%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG075+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 02:05:45 PM UTC 2026
% Result : Theorem 124.57s 28.85s
% Output : CNFRefutation 124.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 39
% Syntax : Number of formulae : 332 ( 170 unt; 0 def)
% Number of atoms : 766 ( 257 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 750 ( 316 ~; 319 |; 83 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 247 ( 3 sgn 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSPN,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> sdtasasdt0(X1,X2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPN) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1692) ).
fof(m__1726,hypothesis,
( xq = sziznziztdt0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xq,X1) = sdtlbdtrb0(xt,X1) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
fof(m__1766,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1678,hypothesis,
( aVector0(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
fof(mScPr,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> aScalar0(sdtasasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
fof(m__1854,hypothesis,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',mMNeg) ).
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/sandbox/benchmark/theBenchmark.p',mScZero) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
fof(m__1873,hypothesis,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1873) ).
fof(m__1746,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
fof(mLETrn,axiom,
! [X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).
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/sandbox/benchmark/theBenchmark.p',mPosMon) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(m__1783,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
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/sandbox/benchmark/theBenchmark.p',mLEMonM) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
fof(m__1709,hypothesis,
( xp = sziznziztdt0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xp,X1) = sdtlbdtrb0(xs,X1) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).
fof(mLETot,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',mLEMon) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(m__1837,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__1949,hypothesis,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
fof(mLERef,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mSqrt) ).
fof(mLEASm,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
fof(mMDNeg,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).
fof(m__1820,hypothesis,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1820) ).
fof(m__,conjecture,
sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__1967,hypothesis,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1967) ).
fof(c_0_39,plain,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> sdtasasdt0(X1,X2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2)))) ) ),
inference(fof_simplification,[status(thm)],[mDefSPN]) ).
fof(c_0_40,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1692]) ).
fof(c_0_41,plain,
! [X73,X74] :
( sdtasasdt0(X73,X74) = sdtpldt0(sdtasasdt0(sziznziztdt0(X73),sziznziztdt0(X74)),sdtasdt0(sdtlbdtrb0(X73,aDimensionOf0(X73)),sdtlbdtrb0(X74,aDimensionOf0(X74))))
| aDimensionOf0(X74) = sz00
| aDimensionOf0(X73) != aDimensionOf0(X74)
| ~ aVector0(X74)
| ~ aVector0(X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
fof(c_0_42,hypothesis,
! [X79] :
( xq = sziznziztdt0(xt)
& ( sdtlbdtrb0(xq,X79) = sdtlbdtrb0(xt,X79)
| ~ aNaturalNumber0(X79) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1726])])])]) ).
cnf(c_0_43,hypothesis,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_44,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
fof(c_0_45,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_40]) ).
cnf(c_0_46,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| sdtasasdt0(X1,X2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2))))
| aDimensionOf0(X2) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,hypothesis,
sdtlbdtrb0(xt,aDimensionOf0(xs)) = xB,
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
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_45]) ).
fof(c_0_51,plain,
! [X69,X70] :
( aScalar0(sdtasasdt0(X69,X70))
| aDimensionOf0(X69) != aDimensionOf0(X70)
| ~ aVector0(X70)
| ~ aVector0(X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScPr])])]) ).
cnf(c_0_52,hypothesis,
( ~ aVector0(X1)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| sdtpldt0(sdtasasdt0(sziznziztdt0(X1),xq),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),xB)) = sdtasasdt0(X1,xt) ),
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_44]),c_0_47]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_53,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_54,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
fof(c_0_55,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_56,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| aScalar0(sdtasasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_57,hypothesis,
sdtasasdt0(xt,xt) = sdtpldt0(xD,xG),
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_52,c_0_44]),c_0_47]),c_0_53]),c_0_48]),c_0_54]),c_0_49])]) ).
fof(c_0_58,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_59,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,hypothesis,
aScalar0(sdtpldt0(xD,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_49])]) ).
fof(c_0_61,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])])])]) ).
fof(c_0_62,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])])]) ).
fof(c_0_63,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_64,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_66,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_67,plain,
( ~ aScalar0(X1)
| smndt0(smndt0(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_68,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,hypothesis,
xH = sdtasdt0(xA,xB),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_70,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_71,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_72,plain,
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,hypothesis,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| smndt0(sdtasdt0(X1,X2)) = sdtasdt0(X2,smndt0(X1)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,hypothesis,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| smndt0(sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X2),X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_65]) ).
cnf(c_0_75,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_64]),c_0_68]) ).
cnf(c_0_76,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_64,c_0_69]),c_0_70]),c_0_71])]) ).
cnf(c_0_77,hypothesis,
sdtasdt0(xB,smndt0(xB)) = smndt0(xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_54]),c_0_70])]) ).
cnf(c_0_78,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| aScalar0(sdtasdt0(X1,smndt0(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_68]) ).
cnf(c_0_79,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_80,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| smndt0(sdtasdt0(smndt0(X1),X2)) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_68]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(smndt0(xB),xA) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_69]),c_0_71]),c_0_70])]) ).
cnf(c_0_82,hypothesis,
smndt0(smndt0(xH)) = xH,
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_76]),c_0_69]),c_0_70]),c_0_71])]) ).
cnf(c_0_83,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_84,plain,
( ~ aScalar0(X1)
| sdtpldt0(smndt0(X1),X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_85,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_86,hypothesis,
smndt0(smndt0(xG)) = xG,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_77]),c_0_54]),c_0_70])]) ).
cnf(c_0_87,hypothesis,
aScalar0(smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_77]),c_0_70])]) ).
cnf(c_0_88,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xB,sdtasdt0(xB,X1)) = sdtasdt0(xG,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_54]),c_0_70])]) ).
cnf(c_0_89,hypothesis,
sdtasdt0(xB,xA) = xH,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_71]),c_0_70])]) ).
fof(c_0_90,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_91,plain,
! [X40,X41,X42] :
( sdtlseqdt0(X40,X42)
| ~ sdtlseqdt0(X41,X42)
| ~ sdtlseqdt0(X40,X41)
| ~ aScalar0(X42)
| ~ aScalar0(X41)
| ~ aScalar0(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])])]) ).
fof(c_0_92,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])])])]) ).
fof(c_0_93,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_94,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_72]) ).
cnf(c_0_95,hypothesis,
sdtpldt0(smndt0(xG),xG) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_96,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_97,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_98,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_99,hypothesis,
sdtasdt0(xG,xA) = sdtasdt0(xB,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_71])]) ).
fof(c_0_100,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_101,plain,
( ~ aScalar0(X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_102,plain,
( ~ aScalar0(X1)
| sdtasdt0(sz0z00,X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_103,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_104,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_105,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtlseqdt0(sz0z00,sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_106,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_107,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,sz0z00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_108,hypothesis,
sdtpldt0(xG,sz0z00) = sdtpldt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_86]),c_0_96]),c_0_87])]) ).
cnf(c_0_109,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_64,c_0_97]),c_0_96]),c_0_98])]) ).
fof(c_0_110,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])])]) ).
fof(c_0_111,hypothesis,
! [X78] :
( xp = sziznziztdt0(xs)
& ( sdtlbdtrb0(xp,X78) = sdtlbdtrb0(xs,X78)
| ~ aNaturalNumber0(X78) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1709])])])]) ).
fof(c_0_112,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])])]) ).
fof(c_0_113,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_114,hypothesis,
sdtpldt0(xG,smndt0(xG)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_86]),c_0_87])]) ).
cnf(c_0_115,hypothesis,
sdtasdt0(xB,xH) = sdtasdt0(xA,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_99]),c_0_71]),c_0_96])]) ).
cnf(c_0_116,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_117,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xA,sdtasdt0(xB,X1)) = sdtasdt0(xH,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_69]),c_0_70]),c_0_71])]) ).
cnf(c_0_118,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_100]) ).
cnf(c_0_119,plain,
( ~ aScalar0(X1)
| sdtasdt0(X1,sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_120,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103])]) ).
cnf(c_0_121,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(X1,sz0z00)
| sdtlseqdt0(X1,sdtpldt0(X2,X3)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_103])]),c_0_106]) ).
cnf(c_0_122,hypothesis,
sdtpldt0(sz0z00,xG) = xG,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_96])]) ).
cnf(c_0_123,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_54]),c_0_70])]) ).
fof(c_0_124,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_125,hypothesis,
sdtasdt0(smndt0(xG),xC) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_97]),c_0_98]),c_0_96])]) ).
cnf(c_0_126,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_75,c_0_109]),c_0_97]),c_0_96]),c_0_98])]) ).
cnf(c_0_127,plain,
( ~ aVector0(X1)
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_128,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_129,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_130,hypothesis,
sdtasdt0(xG,smndt0(xC)) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_97]),c_0_98]),c_0_96])]) ).
cnf(c_0_131,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_132,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_133,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_134,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_135,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_136,hypothesis,
sdtpldt0(smndt0(xG),sz0z00) = sdtpldt0(sz0z00,smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_114]),c_0_87]),c_0_96])]) ).
cnf(c_0_137,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| smndt0(sdtasdt0(X1,sdtasdt0(X2,X3))) = sdtasdt0(sdtasdt0(X1,X2),smndt0(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_79]),c_0_68]) ).
cnf(c_0_138,hypothesis,
sdtasdt0(xB,sdtasdt0(xA,xG)) = sdtasdt0(xG,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_115]),c_0_116])]) ).
cnf(c_0_139,plain,
( ~ aScalar0(X1)
| smndt0(sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_140,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_141,hypothesis,
sdtasdt0(xA,sdtasdt0(xA,xG)) = sdtasdt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_115]),c_0_116])]) ).
cnf(c_0_142,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_143,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X3,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_103])]),c_0_120])]) ).
cnf(c_0_144,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(X1,sz0z00)
| sdtlseqdt0(X1,xG) ),
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_121,c_0_122]),c_0_123]),c_0_120]),c_0_96]),c_0_103])]) ).
fof(c_0_145,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_146,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_124]) ).
cnf(c_0_147,plain,
( ~ aScalar0(X1)
| sdtpldt0(sz0z00,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_148,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,smndt0(X2))) = sz0z00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_64]),c_0_68]) ).
cnf(c_0_149,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_150,hypothesis,
sdtasdt0(xG,xC) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_125]),c_0_126]),c_0_98]),c_0_96])]) ).
cnf(c_0_151,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129])]) ).
cnf(c_0_152,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_130]),c_0_98]),c_0_96])]) ).
cnf(c_0_153,hypothesis,
sdtasdt0(xD,xF) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_65]),c_0_132]),c_0_133])]) ).
cnf(c_0_154,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(xH,X1)
| sdtlseqdt0(X1,xH) ),
inference(spm,[status(thm)],[c_0_134,c_0_116]) ).
cnf(c_0_155,hypothesis,
aScalar0(sdtasdt0(xA,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_115]),c_0_116]),c_0_70])]) ).
cnf(c_0_156,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| aScalar0(sdtasdt0(sdtpldt0(X1,X2),X3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_135]),c_0_68]),c_0_68]) ).
cnf(c_0_157,hypothesis,
sdtpldt0(sz0z00,smndt0(xG)) = smndt0(xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_136]),c_0_87])]) ).
cnf(c_0_158,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| smndt0(sdtasdt0(X1,sdtasdt0(X2,X3))) = sdtasdt0(smndt0(sdtasdt0(X1,X2)),X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_79]),c_0_68]) ).
cnf(c_0_159,hypothesis,
smndt0(sdtasdt0(xG,xH)) = sdtasdt0(xH,smndt0(xG)),
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_137,c_0_138]),c_0_89]),c_0_96]),c_0_71]),c_0_70])]) ).
cnf(c_0_160,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_73,c_0_69]),c_0_71]),c_0_70])]) ).
cnf(c_0_161,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_162,hypothesis,
smndt0(sdtasdt0(xH,xH)) = sdtasdt0(xF,smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_141]),c_0_142]),c_0_96]),c_0_71])]) ).
cnf(c_0_163,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xA,sdtasdt0(xA,X1)) = sdtasdt0(xF,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_142]),c_0_71])]) ).
cnf(c_0_164,hypothesis,
sdtasdt0(xA,smndt0(xA)) = smndt0(xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_142]),c_0_71])]) ).
cnf(c_0_165,hypothesis,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(X2,X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,xG)) ),
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_144]),c_0_96]),c_0_120]),c_0_103])]) ).
cnf(c_0_166,plain,
( ~ aScalar0(X1)
| sdtlseqdt0(X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_167,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_146,c_0_147]),c_0_103])]) ).
cnf(c_0_168,hypothesis,
sdtpldt0(xR,smndt0(xR)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_109]),c_0_97]),c_0_96]),c_0_98])]) ).
cnf(c_0_169,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_149,c_0_150]),c_0_151]),c_0_123]),c_0_98]),c_0_96])]) ).
cnf(c_0_170,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_171,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(smndt0(xR),X1)
| sdtlseqdt0(X1,smndt0(xR)) ),
inference(spm,[status(thm)],[c_0_134,c_0_152]) ).
cnf(c_0_172,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_64,c_0_153]),c_0_132]),c_0_133])]) ).
cnf(c_0_173,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_64,c_0_131]),c_0_133]),c_0_132])]) ).
cnf(c_0_174,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_175,hypothesis,
sdtlseqdt0(xH,xH),
inference(spm,[status(thm)],[c_0_154,c_0_116]) ).
cnf(c_0_176,hypothesis,
aScalar0(sdtasdt0(xG,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_138]),c_0_155]),c_0_70])]) ).
cnf(c_0_177,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(smndt0(xG),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_87]),c_0_103])]) ).
cnf(c_0_178,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(smndt0(X1),X2) = sdtasdt0(X1,smndt0(X2)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_179,hypothesis,
sdtasdt0(smndt0(xH),xG) = sdtasdt0(xH,smndt0(xG)),
inference(rw,[status(thm)],[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_158,c_0_138]),c_0_89]),c_0_96]),c_0_71]),c_0_70])]),c_0_159]) ).
cnf(c_0_180,hypothesis,
aScalar0(smndt0(xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_160]),c_0_71]),c_0_70])]) ).
fof(c_0_181,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_182,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_73,c_0_119]),c_0_161]),c_0_103])]) ).
cnf(c_0_183,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_146,c_0_147]),c_0_103])]) ).
cnf(c_0_184,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_148,c_0_76]),c_0_69]),c_0_70]),c_0_71])]) ).
cnf(c_0_185,hypothesis,
sdtasdt0(xF,smndt0(xG)) = sdtasdt0(xH,smndt0(xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_162]),c_0_116])]) ).
cnf(c_0_186,hypothesis,
sdtasdt0(xF,xG) = sdtasdt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_141]),c_0_96])]) ).
cnf(c_0_187,hypothesis,
aScalar0(smndt0(xF)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_164]),c_0_71])]) ).
fof(c_0_188,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])])]) ).
cnf(c_0_189,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,xG)) ),
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_190,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_66,c_0_97]),c_0_96]),c_0_98])]) ).
cnf(c_0_191,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(X1,smndt0(xR))
| 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_167,c_0_168]),c_0_169]),c_0_152]),c_0_170])]) ).
cnf(c_0_192,hypothesis,
sdtlseqdt0(smndt0(xR),smndt0(xR)),
inference(spm,[status(thm)],[c_0_171,c_0_152]) ).
cnf(c_0_193,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_75,c_0_172]),c_0_153]),c_0_132]),c_0_133])]) ).
cnf(c_0_194,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_173]),c_0_133]),c_0_132])]) ).
cnf(c_0_195,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_142]),c_0_71])]) ).
cnf(c_0_196,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_53]),c_0_174])]) ).
cnf(c_0_197,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xH,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_175]),c_0_116])]) ).
cnf(c_0_198,hypothesis,
aScalar0(sdtasdt0(xH,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_65]),c_0_116]),c_0_96])]) ).
cnf(c_0_199,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(xG,smndt0(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_96])]) ).
cnf(c_0_200,hypothesis,
smndt0(sdtasdt0(xH,smndt0(xG))) = sdtasdt0(xH,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_179]),c_0_82]),c_0_96]),c_0_180])]) ).
cnf(c_0_201,hypothesis,
aScalar0(sdtasdt0(xH,smndt0(xG))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_159]),c_0_176])]) ).
cnf(c_0_202,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_181]) ).
cnf(c_0_203,hypothesis,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_161]),c_0_103])]) ).
cnf(c_0_204,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_183,c_0_184]),c_0_180]),c_0_116])]) ).
cnf(c_0_205,hypothesis,
smndt0(sdtasdt0(xH,smndt0(xH))) = sdtasdt0(xH,xH),
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_64,c_0_185]),c_0_86]),c_0_186]),c_0_87]),c_0_132])]) ).
cnf(c_0_206,hypothesis,
sdtpldt0(xF,smndt0(xF)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_164]),c_0_142]),c_0_71])]) ).
cnf(c_0_207,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(smndt0(xF),X1)
| sdtlseqdt0(X1,smndt0(xF)) ),
inference(spm,[status(thm)],[c_0_134,c_0_187]) ).
cnf(c_0_208,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_188]) ).
cnf(c_0_209,hypothesis,
( ~ aScalar0(smndt0(xC))
| sdtlseqdt0(sz0z00,smndt0(xR)) ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_210,hypothesis,
sdtlseqdt0(smndt0(xR),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_152])]) ).
cnf(c_0_211,hypothesis,
sdtpldt0(xS,smndt0(xS)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_193]),c_0_194])]) ).
cnf(c_0_212,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_149,c_0_153]),c_0_195]),c_0_196]),c_0_132]),c_0_133])]) ).
cnf(c_0_213,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_214,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(smndt0(xS),X1)
| sdtlseqdt0(X1,smndt0(xS)) ),
inference(spm,[status(thm)],[c_0_134,c_0_194]) ).
cnf(c_0_215,hypothesis,
smndt0(smndt0(xF)) = xF,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_164]),c_0_142]),c_0_71])]) ).
cnf(c_0_216,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(sdtasdt0(xH,xG),xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_197]),c_0_198]),c_0_103])]) ).
cnf(c_0_217,hypothesis,
aScalar0(sdtasdt0(xG,sdtasdt0(xH,xG))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_201])]) ).
cnf(c_0_218,hypothesis,
( ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X2,sdtasdt0(X3,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_65]),c_0_68]) ).
cnf(c_0_219,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_202,c_0_166]),c_0_103])]),c_0_203]) ).
cnf(c_0_220,hypothesis,
( ~ sdtlseqdt0(xH,sz0z00)
| sdtlseqdt0(sz0z00,smndt0(xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_166]),c_0_180])]) ).
cnf(c_0_221,hypothesis,
sdtasdt0(smndt0(xH),smndt0(xH)) = sdtasdt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_205]),c_0_180]),c_0_116])]) ).
cnf(c_0_222,hypothesis,
sdtasdt0(sz0z00,xG) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_86]),c_0_87])]) ).
cnf(c_0_223,hypothesis,
sdtasdt0(smndt0(xF),xG) = sdtasdt0(xF,smndt0(xG)),
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_158,c_0_141]),c_0_142]),c_0_96]),c_0_71])]),c_0_162]) ).
cnf(c_0_224,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(xG,X1)
| sdtlseqdt0(X1,xG) ),
inference(spm,[status(thm)],[c_0_134,c_0_96]) ).
cnf(c_0_225,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(X1,smndt0(xF))
| 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_167,c_0_206]),c_0_195]),c_0_187]),c_0_132])]) ).
cnf(c_0_226,hypothesis,
sdtlseqdt0(smndt0(xF),smndt0(xF)),
inference(spm,[status(thm)],[c_0_207,c_0_187]) ).
cnf(c_0_227,hypothesis,
aScalar0(sdtasdt0(xH,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_141]),c_0_155]),c_0_71])]) ).
cnf(c_0_228,hypothesis,
( ~ aScalar0(smndt0(xC))
| smndt0(xR) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_210]),c_0_103]),c_0_152])]) ).
fof(c_0_229,plain,
! [X33,X34] :
( sdtasdt0(smndt0(X33),smndt0(X34)) = sdtasdt0(X33,X34)
| ~ aScalar0(X34)
| ~ aScalar0(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMDNeg])])]) ).
cnf(c_0_230,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(X1,smndt0(xS))
| 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_167,c_0_211]),c_0_212]),c_0_194]),c_0_213])]) ).
cnf(c_0_231,hypothesis,
sdtlseqdt0(smndt0(xS),smndt0(xS)),
inference(spm,[status(thm)],[c_0_214,c_0_194]) ).
cnf(c_0_232,hypothesis,
sdtasdt0(smndt0(xF),xD) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_131]),c_0_133]),c_0_132])]) ).
cnf(c_0_233,hypothesis,
sdtasdt0(sz0z00,xF) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_215]),c_0_187])]) ).
cnf(c_0_234,hypothesis,
sdtpldt0(smndt0(xS),xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_193]),c_0_194])]) ).
cnf(c_0_235,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtasdt0(X1,X1) != sdtasdt0(xG,xG)
| X1 = xG ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_123]),c_0_96])]) ).
cnf(c_0_236,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xH,sdtasdt0(xG,xG))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_79]),c_0_96]),c_0_116])]) ).
cnf(c_0_237,hypothesis,
aScalar0(sdtasdt0(xH,sdtasdt0(xG,xG))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_96]),c_0_116])]) ).
cnf(c_0_238,hypothesis,
( ~ sdtlseqdt0(xH,sz0z00)
| sdtasdt0(xH,xH) != sz0z00
| smndt0(xH) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_221]),c_0_180])]) ).
cnf(c_0_239,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X2,xG)
| ~ sdtlseqdt0(sz0z00,X2)
| sdtlseqdt0(sdtasdt0(X1,X2),sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_222]),c_0_96]),c_0_103])]) ).
cnf(c_0_240,hypothesis,
sdtasdt0(smndt0(xF),xG) = sdtasdt0(xH,smndt0(xH)),
inference(rw,[status(thm)],[c_0_223,c_0_185]) ).
cnf(c_0_241,hypothesis,
sdtlseqdt0(xG,xG),
inference(spm,[status(thm)],[c_0_224,c_0_96]) ).
cnf(c_0_242,hypothesis,
sdtlseqdt0(smndt0(xF),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_187])]) ).
cnf(c_0_243,hypothesis,
aScalar0(sdtasdt0(xF,smndt0(xG))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_162]),c_0_227])]) ).
cnf(c_0_244,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xC,sdtasdt0(smndt0(xG),X1)) = sdtasdt0(smndt0(xR),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_109]),c_0_98])]),c_0_87])]) ).
cnf(c_0_245,hypothesis,
smndt0(xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_72]),c_0_98])]) ).
cnf(c_0_246,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_247,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(smndt0(xG),X1)
| sdtlseqdt0(X1,smndt0(xG)) ),
inference(spm,[status(thm)],[c_0_134,c_0_87]) ).
cnf(c_0_248,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_249,hypothesis,
sdtlseqdt0(smndt0(xS),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_194])]) ).
cnf(c_0_250,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X2,xD)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X1,smndt0(xF))
| sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_232]),c_0_133])]),c_0_187])]) ).
cnf(c_0_251,hypothesis,
sdtasdt0(smndt0(xF),sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_233]),c_0_161]),c_0_103]),c_0_132])]) ).
cnf(c_0_252,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_94,c_0_234]),c_0_193]),c_0_213]),c_0_194])]) ).
cnf(c_0_253,hypothesis,
sdtpldt0(smndt0(xR),xR) = 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_148,c_0_109]),c_0_86]),c_0_97]),c_0_87]),c_0_98])]) ).
cnf(c_0_254,hypothesis,
( sdtasdt0(sdtasdt0(xH,sdtasdt0(xG,xG)),sdtasdt0(xH,sdtasdt0(xG,xG))) != sdtasdt0(xG,xG)
| sdtasdt0(xH,sdtasdt0(xG,xG)) = xG ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_237])]) ).
cnf(c_0_255,hypothesis,
aScalar0(sdtasdt0(xG,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_86]),c_0_87])]) ).
cnf(c_0_256,hypothesis,
( ~ sdtlseqdt0(xH,sz0z00)
| sdtasdt0(xH,xH) != sz0z00
| xH = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_238]),c_0_161]),c_0_116])]) ).
cnf(c_0_257,hypothesis,
( sdtlseqdt0(sz0z00,xH)
| sdtlseqdt0(xH,sz0z00) ),
inference(spm,[status(thm)],[c_0_154,c_0_103]) ).
cnf(c_0_258,hypothesis,
sdtlseqdt0(sdtasdt0(xH,smndt0(xH)),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_123]),c_0_241]),c_0_242]),c_0_96]),c_0_187])]) ).
cnf(c_0_259,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xH,smndt0(xH))),
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_226]),c_0_223]),c_0_185]),c_0_187])]) ).
cnf(c_0_260,hypothesis,
aScalar0(sdtasdt0(xH,smndt0(xH))),
inference(rw,[status(thm)],[c_0_243,c_0_185]) ).
cnf(c_0_261,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xC,sdtasdt0(smndt0(xG),X1)) = sdtasdt0(sz0z00,X1) ),
inference(rw,[status(thm)],[c_0_244,c_0_245]) ).
cnf(c_0_262,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),xG) = sdtasdt0(X1,smndt0(xG)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_86]),c_0_87])]) ).
cnf(c_0_263,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(smndt0(xG),smndt0(X1)) = sdtasdt0(xG,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_86]),c_0_87])]) ).
cnf(c_0_264,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(X1,smndt0(xG))
| 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_167,c_0_114]),c_0_123]),c_0_87]),c_0_96])]) ).
cnf(c_0_265,hypothesis,
sdtlseqdt0(smndt0(xG),smndt0(xG)),
inference(spm,[status(thm)],[c_0_247,c_0_87]) ).
cnf(c_0_266,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_248,c_0_60]) ).
cnf(c_0_267,hypothesis,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_268,hypothesis,
xp = sziznziztdt0(xs),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_269,hypothesis,
xE = sdtasasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_270,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_271,hypothesis,
( ~ sdtlseqdt0(sz0z00,smndt0(xS))
| smndt0(xS) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_249]),c_0_194]),c_0_103])]) ).
cnf(c_0_272,hypothesis,
sdtlseqdt0(sz0z00,smndt0(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)],[inference(spm,[status(thm)],[c_0_250,c_0_251]),c_0_226]),c_0_120]),c_0_196]),c_0_103]),c_0_187])]) ).
cnf(c_0_273,hypothesis,
sdtpldt0(sz0z00,xS) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_252]),c_0_213])]) ).
cnf(c_0_274,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_94,c_0_253]),c_0_126]),c_0_170]),c_0_152])]) ).
cnf(c_0_275,hypothesis,
( sdtasdt0(xH,sdtasdt0(sdtasdt0(xG,xG),sdtasdt0(xH,sdtasdt0(xG,xG)))) != sdtasdt0(xG,xG)
| sdtasdt0(xH,sdtasdt0(xG,xG)) = xG ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_218]),c_0_237]),c_0_255]),c_0_116])]) ).
cnf(c_0_276,hypothesis,
( sdtasdt0(xH,xH) != sz0z00
| sdtlseqdt0(sz0z00,xH)
| xH = sz0z00 ),
inference(spm,[status(thm)],[c_0_256,c_0_257]) ).
cnf(c_0_277,hypothesis,
sdtasdt0(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_208,c_0_258]),c_0_259]),c_0_260]),c_0_103])]) ).
cnf(c_0_278,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X1)
| smndt0(sdtasdt0(X1,sdtasdt0(X2,X3))) = sdtasdt0(X1,sdtasdt0(X2,smndt0(X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_75]),c_0_78]) ).
cnf(c_0_279,hypothesis,
sdtasdt0(xC,sdtasdt0(xG,smndt0(xG))) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_262]),c_0_222]),c_0_96])]) ).
cnf(c_0_280,hypothesis,
sdtasdt0(smndt0(xG),xG) = sdtasdt0(xG,smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_86]),c_0_87])]) ).
cnf(c_0_281,hypothesis,
sdtlseqdt0(smndt0(xG),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_265]),c_0_87])]) ).
cnf(c_0_282,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(smndt0(xG),xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_265]),c_0_87])]) ).
cnf(c_0_283,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,xG)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_86]),c_0_87])]) ).
cnf(c_0_284,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(smndt0(xG),X1) = sdtasdt0(xG,smndt0(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_86]),c_0_87])]) ).
cnf(c_0_285,hypothesis,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(X1),xq))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),xB))
| ~ aVector0(X1)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| sdtpldt0(sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),xB),sdtasasdt0(sziznziztdt0(X1),xq)) = sdtasasdt0(X1,xt) ),
inference(spm,[status(thm)],[c_0_52,c_0_266]) ).
cnf(c_0_286,hypothesis,
sdtasasdt0(xs,xt) = sdtpldt0(xE,xH),
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_52,c_0_267]),c_0_268]),c_0_269]),c_0_69]),c_0_270])]) ).
cnf(c_0_287,hypothesis,
aScalar0(xE),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_288,hypothesis,
smndt0(xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_271,c_0_272])]) ).
cnf(c_0_289,hypothesis,
sdtpldt0(xS,sz0z00) = xS,
inference(rw,[status(thm)],[c_0_252,c_0_273]) ).
cnf(c_0_290,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_113]) ).
cnf(c_0_291,hypothesis,
sdtpldt0(sz0z00,xR) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_274]),c_0_170])]) ).
fof(c_0_292,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_293,hypothesis,
( sdtasdt0(xH,sdtasdt0(xG,sdtasdt0(xG,sdtasdt0(xH,sdtasdt0(xG,xG))))) != sdtasdt0(xG,xG)
| sdtasdt0(xH,sdtasdt0(xG,xG)) = xG ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_79]),c_0_237]),c_0_96])]) ).
cnf(c_0_294,hypothesis,
( sdtasdt0(xH,xH) != sz0z00
| xH = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_276]),c_0_116])]) ).
cnf(c_0_295,hypothesis,
sdtasdt0(xH,xH) = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_277]),c_0_161]) ).
cnf(c_0_296,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(sz0z00,sdtasdt0(X1,X2)) = sdtasdt0(sz0z00,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_102]),c_0_103])]) ).
cnf(c_0_297,hypothesis,
sdtasdt0(xC,sdtasdt0(xG,xG)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_279]),c_0_161]),c_0_86]),c_0_98]),c_0_87]),c_0_96])]) ).
cnf(c_0_298,hypothesis,
sdtlseqdt0(sdtasdt0(xG,smndt0(xG)),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_280]),c_0_123]),c_0_241]),c_0_281]),c_0_96]),c_0_87])]) ).
cnf(c_0_299,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xG,smndt0(xG))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_65]),c_0_96]),c_0_87])]) ).
cnf(c_0_300,hypothesis,
aScalar0(sdtasdt0(xG,smndt0(xG))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_284]),c_0_87]),c_0_96])]) ).
cnf(c_0_301,hypothesis,
sdtpldt0(xH,xE) = sdtpldt0(xE,xH),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_268]),c_0_267]),c_0_69]),c_0_269]),c_0_286]),c_0_270]),c_0_267]),c_0_69]),c_0_116]),c_0_269]),c_0_287])]) ).
cnf(c_0_302,hypothesis,
sdtpldt0(xG,xD) = sdtpldt0(xD,xG),
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)],[inference(rw,[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)],[inference(spm,[status(thm)],[c_0_285,c_0_47]),c_0_44]),c_0_48]),c_0_54]),c_0_53]),c_0_57]),c_0_44]),c_0_49]),c_0_44]),c_0_48]),c_0_54]),c_0_96]),c_0_53]),c_0_133])]) ).
cnf(c_0_303,hypothesis,
( ~ aScalar0(X1)
| sdtpldt0(xS,sdtasdt0(X1,xD)) = sdtasdt0(sdtpldt0(xF,X1),xD) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_131]),c_0_133]),c_0_132])]) ).
cnf(c_0_304,hypothesis,
xS = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_288]),c_0_289]) ).
cnf(c_0_305,hypothesis,
( ~ aScalar0(X1)
| sdtpldt0(xR,sdtasdt0(xC,X1)) = sdtasdt0(xC,sdtpldt0(xG,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_290,c_0_97]),c_0_96]),c_0_98])]) ).
cnf(c_0_306,hypothesis,
xR = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_253,c_0_245]),c_0_291]) ).
fof(c_0_307,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(fof_simplification,[status(thm)],[c_0_292]) ).
cnf(c_0_308,hypothesis,
( sdtasdt0(xH,sdtasdt0(xG,sdtasdt0(xH,sdtasdt0(sdtasdt0(xG,xG),xG)))) != sdtasdt0(xG,xG)
| sdtasdt0(xH,sdtasdt0(xG,xG)) = xG ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_218]),c_0_96]),c_0_255]),c_0_116])]) ).
cnf(c_0_309,hypothesis,
xH = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_294,c_0_295])]) ).
cnf(c_0_310,hypothesis,
sdtasdt0(sz0z00,sdtasdt0(xG,xG)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_297]),c_0_203]),c_0_255]),c_0_98])]) ).
cnf(c_0_311,hypothesis,
sdtasdt0(xG,smndt0(xG)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_298]),c_0_299]),c_0_300]),c_0_103])]) ).
cnf(c_0_312,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),sz0z00) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_102]),c_0_161]),c_0_103])]) ).
cnf(c_0_313,hypothesis,
( ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X2,sdtpldt0(X3,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_266]),c_0_106]) ).
cnf(c_0_314,hypothesis,
sdtpldt0(smndt0(xH),sdtpldt0(xE,xH)) = sdtpldt0(sz0z00,xE),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_301]),c_0_287]),c_0_116])]) ).
cnf(c_0_315,hypothesis,
sdtpldt0(smndt0(xG),sdtpldt0(xD,xG)) = sdtpldt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_302]),c_0_133]),c_0_96])]) ).
cnf(c_0_316,hypothesis,
( ~ aScalar0(X1)
| sdtpldt0(sz0z00,sdtasdt0(X1,xD)) = sdtasdt0(sdtpldt0(xF,X1),xD) ),
inference(rw,[status(thm)],[c_0_303,c_0_304]) ).
cnf(c_0_317,hypothesis,
( ~ aScalar0(X1)
| sdtpldt0(sz0z00,sdtasdt0(xC,X1)) = sdtasdt0(xC,sdtpldt0(xG,X1)) ),
inference(rw,[status(thm)],[c_0_305,c_0_306]) ).
fof(c_0_318,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(fof_nnf,[status(thm)],[c_0_307]) ).
cnf(c_0_319,hypothesis,
( sdtasdt0(sz0z00,sdtasdt0(xG,sdtasdt0(sz0z00,sdtasdt0(sdtasdt0(xG,xG),xG)))) != sdtasdt0(xG,xG)
| xG = sz0z00 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_308,c_0_309]),c_0_310]),c_0_309]),c_0_309]) ).
cnf(c_0_320,hypothesis,
sdtasdt0(xG,xG) = 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_64,c_0_311]),c_0_161]),c_0_86]),c_0_87]),c_0_96])]) ).
cnf(c_0_321,hypothesis,
sdtasdt0(xG,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_312,c_0_86]),c_0_87])]) ).
cnf(c_0_322,hypothesis,
sdtpldt0(xE,sz0z00) = sdtpldt0(sz0z00,xE),
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_313,c_0_314]),c_0_184]),c_0_180]),c_0_116]),c_0_287])]) ).
cnf(c_0_323,hypothesis,
sdtpldt0(xD,sz0z00) = sdtpldt0(sz0z00,xD),
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_313,c_0_315]),c_0_114]),c_0_87]),c_0_96]),c_0_133])]) ).
cnf(c_0_324,hypothesis,
sdtasdt0(sdtpldt0(xF,xC),xD) = sdtasdt0(xC,sdtpldt0(xD,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_317]),c_0_302]),c_0_98]),c_0_133])]) ).
cnf(c_0_325,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(sdtpldt0(xE,xH),sdtpldt0(xE,xH)),sdtasdt0(sdtpldt0(xC,xF),sdtpldt0(xD,xG))),
inference(split_conjunct,[status(thm)],[c_0_318]) ).
cnf(c_0_326,hypothesis,
xG = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_319,c_0_320]),c_0_222]),c_0_203]),c_0_321]),c_0_203]),c_0_320])]) ).
cnf(c_0_327,hypothesis,
sdtpldt0(sz0z00,xE) = xE,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_322]),c_0_287])]) ).
cnf(c_0_328,hypothesis,
sdtpldt0(sz0z00,xD) = xD,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_323]),c_0_133])]) ).
cnf(c_0_329,hypothesis,
sdtasdt0(sdtpldt0(xC,xF),xD) = sdtasdt0(xC,sdtpldt0(xD,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_266]),c_0_98]),c_0_132])]) ).
cnf(c_0_330,hypothesis,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(split_conjunct,[status(thm)],[m__1967]) ).
cnf(c_0_331,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)],[inference(rw,[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)],[inference(spm,[status(thm)],[c_0_325,c_0_326]),c_0_309]),c_0_322]),c_0_327]),c_0_309]),c_0_322]),c_0_327]),c_0_323]),c_0_328]),c_0_329]),c_0_326]),c_0_323]),c_0_328]),c_0_330])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG075+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/10.58 % Computer : n020.cluster.edu
% 0.11/10.58 % Model : x86_64 x86_64
% 0.11/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.58 % Memory : 8046.5625MB
% 0.11/10.58 % OS : Linux 6.8.0-71-generic
% 0.11/10.58 % CPULimit : 300
% 0.11/10.58 % WCLimit : 300
% 0.11/10.58 % DateTime : Mon Sep 21 04:18:43 UTC 2026
% 0.11/10.58 % CPUTime :
% 0.11/10.59 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/10.63 Running first-order theorem proving
% 0.13/10.63 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 124.57/28.85 % Version: 3.5.1
% 124.57/28.85 % Preprocessing class: FSLSSMSMSSSNFFN.
% 124.57/28.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 124.57/28.85 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 124.57/28.85 % Starting new_bool_3 with 300s (1) cores
% 124.57/28.85 % Starting new_bool_1 with 300s (1) cores
% 124.57/28.85 % Starting sh5l with 300s (1) cores
% 124.57/28.85 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1983553 completed with status 0
% 124.57/28.85 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 124.57/28.85 % Preprocessing class: FSLSSMSMSSSNFFN.
% 124.57/28.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 124.57/28.85 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 124.57/28.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 124.57/28.85 % No SInE strategy applied
% 124.57/28.85 % Search class: FGHSF-FFMM21-MFFFFFNN
% 124.57/28.85 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 124.57/28.85 % Starting SubtermCWHack with 136s (1) cores
% 124.57/28.85 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 124.57/28.85 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 124.57/28.85 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 124.57/28.85 % Starting new_bool_3 with 136s (1) cores
% 124.57/28.85 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 1983562 completed with status 0
% 124.57/28.85 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 124.57/28.85 % Preprocessing class: FSLSSMSMSSSNFFN.
% 124.57/28.85 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 124.57/28.85 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 124.57/28.85 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 124.57/28.85 % No SInE strategy applied
% 124.57/28.85 % Search class: FGHSF-FFMM21-MFFFFFNN
% 124.57/28.85 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 124.57/28.85 % Starting SubtermCWHack with 136s (1) cores
% 124.57/28.85 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 124.57/28.85 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 124.57/28.85 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 124.57/28.85 % Preprocessing time : 0.002 s
% 124.57/28.85 % Presaturation interreduction done
% 124.57/28.85
% 124.57/28.85 % Proof found!
% 124.57/28.85 % SZS status Theorem
% 124.57/28.85 % SZS output start CNFRefutation
% See solution above
% 124.57/28.85 % Parsed axioms : 58
% 124.57/28.85 % Removed by relevancy pruning/SinE : 0
% 124.57/28.85 % Initial clauses : 96
% 124.57/28.85 % Removed in clause preprocessing : 5
% 124.57/28.85 % Initial clauses in saturation : 91
% 124.57/28.85 % Processed clauses : 31701
% 124.57/28.85 % ...of these trivial : 2201
% 124.57/28.85 % ...subsumed : 20407
% 124.57/28.85 % ...remaining for further processing : 9093
% 124.57/28.85 % Other redundant clauses eliminated : 6
% 124.57/28.85 % Clauses deleted for lack of memory : 0
% 124.57/28.85 % Backward-subsumed : 550
% 124.57/28.85 % Backward-rewritten : 5659
% 124.57/28.85 % Generated clauses : 876213
% 124.57/28.85 % ...of the previous two non-redundant : 802421
% 124.57/28.85 % ...aggressively subsumed : 0
% 124.57/28.85 % Contextual simplify-reflections : 358
% 124.57/28.85 % Paramodulations : 876186
% 124.57/28.85 % Factorizations : 0
% 124.57/28.85 % NegExts : 0
% 124.57/28.85 % Equation resolutions : 27
% 124.57/28.85 % Disequality decompositions : 0
% 124.57/28.85 % Total rewrite steps : 1906637
% 124.57/28.85 % ...of those cached : 1905236
% 124.57/28.85 % Propositional unsat checks : 1
% 124.57/28.85 % Propositional check models : 0
% 124.57/28.85 % Propositional check unsatisfiable : 0
% 124.57/28.85 % Propositional clauses : 0
% 124.57/28.85 % Propositional clauses after purity: 0
% 124.57/28.85 % Propositional unsat core size : 0
% 124.57/28.85 % Propositional preprocessing time : 0.000
% 124.57/28.85 % Propositional encoding time : 0.474
% 124.57/28.85 % Propositional solver time : 0.351
% 124.57/28.85 % Success case prop preproc time : 0.000
% 124.57/28.85 % Success case prop encoding time : 0.000
% 124.57/28.85 % Success case prop solver time : 0.000
% 124.57/28.85 % Current number of processed clauses : 2790
% 124.57/28.85 % Positive orientable unit clauses : 818
% 124.57/28.85 % Positive unorientable unit clauses: 0
% 124.57/28.85 % Negative unit clauses : 6
% 124.57/28.85 % Non-unit-clauses : 1966
% 124.57/28.85 % Current number of unprocessed clauses: 764978
% 124.57/28.85 % ...number of literals in the above : 2936140
% 124.57/28.85 % Current number of archived formulas : 0
% 124.57/28.85 % Current number of archived clauses : 6300
% 124.57/28.85 % Clause-clause subsumption calls (NU) : 3728529
% 124.57/28.85 % Rec. Clause-clause subsumption calls : 1947587
% 124.57/28.85 % Non-unit clause-clause subsumptions : 21103
% 124.57/28.85 % Unit Clause-clause subsumption calls : 283054
% 124.57/28.85 % Rewrite failures with RHS unbound : 0
% 124.57/28.85 % BW rewrite match attempts : 963
% 124.57/28.85 % BW rewrite match successes : 152
% 124.57/28.85 % Condensation attempts : 0
% 124.57/28.85 % Condensation successes : 0
% 124.57/28.85 % Termbank termtop insertions : 26401494
% 124.57/28.85 % Search garbage collected termcells : 913
% 124.57/28.85
% 124.57/28.85 % -------------------------------------------------
% 124.57/28.85 % User time : 16.769 s
% 124.57/28.85 % System time : 0.680 s
% 124.57/28.85 % Total time : 17.449 s
% 124.57/28.85 % Maximum resident set size: 3704 pages
% 124.57/28.85
% 124.57/28.85 % -------------------------------------------------
% 124.57/28.85 % User time : 84.822 s
% 124.57/28.85 % System time : 3.426 s
% 124.57/28.85 % Total time : 88.248 s
% 124.57/28.85 % Maximum resident set size: 4864 pages
% 124.57/28.85 % E exiting
%------------------------------------------------------------------------------