt; 0 def)
% Number of atoms : 665 ( 199 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 701 ( 294 ~; 299 |; 75 &)
% ( 2 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 18 con; 0-2 aty)
% Number of variables : 199 ( 3 sgn 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefInit,axiom,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) )
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& aVector0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
fof(mSuccEqu,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
fof(m__1726,hypothesis,
( xq = sziznziztdt0(xt)
& aVector0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1678,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(m__1709,hypothesis,
( xp = sziznziztdt0(xs)
& aVector0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
fof(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(mElmSc,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aVector0(X1) )
=> aScalar0(sdtlbdtrb0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
fof(mArith,axiom,
! [X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(mMNeg,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
& sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(m__1854,hypothesis,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
fof(m__1783,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1949,hypothesis,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
fof(m__1837,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(mScZero,axiom,
! [X1] :
( aScalar0(X1)
=> ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(X1)) = X1
& sdtpldt0(smndt0(X1),X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtpldt0(sz0z00,X1) = X1
& sdtpldt0(X1,sz0z00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(m__1911,hypothesis,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
fof(m__1873,hypothesis,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
fof(m__1820,hypothesis,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
fof(mPosMon,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(sz0z00,X1) )
=> ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtpldt0(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
fof(m__1766,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
fof(m__1746,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
fof(mDistr,axiom,
! [X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
fof(mLEMon,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X4)
& aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X3,X4)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
fof(mLETot,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mLEASm,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEASm) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
fof(mLEMonM,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X4)
& aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X3,X4)
& sdtlseqdt0(sz0z00,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
fof(m__2004,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mLERef,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
fof(mSqrt,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtasdt0(X1,X1) = sdtasdt0(X2,X2)
& sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(sz0z00,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqrt) ).
fof(c_0_40,plain,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) )
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& aVector0(X2) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefInit]) ).
fof(c_0_41,plain,
! [X62,X63,X64,X65] :
( ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X65 = sziznziztdt0(X62)
| szszuzczcdt0(aDimensionOf0(X65)) != aDimensionOf0(X62)
| ~ aVector0(X65)
| sdtlbdtrb0(X65,esk2_2(X62,X65)) != sdtlbdtrb0(X62,esk2_2(X62,X65)) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X65 = sziznziztdt0(X62)
| szszuzczcdt0(aDimensionOf0(X65)) != aDimensionOf0(X62)
| ~ aVector0(X65)
| aNaturalNumber0(esk2_2(X62,X65)) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X63 != sziznziztdt0(X62)
| sdtlbdtrb0(X63,X64) = sdtlbdtrb0(X62,X64)
| ~ aNaturalNumber0(X64) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X63 != sziznziztdt0(X62)
| szszuzczcdt0(aDimensionOf0(X63)) = aDimensionOf0(X62) )
& ( ~ aVector0(X62)
| aDimensionOf0(X62) = sz00
| X63 != sziznziztdt0(X62)
| aVector0(X63) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])])])]) ).
fof(c_0_42,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1692]) ).
cnf(c_0_43,plain,
( ~ aVector0(X2)
| X1 != sziznziztdt0(X2)
| aDimensionOf0(X2) = sz00
| szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_44,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_42]) ).
fof(c_0_45,plain,
! [X9,X10] :
( X9 = X10
| szszuzczcdt0(X9) != szszuzczcdt0(X10)
| ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccEqu])])]) ).
cnf(c_0_46,plain,
( ~ aVector0(X1)
| aDimensionOf0(X1) = sz00
| szszuzczcdt0(aDimensionOf0(sziznziztdt0(X1))) = aDimensionOf0(X1) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_47,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_48,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_49,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_50,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( szszuzczcdt0(X1) != szszuzczcdt0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_52,hypothesis,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xs),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_53,hypothesis,
xp = sziznziztdt0(xs),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_54,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_55,plain,
( ~ aVector0(X3)
| X2 != sziznziztdt0(X3)
| ~ aNaturalNumber0(X1)
| aDimensionOf0(X3) = sz00
| sdtlbdtrb0(X2,X1) = sdtlbdtrb0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_56,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(aDimensionOf0(xq))
| szszuzczcdt0(X1) != aDimensionOf0(xs)
| aDimensionOf0(xq) = X1 ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,hypothesis,
szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_53]),c_0_54])]),c_0_50]) ).
fof(c_0_58,plain,
! [X59] :
( aNaturalNumber0(aDimensionOf0(X59))
| ~ aVector0(X59) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])])]) ).
fof(c_0_59,plain,
! [X60,X61] :
( aScalar0(sdtlbdtrb0(X60,X61))
| ~ aNaturalNumber0(X61)
| ~ aVector0(X60) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mElmSc])])]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X2)
| ~ aVector0(X1)
| aDimensionOf0(X1) = sz00
| sdtlbdtrb0(sziznziztdt0(X1),X2) = sdtlbdtrb0(X1,X2) ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_61,hypothesis,
( ~ aNaturalNumber0(aDimensionOf0(xp))
| ~ aNaturalNumber0(aDimensionOf0(xq))
| aDimensionOf0(xp) = aDimensionOf0(xq) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
( ~ aVector0(X1)
| aNaturalNumber0(aDimensionOf0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[m__1709]) ).
fof(c_0_64,plain,
! [X21,X22,X23] :
( ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtasdt0(X21,X22) = sdtasdt0(X22,X21) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtasdt0(sdtasdt0(X21,X22),X23) = sdtasdt0(X21,sdtasdt0(X22,X23)) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtpldt0(X21,X22) = sdtpldt0(X22,X21) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtpldt0(sdtpldt0(X21,X22),X23) = sdtpldt0(X21,sdtpldt0(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])])]) ).
cnf(c_0_65,plain,
( ~ aNaturalNumber0(X2)
| ~ aVector0(X1)
| aScalar0(sdtlbdtrb0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(xt,X1) = sdtlbdtrb0(xq,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_47]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_67,hypothesis,
( ~ aNaturalNumber0(aDimensionOf0(xq))
| aDimensionOf0(xp) = aDimensionOf0(xq) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
cnf(c_0_68,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_69,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_70,hypothesis,
( ~ aNaturalNumber0(X1)
| aScalar0(sdtlbdtrb0(xq,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_49])]) ).
cnf(c_0_71,hypothesis,
aDimensionOf0(xp) = aDimensionOf0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_62]),c_0_68])]) ).
fof(c_0_72,plain,
! [X31,X32] :
( ( ~ aScalar0(X32)
| ~ aScalar0(X31)
| sdtasdt0(smndt0(X31),X32) = smndt0(sdtasdt0(X31,X32)) )
& ( ~ aScalar0(X32)
| ~ aScalar0(X31)
| sdtasdt0(X31,smndt0(X32)) = smndt0(sdtasdt0(X31,X32)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])])]) ).
cnf(c_0_73,hypothesis,
( ~ aNaturalNumber0(X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,hypothesis,
aNaturalNumber0(aDimensionOf0(xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_71]),c_0_63])]) ).
cnf(c_0_75,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_76,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_77,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_78,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
fof(c_0_79,plain,
! [X17,X18] :
( aScalar0(sdtasdt0(X17,X18))
| ~ aScalar0(X18)
| ~ aScalar0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])])]) ).
cnf(c_0_80,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(smndt0(xC),xG) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),c_0_78])]) ).
cnf(c_0_82,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_83,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_84,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_85,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_86,hypothesis,
( ~ aScalar0(smndt0(xC))
| sdtasdt0(xG,smndt0(xC)) = smndt0(xR) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_77])]) ).
fof(c_0_87,plain,
! [X19] :
( aScalar0(smndt0(X19))
| ~ aScalar0(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])])]) ).
cnf(c_0_88,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_89,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_90,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_91,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_75,c_0_82]),c_0_83]),c_0_84])]) ).
cnf(c_0_92,hypothesis,
( ~ aScalar0(smndt0(xC))
| aScalar0(smndt0(xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_77])]) ).
cnf(c_0_93,plain,
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_94,plain,
! [X20] :
( ( ~ aScalar0(X20)
| smndt0(sz0z00) = sz0z00 )
& ( ~ aScalar0(X20)
| smndt0(smndt0(X20)) = X20 )
& ( ~ aScalar0(X20)
| sdtpldt0(smndt0(X20),X20) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtpldt0(X20,smndt0(X20)) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtasdt0(sz0z00,X20) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtasdt0(X20,sz0z00) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtpldt0(sz0z00,X20) = X20 )
& ( ~ aScalar0(X20)
| sdtpldt0(X20,sz0z00) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])])]) ).
cnf(c_0_95,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(xD,xF) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_80]),c_0_89]),c_0_90])]) ).
cnf(c_0_97,hypothesis,
( ~ aScalar0(smndt0(xR))
| sdtasdt0(xS,smndt0(xR)) = smndt0(xN) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_80]),c_0_83])]) ).
cnf(c_0_98,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_78])]) ).
cnf(c_0_99,hypothesis,
xP = sdtasdt0(xE,xH),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_100,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_101,hypothesis,
aScalar0(xE),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_102,plain,
( ~ aScalar0(X1)
| smndt0(smndt0(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_103,hypothesis,
sdtasdt0(xD,smndt0(xF)) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_89]),c_0_90])]) ).
cnf(c_0_104,hypothesis,
sdtasdt0(xS,smndt0(xR)) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_105,hypothesis,
sdtasdt0(smndt0(xE),xH) = smndt0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_99]),c_0_100]),c_0_101])]) ).
cnf(c_0_106,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_95]),c_0_85]) ).
cnf(c_0_107,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_95,c_0_88]),c_0_90]),c_0_89])]) ).
cnf(c_0_108,hypothesis,
( ~ aScalar0(smndt0(xF))
| aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_103]),c_0_90])]) ).
cnf(c_0_109,hypothesis,
sdtasdt0(xS,smndt0(smndt0(xR))) = smndt0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_104]),c_0_98]),c_0_83])]) ).
fof(c_0_110,plain,
! [X55] :
( sdtlseqdt0(sz0z00,sdtasdt0(X55,X55))
| ~ aScalar0(X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])])]) ).
fof(c_0_111,plain,
! [X75] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X75,X75))
| ~ aVector0(X75) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])])]) ).
cnf(c_0_112,hypothesis,
( ~ aScalar0(smndt0(xE))
| sdtasdt0(xH,smndt0(xE)) = smndt0(xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_105]),c_0_100])]) ).
cnf(c_0_113,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_114,plain,
( ~ aScalar0(X1)
| sdtpldt0(smndt0(X1),X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_115,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_116,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_106,c_0_107]),c_0_88]),c_0_90]),c_0_89])]) ).
cnf(c_0_117,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_93]),c_0_89])]) ).
cnf(c_0_118,hypothesis,
smndt0(smndt0(xN)) = sdtasdt0(xS,xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_102]),c_0_84])]) ).
cnf(c_0_119,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
fof(c_0_120,plain,
! [X53,X54] :
( ( ~ aScalar0(X54)
| ~ aScalar0(X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ sdtlseqdt0(sz0z00,X53)
| sdtlseqdt0(sz0z00,sdtasdt0(X53,X54)) )
& ( ~ aScalar0(X54)
| ~ aScalar0(X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ sdtlseqdt0(sz0z00,X53)
| sdtlseqdt0(sz0z00,sdtpldt0(X53,X54)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])])]) ).
cnf(c_0_121,plain,
( ~ aScalar0(X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_122,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_123,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_124,plain,
( ~ aVector0(X1)
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_125,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_126,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_127,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_128,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_129,plain,
( ~ aScalar0(X1)
| smndt0(sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_130,hypothesis,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| smndt0(sdtasdt0(X1,X2)) = sdtasdt0(X2,smndt0(X1)) ),
inference(spm,[status(thm)],[c_0_95,c_0_80]) ).
cnf(c_0_131,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_95,c_0_99]),c_0_100]),c_0_101])]) ).
cnf(c_0_132,hypothesis,
( ~ aScalar0(smndt0(xE))
| aScalar0(smndt0(xP)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_112]),c_0_100])]) ).
fof(c_0_133,plain,
! [X24,X25,X26] :
( ( ~ aScalar0(X26)
| ~ aScalar0(X25)
| ~ aScalar0(X24)
| sdtasdt0(sdtpldt0(X24,X25),X26) = sdtpldt0(sdtasdt0(X24,X26),sdtasdt0(X25,X26)) )
& ( ~ aScalar0(X26)
| ~ aScalar0(X25)
| ~ aScalar0(X24)
| sdtasdt0(X24,sdtpldt0(X25,X26)) = sdtpldt0(sdtasdt0(X24,X25),sdtasdt0(X24,X26)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])])]) ).
cnf(c_0_134,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_93]) ).
cnf(c_0_135,hypothesis,
sdtpldt0(smndt0(xS),xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117])]) ).
fof(c_0_136,plain,
! [X43,X44,X45,X46] :
( sdtlseqdt0(sdtpldt0(X43,X45),sdtpldt0(X44,X46))
| ~ sdtlseqdt0(X45,X46)
| ~ sdtlseqdt0(X43,X44)
| ~ aScalar0(X46)
| ~ aScalar0(X45)
| ~ aScalar0(X44)
| ~ aScalar0(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])])]) ).
cnf(c_0_137,hypothesis,
sdtasdt0(xS,xR) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_118]),c_0_119])]) ).
cnf(c_0_138,hypothesis,
( ~ aScalar0(smndt0(xR))
| aScalar0(smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_97]),c_0_83])]) ).
cnf(c_0_139,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_140,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).
cnf(c_0_141,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_63])]) ).
cnf(c_0_142,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_126]),c_0_68])]) ).
cnf(c_0_143,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_127]),c_0_128])]) ).
fof(c_0_144,plain,
! [X51,X52] :
( sdtlseqdt0(X52,X51)
| sdtlseqdt0(X51,X52)
| ~ aScalar0(X52)
| ~ aScalar0(X51) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])])]) ).
cnf(c_0_145,plain,
( ~ aScalar0(X1)
| sdtasdt0(X1,sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_146,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_129,c_0_119]) ).
cnf(c_0_147,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_148,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_95,c_0_76]),c_0_77]),c_0_78])]) ).
cnf(c_0_149,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| aScalar0(sdtasdt0(X1,smndt0(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_130]),c_0_85]) ).
cnf(c_0_150,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_106,c_0_131]),c_0_99]),c_0_100]),c_0_101])]) ).
cnf(c_0_151,hypothesis,
aScalar0(smndt0(xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_93]),c_0_101])]) ).
fof(c_0_152,plain,
! [X38,X39] :
( X38 = X39
| ~ sdtlseqdt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aScalar0(X39)
| ~ aScalar0(X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])])]) ).
fof(c_0_153,plain,
! [X15,X16] :
( aScalar0(sdtpldt0(X15,X16))
| ~ aScalar0(X16)
| ~ aScalar0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])])]) ).
cnf(c_0_154,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_155,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,sz0z00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_156,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_134,c_0_135]),c_0_116]),c_0_83]),c_0_117])]) ).
cnf(c_0_157,plain,
( ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_158,plain,
( ~ aScalar0(X1)
| sdtpldt0(sz0z00,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_159,hypothesis,
smndt0(smndt0(xN)) = xN,
inference(rw,[status(thm)],[c_0_118,c_0_137]) ).
cnf(c_0_160,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_98])]) ).
cnf(c_0_161,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_139,c_0_76]),c_0_140]),c_0_141]),c_0_77]),c_0_78])]) ).
cnf(c_0_162,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_139,c_0_88]),c_0_142]),c_0_143]),c_0_90]),c_0_89])]) ).
cnf(c_0_163,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_164,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(sz0z00,smndt0(X1)) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_145]),c_0_146]),c_0_147])]) ).
cnf(c_0_165,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_106,c_0_148]),c_0_76]),c_0_77]),c_0_78])]) ).
cnf(c_0_166,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,xP)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151])]) ).
cnf(c_0_167,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(smndt0(X1),X2) = sdtasdt0(X1,smndt0(X2)) ),
inference(spm,[status(thm)],[c_0_95,c_0_75]) ).
cnf(c_0_168,hypothesis,
aScalar0(xP),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_169,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_152]) ).
cnf(c_0_170,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtlseqdt0(sz0z00,sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_171,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_172,hypothesis,
( ~ aScalar0(X1)
| sdtpldt0(sdtasdt0(smndt0(xR),X1),smndt0(xN)) = sdtasdt0(smndt0(xR),sdtpldt0(X1,xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_91]),c_0_83])]),c_0_98])]) ).
cnf(c_0_173,hypothesis,
sdtpldt0(sz0z00,xS) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_83])]) ).
cnf(c_0_174,plain,
( ~ aScalar0(X1)
| sdtasdt0(sz0z00,X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_175,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X1,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| sdtlseqdt0(X1,sdtpldt0(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_147])]) ).
cnf(c_0_176,hypothesis,
sdtpldt0(xN,smndt0(xN)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_159]),c_0_160])]) ).
cnf(c_0_177,hypothesis,
sdtlseqdt0(sz0z00,xN),
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_139,c_0_137]),c_0_161]),c_0_162]),c_0_84]),c_0_83])]) ).
cnf(c_0_178,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(smndt0(xN),X1)
| sdtlseqdt0(X1,smndt0(xN)) ),
inference(spm,[status(thm)],[c_0_163,c_0_160]) ).
fof(c_0_179,plain,
! [X47,X48,X49,X50] :
( sdtlseqdt0(sdtasdt0(X47,X49),sdtasdt0(X48,X50))
| ~ sdtlseqdt0(X49,X50)
| ~ sdtlseqdt0(sz0z00,X49)
| ~ sdtlseqdt0(X47,X48)
| ~ aScalar0(X50)
| ~ aScalar0(X49)
| ~ aScalar0(X48)
| ~ aScalar0(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])])]) ).
cnf(c_0_180,hypothesis,
sdtasdt0(sz0z00,xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_98])]) ).
cnf(c_0_181,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,smndt0(xP))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_168])]),c_0_93]) ).
cnf(c_0_182,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sdtpldt0(X1,X2),sz0z00)
| sdtpldt0(X1,X2) = sz0z00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_147])]),c_0_171]) ).
cnf(c_0_183,hypothesis,
sdtpldt0(sz0z00,smndt0(xN)) = smndt0(xN),
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_172,c_0_145]),c_0_173]),c_0_91]),c_0_147]),c_0_98])]) ).
cnf(c_0_184,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_174]),c_0_147])]) ).
cnf(c_0_185,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(X1,smndt0(xN))
| sdtlseqdt0(X1,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_177]),c_0_160]),c_0_119])]) ).
cnf(c_0_186,hypothesis,
sdtlseqdt0(smndt0(xN),smndt0(xN)),
inference(spm,[status(thm)],[c_0_178,c_0_160]) ).
cnf(c_0_187,plain,
( ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_179]) ).
cnf(c_0_188,hypothesis,
sdtasdt0(xR,sz0z00) = sz0z00,
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_130,c_0_180]),c_0_146]),c_0_146]),c_0_147]),c_0_84])]) ).
cnf(c_0_189,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(smndt0(xR),X1)
| sdtlseqdt0(X1,smndt0(xR)) ),
inference(spm,[status(thm)],[c_0_163,c_0_98]) ).
cnf(c_0_190,hypothesis,
sdtpldt0(smndt0(xN),xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_159]),c_0_160])]) ).
cnf(c_0_191,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(smndt0(xP),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_80]),c_0_151])]) ).
cnf(c_0_192,hypothesis,
( ~ sdtlseqdt0(sz0z00,smndt0(xN))
| ~ sdtlseqdt0(smndt0(xN),sz0z00)
| smndt0(xN) = sz0z00 ),
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_184]),c_0_160]),c_0_147])]) ).
cnf(c_0_193,hypothesis,
sdtlseqdt0(smndt0(xN),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_160])]) ).
cnf(c_0_194,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X2,xS)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X1,smndt0(xR))
| sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_91]),c_0_83])]),c_0_98])]) ).
cnf(c_0_195,hypothesis,
sdtasdt0(smndt0(xR),sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_188]),c_0_146]),c_0_147]),c_0_84])]) ).
cnf(c_0_196,hypothesis,
sdtlseqdt0(smndt0(xR),smndt0(xR)),
inference(spm,[status(thm)],[c_0_189,c_0_98]) ).
cnf(c_0_197,hypothesis,
sdtpldt0(xN,sz0z00) = sdtpldt0(sz0z00,xN),
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_134,c_0_190]),c_0_118]),c_0_137]),c_0_119]),c_0_160])]) ).
cnf(c_0_198,hypothesis,
xH = sdtasdt0(xA,xB),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_199,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(split_conjunct,[status(thm)],[m__2004]) ).
cnf(c_0_200,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(xP,smndt0(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_167]),c_0_168])]) ).
cnf(c_0_201,hypothesis,
( ~ sdtlseqdt0(sz0z00,smndt0(xN))
| smndt0(xN) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_193])]) ).
cnf(c_0_202,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xN)),
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(spm,[status(thm)],[c_0_194,c_0_195]),c_0_196]),c_0_184]),c_0_162]),c_0_147]),c_0_98])]) ).
cnf(c_0_203,hypothesis,
sdtpldt0(sz0z00,xN) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_197]),c_0_119])]) ).
cnf(c_0_204,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_205,hypothesis,
sdtasdt0(xB,smndt0(xA)) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_198]),c_0_128]),c_0_123])]) ).
cnf(c_0_206,hypothesis,
sdtasdt0(sz0z00,xP) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_150]),c_0_151])]) ).
cnf(c_0_207,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,smndt0(X2))) = sz0z00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_95]),c_0_85]) ).
cnf(c_0_208,hypothesis,
sdtasdt0(xA,smndt0(xB)) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_198]),c_0_123]),c_0_128])]) ).
cnf(c_0_209,hypothesis,
( ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(xN,sdtasdt0(xP,xP))
| sdtasdt0(xP,xP) = xN ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_199]),c_0_119])]) ).
cnf(c_0_210,hypothesis,
aScalar0(sdtasdt0(xP,xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_150]),c_0_151])]) ).
cnf(c_0_211,hypothesis,
smndt0(xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_202])]) ).
cnf(c_0_212,hypothesis,
sdtpldt0(xN,sz0z00) = xN,
inference(rw,[status(thm)],[c_0_197,c_0_203]) ).
cnf(c_0_213,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,sdtasdt0(X2,sdtasdt0(X1,X2)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_204]),c_0_85]) ).
cnf(c_0_214,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xE,sdtasdt0(xH,X1)) = sdtasdt0(xP,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_99]),c_0_100]),c_0_101])]) ).
fof(c_0_215,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_216,hypothesis,
aScalar0(smndt0(xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_205]),c_0_128]),c_0_123])]) ).
cnf(c_0_217,hypothesis,
sdtasdt0(xP,sz0z00) = sz0z00,
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_130,c_0_206]),c_0_146]),c_0_146]),c_0_147]),c_0_168])]) ).
cnf(c_0_218,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(xE,X1)
| sdtlseqdt0(X1,xE) ),
inference(spm,[status(thm)],[c_0_163,c_0_101]) ).
cnf(c_0_219,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,sz0z00)
| sdtlseqdt0(sdtpldt0(X1,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_147])]) ).
cnf(c_0_220,hypothesis,
sdtpldt0(xH,smndt0(xH)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_208]),c_0_198]),c_0_123]),c_0_128])]) ).
fof(c_0_221,plain,
! [X37] :
( sdtlseqdt0(X37,X37)
| ~ aScalar0(X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])])]) ).
cnf(c_0_222,hypothesis,
( ~ sdtlseqdt0(xN,sdtasdt0(xP,xP))
| sdtasdt0(xP,xP) = xN ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_210])]) ).
cnf(c_0_223,hypothesis,
xN = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_176,c_0_211]),c_0_212]) ).
cnf(c_0_224,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xP,xP)),
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(spm,[status(thm)],[c_0_213,c_0_214]),c_0_99]),c_0_100]),c_0_101]),c_0_99]),c_0_168])]) ).
fof(c_0_225,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(fof_simplification,[status(thm)],[c_0_215]) ).
fof(c_0_226,plain,
! [X56,X57] :
( X56 = X57
| sdtasdt0(X56,X56) != sdtasdt0(X57,X57)
| ~ sdtlseqdt0(sz0z00,X57)
| ~ sdtlseqdt0(sz0z00,X56)
| ~ aScalar0(X57)
| ~ aScalar0(X56) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqrt])])]) ).
cnf(c_0_227,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,xE)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,smndt0(xH))
| sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xP)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_131]),c_0_101])]),c_0_216])]) ).
cnf(c_0_228,hypothesis,
sdtasdt0(xE,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_145]),c_0_217]),c_0_147]),c_0_100])]) ).
cnf(c_0_229,hypothesis,
sdtlseqdt0(xE,xE),
inference(spm,[status(thm)],[c_0_218,c_0_101]) ).
cnf(c_0_230,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(xH,sz0z00)
| ~ sdtlseqdt0(smndt0(xH),X1)
| sdtlseqdt0(sz0z00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_216]),c_0_100])]) ).
cnf(c_0_231,plain,
( ~ aScalar0(X1)
| sdtlseqdt0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_232,hypothesis,
sdtasdt0(xP,xP) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_222,c_0_223]),c_0_223]),c_0_224])]) ).
fof(c_0_233,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(fof_nnf,[status(thm)],[c_0_225]) ).
cnf(c_0_234,plain,
( sdtasdt0(X1,X1) != sdtasdt0(X2,X2)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_226]) ).
cnf(c_0_235,hypothesis,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_146]),c_0_147])]) ).
cnf(c_0_236,hypothesis,
( ~ sdtlseqdt0(sz0z00,smndt0(xH))
| sdtlseqdt0(sz0z00,smndt0(xP)) ),
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_227,c_0_228]),c_0_184]),c_0_229]),c_0_147]),c_0_101])]) ).
cnf(c_0_237,hypothesis,
( ~ sdtlseqdt0(xH,sz0z00)
| sdtlseqdt0(sz0z00,smndt0(xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_216])]) ).
cnf(c_0_238,hypothesis,
sdtasdt0(xP,smndt0(xP)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_232]),c_0_146]),c_0_168])]) ).
cnf(c_0_239,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(split_conjunct,[status(thm)],[c_0_233]) ).
cnf(c_0_240,plain,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtasdt0(X1,X1) != sz0z00
| X1 = sz0z00 ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_231]),c_0_147])]),c_0_235]) ).
cnf(c_0_241,hypothesis,
( ~ sdtlseqdt0(xH,sz0z00)
| sdtlseqdt0(sz0z00,smndt0(xP)) ),
inference(spm,[status(thm)],[c_0_236,c_0_237]) ).
cnf(c_0_242,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_75,c_0_238]),c_0_146]),c_0_151]),c_0_168])]) ).
cnf(c_0_243,negated_conjecture,
( ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)) ),
inference(spm,[status(thm)],[c_0_239,c_0_187]) ).
cnf(c_0_244,hypothesis,
( ~ sdtlseqdt0(xH,sz0z00)
| smndt0(xP) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_241]),c_0_242]),c_0_151])]) ).
cnf(c_0_245,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(xH,X1)
| sdtlseqdt0(X1,xH) ),
inference(spm,[status(thm)],[c_0_163,c_0_100]) ).
cnf(c_0_246,negated_conjecture,
( ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(xP,xR)
| ~ sdtlseqdt0(xP,xS)
| ~ sdtlseqdt0(sz0z00,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_243,c_0_157]),c_0_83]),c_0_168]),c_0_84])]) ).
cnf(c_0_247,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,xE)
| ~ sdtlseqdt0(X2,xH)
| ~ sdtlseqdt0(sz0z00,X2)
| sdtlseqdt0(sdtasdt0(X1,X2),xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_99]),c_0_100]),c_0_101])]) ).
cnf(c_0_248,hypothesis,
( ~ sdtlseqdt0(xH,sz0z00)
| xP = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_244]),c_0_146]),c_0_168])]) ).
cnf(c_0_249,hypothesis,
( sdtlseqdt0(sz0z00,xH)
| sdtlseqdt0(xH,sz0z00) ),
inference(spm,[status(thm)],[c_0_245,c_0_147]) ).
cnf(c_0_250,negated_conjecture,
( ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(xP,xR)
| ~ sdtlseqdt0(xP,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_170]),c_0_168])]) ).
cnf(c_0_251,hypothesis,
( ~ sdtlseqdt0(sz0z00,xH)
| sdtlseqdt0(sz0z00,xP) ),
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_247,c_0_228]),c_0_184]),c_0_229]),c_0_147]),c_0_101])]) ).
cnf(c_0_252,hypothesis,
( sdtlseqdt0(sz0z00,xH)
| xP = sz0z00 ),
inference(spm,[status(thm)],[c_0_248,c_0_249]) ).
cnf(c_0_253,negated_conjecture,
( ~ aScalar0(sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(xP,xR)
| ~ sdtlseqdt0(xP,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_171]),c_0_83]),c_0_84])]) ).
cnf(c_0_254,hypothesis,
( sdtlseqdt0(sz0z00,xP)
| xP = sz0z00 ),
inference(spm,[status(thm)],[c_0_251,c_0_252]) ).
cnf(c_0_255,negated_conjecture,
( ~ sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(xP,xR)
| ~ sdtlseqdt0(xP,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_253,c_0_171]),c_0_168])]) ).
cnf(c_0_256,hypothesis,
xP = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_254]),c_0_232]),c_0_168])]) ).
cnf(c_0_257,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_255,c_0_256]),c_0_162]),c_0_256]),c_0_161]),c_0_256]),c_0_184])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG066+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n026.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 04:19:36 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 15.19/2.72 % Version: 3.5.1
% 15.19/2.72 % Preprocessing class: FSLSSMSMSSSNFFN.
% 15.19/2.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.19/2.72 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 15.19/2.72 % Starting new_bool_3 with 300s (1) cores
% 15.19/2.72 % Starting new_bool_1 with 300s (1) cores
% 15.19/2.72 % Starting sh5l with 300s (1) cores
% 15.19/2.72 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1347596 completed with status 0
% 15.19/2.72 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 15.19/2.72 % Preprocessing class: FSLSSMSMSSSNFFN.
% 15.19/2.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.19/2.72 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 15.19/2.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.19/2.72 % No SInE strategy applied
% 15.19/2.72 % Search class: FGHSF-FFMM21-MFFFFFNN
% 15.19/2.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 15.19/2.72 % Starting SubtermCWHack with 136s (1) cores
% 15.19/2.72 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 15.19/2.72 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 15.19/2.72 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 15.19/2.72 % Starting new_bool_3 with 136s (1) cores
% 15.19/2.72 % SAT001_MinMin_p005000_rr_RG with pid 1347605 completed with status 0
% 15.19/2.72 % Result found by SAT001_MinMin_p005000_rr_RG
% 15.19/2.72 % Preprocessing class: FSLSSMSMSSSNFFN.
% 15.19/2.72 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.19/2.72 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 15.19/2.72 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.19/2.72 % No SInE strategy applied
% 15.19/2.72 % Search class: FGHSF-FFMM21-MFFFFFNN
% 15.19/2.72 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 15.19/2.72 % Starting SubtermCWHack with 136s (1) cores
% 15.19/2.72 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 15.19/2.72 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 15.19/2.72 % Preprocessing time : 0.003 s
% 15.19/2.72 % Presaturation interreduction done
% 15.19/2.72
% 15.19/2.72 % Proof found!
% 15.19/2.72 % SZS status Theorem
% 15.19/2.72 % SZS output start CNFRefutation
% See solution above
% 15.19/2.72 % Parsed axioms : 59
% 15.19/2.72 % Removed by relevancy pruning/SinE : 0
% 15.19/2.72 % Initial clauses : 93
% 15.19/2.72 % Removed in clause preprocessing : 5
% 15.19/2.72 % Initial clauses in saturation : 88
% 15.19/2.72 % Processed clauses : 5238
% 15.19/2.72 % ...of these trivial : 347
% 15.19/2.72 % ...subsumed : 2720
% 15.19/2.72 % ...remaining for further processing : 2171
% 15.19/2.72 % Other redundant clauses eliminated : 7
% 15.19/2.72 % Clauses deleted for lack of memory : 0
% 15.19/2.72 % Backward-subsumed : 72
% 15.19/2.72 % Backward-rewritten : 749
% 15.19/2.72 % Generated clauses : 59406
% 15.19/2.72 % ...of the previous two non-redundant : 52134
% 15.19/2.72 % ...aggressively subsumed : 0
% 15.19/2.72 % Contextual simplify-reflections : 107
% 15.19/2.72 % Paramodulations : 59390
% 15.19/2.72 % Factorizations : 2
% 15.19/2.72 % NegExts : 0
% 15.19/2.72 % Equation resolutions : 14
% 15.19/2.72 % Disequality decompositions : 0
% 15.19/2.72 % Total rewrite steps : 85485
% 15.19/2.72 % ...of those cached : 84927
% 15.19/2.72 % Propositional unsat checks : 0
% 15.19/2.72 % Propositional check models : 0
% 15.19/2.72 % Propositional check unsatisfiable : 0
% 15.19/2.72 % Propositional clauses : 0
% 15.19/2.72 % Propositional clauses after purity: 0
% 15.19/2.72 % Propositional unsat core size : 0
% 15.19/2.72 % Propositional preprocessing time : 0.000
% 15.19/2.72 % Propositional encoding time : 0.000
% 15.19/2.72 % Propositional solver time : 0.000
% 15.19/2.72 % Success case prop preproc time : 0.000
% 15.19/2.72 % Success case prop encoding time : 0.000
% 15.19/2.72 % Success case prop solver time : 0.000
% 15.19/2.72 % Current number of processed clauses : 1259
% 15.19/2.72 % Positive orientable unit clauses : 503
% 15.19/2.72 % Positive unorientable unit clauses: 0
% 15.19/2.72 % Negative unit clauses : 2
% 15.19/2.72 % Non-unit-clauses : 754
% 15.19/2.72 % Current number of unprocessed clauses: 46837
% 15.19/2.72 % ...number of literals in the above : 195452
% 15.19/2.72 % Current number of archived formulas : 0
% 15.19/2.72 % Current number of archived clauses : 909
% 15.19/2.72 % Clause-clause subsumption calls (NU) : 312508
% 15.19/2.72 % Rec. Clause-clause subsumption calls : 95577
% 15.19/2.72 % Non-unit clause-clause subsumptions : 2869
% 15.19/2.72 % Unit Clause-clause subsumption calls : 18089
% 15.19/2.72 % Rewrite failures with RHS unbound : 0
% 15.19/2.72 % BW rewrite match attempts : 1333
% 15.19/2.72 % BW rewrite match successes : 71
% 15.19/2.72 % Condensation attempts : 0
% 15.19/2.72 % Condensation successes : 0
% 15.19/2.72 % Termbank termtop insertions : 1202369
% 15.19/2.72 % Search garbage collected termcells : 883
% 15.19/2.72
% 15.19/2.72 % -------------------------------------------------
% 15.19/2.72 % User time : 2.032 s
% 15.19/2.72 % System time : 0.076 s
% 15.19/2.72 % Total time : 2.108 s
% 15.19/2.72 % Maximum resident set size: 3700 pages
% 15.19/2.72
% 15.19/2.72 % -------------------------------------------------
% 15.19/2.72 % User time : 10.218 s
% 15.19/2.72 % System time : 0.395 s
% 15.19/2.72 % Total time : 10.613 s
% 15.19/2.72 % Maximum resident set size: 4608 pages
% 15.19/2.72 % E exiting
%------------------------------------------------------------------------------