%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG076+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:05:14 PM UTC 2026
% Result : Theorem 39.84s 23.68s
% Output : CNFRefutation 40.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 41
% Syntax : Number of formulae : 332 ( 137 unt; 0 def)
% Number of atoms : 820 ( 237 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 848 ( 360 ~; 374 |; 84 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 237 ( 3 sgn 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMNeg,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
& sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
fof(mScZero,axiom,
! [X1] :
( aScalar0(X1)
=> ( sdtpldt0(X1,sz0z00) = X1
& sdtpldt0(sz0z00,X1) = X1
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtpldt0(smndt0(X1),X1) = sz0z00
& smndt0(smndt0(X1)) = X1
& smndt0(sz0z00) = sz0z00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1930,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(m__1800,hypothesis,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(m__1837,hypothesis,
( aScalar0(xF)
& xF = sdtasdt0(xA,xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
fof(m__1726,hypothesis,
( aVector0(xq)
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xq,X1) = sdtlbdtrb0(xt,X1) )
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(m__1873,hypothesis,
( aScalar0(xH)
& xH = sdtasdt0(xA,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
fof(m__1766,hypothesis,
( aScalar0(xB)
& xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
fof(m__1746,hypothesis,
( aScalar0(xA)
& xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
fof(m__1892,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(m__1854,hypothesis,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(mLEMon,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3)
& aScalar0(X4) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X3,X4) )
=> sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
fof(mPosMon,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X2) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
fof(m__1911,hypothesis,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
fof(m__1820,hypothesis,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(mLEMonM,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3)
& aScalar0(X4) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(sz0z00,X3)
& sdtlseqdt0(X3,X4) )
=> sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mLETrn,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETrn) ).
fof(m__1709,hypothesis,
( aVector0(xp)
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xp,X1) = sdtlbdtrb0(xs,X1) )
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
fof(mArith,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(mDistr,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
fof(mLERef,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
fof(m__1949,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
fof(mLEASm,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEASm) ).
fof(mLETot,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).
fof(m__1983,hypothesis,
sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1983) ).
fof(mSqrt,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X2)
& sdtasdt0(X1,X1) = sdtasdt0(X2,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqrt) ).
fof(mDistr2,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3)
& aScalar0(X4) )
=> sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
fof(m__,conjecture,
sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefSPN,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aVector0(X2) )
=> ( ( aDimensionOf0(X1) = aDimensionOf0(X2)
& aDimensionOf0(X2) != sz00 )
=> sdtasasdt0(X1,X2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1678,hypothesis,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
fof(mScPr,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aVector0(X2) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> aScalar0(sdtasasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
fof(m__1967,hypothesis,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1967) ).
fof(c_0_41,plain,
! [X100,X101] :
( ( sdtasdt0(X100,smndt0(X101)) = smndt0(sdtasdt0(X100,X101))
| ~ aScalar0(X100)
| ~ aScalar0(X101) )
& ( sdtasdt0(smndt0(X100),X101) = smndt0(sdtasdt0(X100,X101))
| ~ aScalar0(X100)
| ~ aScalar0(X101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])]) ).
fof(c_0_42,plain,
! [X89] :
( ( sdtpldt0(X89,sz0z00) = X89
| ~ aScalar0(X89) )
& ( sdtpldt0(sz0z00,X89) = X89
| ~ aScalar0(X89) )
& ( sdtasdt0(X89,sz0z00) = sz0z00
| ~ aScalar0(X89) )
& ( sdtasdt0(sz0z00,X89) = sz0z00
| ~ aScalar0(X89) )
& ( sdtpldt0(X89,smndt0(X89)) = sz0z00
| ~ aScalar0(X89) )
& ( sdtpldt0(smndt0(X89),X89) = sz0z00
| ~ aScalar0(X89) )
& ( smndt0(smndt0(X89)) = X89
| ~ aScalar0(X89) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X89) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])]) ).
fof(c_0_43,plain,
! [X86,X87] :
( ~ aScalar0(X86)
| ~ aScalar0(X87)
| aScalar0(sdtasdt0(X86,X87)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])]) ).
cnf(c_0_44,plain,
( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_46,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_47,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_48,plain,
( smndt0(smndt0(X1)) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,plain,
( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,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_44,c_0_45]),c_0_46]),c_0_47])]) ).
fof(c_0_52,plain,
! [X88] :
( ~ aScalar0(X88)
| aScalar0(smndt0(X88)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])]) ).
fof(c_0_53,plain,
! [X141] :
( ~ aVector0(X141)
| sdtlseqdt0(sz0z00,sdtasasdt0(X141,X141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])]) ).
fof(c_0_54,hypothesis,
! [X145] :
( aVector0(xq)
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& ( ~ aNaturalNumber0(X145)
| sdtlbdtrb0(xq,X145) = sdtlbdtrb0(xt,X145) )
& xq = sziznziztdt0(xt) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1726])])]) ).
fof(c_0_55,plain,
! [X122] :
( ~ aScalar0(X122)
| sdtlseqdt0(sz0z00,sdtasdt0(X122,X122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])]) ).
cnf(c_0_56,hypothesis,
xH = sdtasdt0(xA,xB),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_57,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_58,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_59,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_60,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_61,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
fof(c_0_62,plain,
! [X110,X111,X112,X113] :
( ~ aScalar0(X110)
| ~ aScalar0(X111)
| ~ aScalar0(X112)
| ~ aScalar0(X113)
| ~ sdtlseqdt0(X110,X111)
| ~ sdtlseqdt0(X112,X113)
| sdtlseqdt0(sdtpldt0(X110,X112),sdtpldt0(X111,X113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])]) ).
cnf(c_0_63,plain,
( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_64,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_49,c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_65,hypothesis,
( aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xF)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_46])]) ).
cnf(c_0_66,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_67,plain,
! [X120,X121] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X120,X121))
| ~ sdtlseqdt0(sz0z00,X120)
| ~ sdtlseqdt0(sz0z00,X121)
| ~ aScalar0(X120)
| ~ aScalar0(X121) )
& ( sdtlseqdt0(sz0z00,sdtasdt0(X120,X121))
| ~ sdtlseqdt0(sz0z00,X120)
| ~ sdtlseqdt0(sz0z00,X121)
| ~ aScalar0(X120)
| ~ aScalar0(X121) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])]) ).
cnf(c_0_68,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_69,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_70,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_71,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_72,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_73,hypothesis,
xP = sdtasdt0(xE,xH),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_74,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_75,hypothesis,
aScalar0(xE),
inference(split_conjunct,[status(thm)],[m__1820]) ).
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_49,c_0_56]),c_0_57]),c_0_58])]) ).
fof(c_0_77,plain,
! [X114,X115,X116,X117] :
( ~ aScalar0(X114)
| ~ aScalar0(X115)
| ~ aScalar0(X116)
| ~ aScalar0(X117)
| ~ sdtlseqdt0(X114,X115)
| ~ sdtlseqdt0(sz0z00,X116)
| ~ sdtlseqdt0(X116,X117)
| sdtlseqdt0(sdtasdt0(X114,X116),sdtasdt0(X115,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])]) ).
cnf(c_0_78,plain,
( sdtasdt0(sz0z00,X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_79,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
fof(c_0_80,plain,
! [X107,X108,X109] :
( ~ aScalar0(X107)
| ~ aScalar0(X108)
| ~ aScalar0(X109)
| ~ sdtlseqdt0(X107,X108)
| ~ sdtlseqdt0(X108,X109)
| sdtlseqdt0(X107,X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])]) ).
cnf(c_0_81,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_82,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_49,c_0_59]),c_0_60]),c_0_61])]) ).
fof(c_0_83,hypothesis,
! [X144] :
( aVector0(xp)
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& ( ~ aNaturalNumber0(X144)
| sdtlbdtrb0(xp,X144) = sdtlbdtrb0(xs,X144) )
& xp = sziznziztdt0(xs) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1709])])]) ).
cnf(c_0_84,plain,
( sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_85,plain,
( sdtpldt0(sz0z00,X1) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_86,plain,
( sdtpldt0(smndt0(X1),X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_87,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_63,c_0_64]),c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_88,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_47])]) ).
cnf(c_0_89,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_90,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_91,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_58])]) ).
cnf(c_0_92,plain,
( aScalar0(sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_49]),c_0_50]) ).
cnf(c_0_93,hypothesis,
sdtasdt0(xA,smndt0(xA)) = smndt0(xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_72]),c_0_58])]) ).
fof(c_0_94,plain,
! [X90,X91,X92] :
( ( sdtpldt0(sdtpldt0(X90,X91),X92) = sdtpldt0(X90,sdtpldt0(X91,X92))
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtpldt0(X90,X91) = sdtpldt0(X91,X90)
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtasdt0(sdtasdt0(X90,X91),X92) = sdtasdt0(X90,sdtasdt0(X91,X92))
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtasdt0(X90,X91) = sdtasdt0(X91,X90)
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])]) ).
cnf(c_0_95,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_49,c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_96,hypothesis,
( aScalar0(smndt0(xH))
| ~ aScalar0(smndt0(xB)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_76]),c_0_58])]) ).
cnf(c_0_97,plain,
( sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_98,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_99,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_78]),c_0_79])]) ).
cnf(c_0_100,plain,
( sdtlseqdt0(X1,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_101,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_81]),c_0_57])]) ).
cnf(c_0_102,hypothesis,
( aScalar0(smndt0(xR))
| ~ aScalar0(smndt0(xG)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_82]),c_0_61])]) ).
cnf(c_0_103,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_104,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
fof(c_0_105,plain,
! [X93,X94,X95] :
( ( sdtasdt0(X93,sdtpldt0(X94,X95)) = sdtpldt0(sdtasdt0(X93,X94),sdtasdt0(X93,X95))
| ~ aScalar0(X93)
| ~ aScalar0(X94)
| ~ aScalar0(X95) )
& ( sdtasdt0(sdtpldt0(X93,X94),X95) = sdtpldt0(sdtasdt0(X93,X95),sdtasdt0(X94,X95))
| ~ aScalar0(X93)
| ~ aScalar0(X94)
| ~ aScalar0(X95) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])]) ).
cnf(c_0_106,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X3))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aScalar0(X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_79])]) ).
cnf(c_0_107,hypothesis,
sdtpldt0(xS,smndt0(xS)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]) ).
cnf(c_0_108,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_89,c_0_45]),c_0_90]),c_0_91]),c_0_46]),c_0_47])]) ).
cnf(c_0_109,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
fof(c_0_110,plain,
! [X104] :
( ~ aScalar0(X104)
| sdtlseqdt0(X104,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])]) ).
cnf(c_0_111,hypothesis,
aScalar0(smndt0(xF)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_58])]) ).
cnf(c_0_112,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_113,plain,
( sdtpldt0(X1,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_114,hypothesis,
( aScalar0(smndt0(xP))
| ~ aScalar0(smndt0(xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_95]),c_0_75])]) ).
cnf(c_0_115,hypothesis,
aScalar0(smndt0(xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_66]),c_0_57])]) ).
cnf(c_0_116,plain,
( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_117,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_118,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X3,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_79])]) ).
cnf(c_0_119,hypothesis,
( sdtlseqdt0(X1,xG)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_60]),c_0_79])]) ).
cnf(c_0_120,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_63,c_0_82]),c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_121,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_66]),c_0_60])]) ).
cnf(c_0_122,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_103]),c_0_104])]) ).
fof(c_0_123,plain,
! [X84,X85] :
( ~ aScalar0(X84)
| ~ aScalar0(X85)
| aScalar0(sdtpldt0(X84,X85)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])]) ).
cnf(c_0_124,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
fof(c_0_125,plain,
! [X105,X106] :
( ~ aScalar0(X105)
| ~ aScalar0(X106)
| ~ sdtlseqdt0(X105,X106)
| ~ sdtlseqdt0(X106,X105)
| X105 = X106 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])]) ).
cnf(c_0_126,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X1,smndt0(xS))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_88]),c_0_109])]) ).
cnf(c_0_127,plain,
( sdtlseqdt0(X1,X1)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_128,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xS))
| ~ sdtlseqdt0(X1,smndt0(xF))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xD)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_51]),c_0_46])]),c_0_111])]) ).
cnf(c_0_129,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_86]),c_0_66]) ).
cnf(c_0_130,hypothesis,
sdtpldt0(smndt0(xS),xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_87]),c_0_88])]) ).
cnf(c_0_131,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_63,c_0_95]),c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_132,hypothesis,
aScalar0(smndt0(xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_133,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
fof(c_0_134,plain,
! [X118,X119] :
( ~ aScalar0(X118)
| ~ aScalar0(X119)
| sdtlseqdt0(X118,X119)
| sdtlseqdt0(X119,X118) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])]) ).
cnf(c_0_135,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,xG))
| ~ sdtlseqdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_60]),c_0_99]),c_0_79])]) ).
cnf(c_0_136,hypothesis,
sdtpldt0(xR,smndt0(xR)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_120]),c_0_121])]) ).
cnf(c_0_137,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_89,c_0_59]),c_0_101]),c_0_122]),c_0_60]),c_0_61])]) ).
cnf(c_0_138,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_139,plain,
( aScalar0(sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_140,hypothesis,
( sdtpldt0(sdtasdt0(xE,X1),xP) = sdtasdt0(xE,sdtpldt0(X1,xH))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_141,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_142,hypothesis,
sdtlseqdt0(smndt0(xS),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_88])]) ).
cnf(c_0_143,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xS))
| ~ sdtlseqdt0(X1,smndt0(xF))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_98]),c_0_99]),c_0_90]),c_0_79])]) ).
cnf(c_0_144,plain,
( sdtpldt0(X1,sz0z00) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_145,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_129,c_0_130]),c_0_87]),c_0_109]),c_0_88])]) ).
cnf(c_0_146,hypothesis,
sdtpldt0(smndt0(xR),xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_120]),c_0_121])]) ).
cnf(c_0_147,hypothesis,
sdtpldt0(xP,smndt0(xP)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_131]),c_0_132])]) ).
cnf(c_0_148,hypothesis,
aScalar0(xP),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_149,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_150,plain,
( sdtasdt0(smndt0(X1),sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_98]),c_0_133]),c_0_79])]) ).
cnf(c_0_151,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_152,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,xG))
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_135,c_0_127]) ).
cnf(c_0_153,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_44,c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_154,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X1,smndt0(xR))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_136]),c_0_137]),c_0_121]),c_0_138])]) ).
cnf(c_0_155,hypothesis,
sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
inference(split_conjunct,[status(thm)],[m__1983]) ).
cnf(c_0_156,plain,
( aScalar0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_124]),c_0_50]),c_0_50]) ).
cnf(c_0_157,hypothesis,
sdtasdt0(xE,sdtpldt0(xH,xH)) = sdtpldt0(xP,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_73]),c_0_74])]) ).
cnf(c_0_158,hypothesis,
( smndt0(xS) = sz0z00
| ~ sdtlseqdt0(sz0z00,smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_88]),c_0_79])]) ).
cnf(c_0_159,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_127]),c_0_111])]) ).
cnf(c_0_160,hypothesis,
sdtpldt0(sz0z00,xS) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_109])]) ).
cnf(c_0_161,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_129,c_0_146]),c_0_120]),c_0_138]),c_0_121])]) ).
cnf(c_0_162,hypothesis,
( sdtpldt0(sdtasdt0(xA,X1),xH) = sdtasdt0(xA,sdtpldt0(X1,xB))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_163,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X1,smndt0(xP))
| ~ sdtlseqdt0(sz0z00,xP)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_147]),c_0_132]),c_0_148])]) ).
cnf(c_0_164,hypothesis,
( sdtasdt0(xE,sdtasdt0(xH,X1)) = sdtasdt0(xP,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_165,hypothesis,
sdtasdt0(xP,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_131]),c_0_132])]) ).
cnf(c_0_166,hypothesis,
( sdtlseqdt0(X1,xE)
| sdtlseqdt0(xE,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_75]) ).
cnf(c_0_167,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_63,c_0_76]),c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_168,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xR))
| ~ aScalar0(smndt0(xC)) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_169,hypothesis,
sdtlseqdt0(smndt0(xR),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_127]),c_0_121])]) ).
cnf(c_0_170,hypothesis,
( sdtlseqdt0(X1,sdtpldt0(xR,xS))
| ~ sdtlseqdt0(X1,sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_155]) ).
cnf(c_0_171,hypothesis,
aScalar0(sdtpldt0(xP,xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_74]),c_0_75])]) ).
cnf(c_0_172,hypothesis,
smndt0(xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_159])]) ).
cnf(c_0_173,hypothesis,
sdtpldt0(xS,sz0z00) = xS,
inference(rw,[status(thm)],[c_0_145,c_0_160]) ).
cnf(c_0_174,hypothesis,
sdtpldt0(sz0z00,xR) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_161]),c_0_138])]) ).
cnf(c_0_175,hypothesis,
sdtasdt0(xA,sdtpldt0(xB,xB)) = sdtpldt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_56]),c_0_57])]) ).
cnf(c_0_176,hypothesis,
( sdtlseqdt0(smndt0(xP),sz0z00)
| ~ sdtlseqdt0(sz0z00,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_127]),c_0_132])]) ).
cnf(c_0_177,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xP))
| ~ sdtlseqdt0(X2,smndt0(xH))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X1,xE)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_95]),c_0_75])]),c_0_115])]) ).
cnf(c_0_178,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_164,c_0_98]),c_0_165]),c_0_79]),c_0_74])]) ).
cnf(c_0_179,hypothesis,
sdtlseqdt0(xE,xE),
inference(spm,[status(thm)],[c_0_166,c_0_75]) ).
cnf(c_0_180,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),X3)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X2,X3)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_79])]) ).
cnf(c_0_181,hypothesis,
sdtpldt0(xH,smndt0(xH)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_167]),c_0_115])]) ).
cnf(c_0_182,hypothesis,
( sdtlseqdt0(X1,xB)
| sdtlseqdt0(xB,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_57]) ).
cnf(c_0_183,hypothesis,
( sdtasdt0(xB,sdtasdt0(xB,X1)) = sdtasdt0(xG,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_81]),c_0_57])]) ).
cnf(c_0_184,hypothesis,
( smndt0(xR) = sz0z00
| ~ aScalar0(smndt0(xC)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_168]),c_0_169]),c_0_79]),c_0_121])]) ).
cnf(c_0_185,hypothesis,
( sdtlseqdt0(X1,sdtpldt0(xR,xS))
| ~ sdtlseqdt0(X1,sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171])]) ).
cnf(c_0_186,hypothesis,
xS = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_172]),c_0_173]) ).
cnf(c_0_187,hypothesis,
sdtpldt0(xR,sz0z00) = xR,
inference(rw,[status(thm)],[c_0_161,c_0_174]) ).
cnf(c_0_188,hypothesis,
( sdtlseqdt0(xP,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,xH)
| ~ sdtlseqdt0(xH,X2)
| ~ sdtlseqdt0(xE,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_189,hypothesis,
aScalar0(sdtpldt0(xH,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_175]),c_0_57]),c_0_58])]) ).
cnf(c_0_190,hypothesis,
( smndt0(xP) = sz0z00
| ~ sdtlseqdt0(sz0z00,smndt0(xP))
| ~ sdtlseqdt0(sz0z00,xP) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_176]),c_0_132]),c_0_79])]) ).
cnf(c_0_191,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xP))
| ~ sdtlseqdt0(sz0z00,smndt0(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_177,c_0_178]),c_0_99]),c_0_179]),c_0_79]),c_0_75])]) ).
cnf(c_0_192,hypothesis,
( sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(smndt0(xH),X1)
| ~ sdtlseqdt0(xH,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_115]),c_0_74])]) ).
cnf(c_0_193,hypothesis,
sdtlseqdt0(xB,xB),
inference(spm,[status(thm)],[c_0_182,c_0_57]) ).
cnf(c_0_194,hypothesis,
sdtasdt0(xG,xB) = sdtasdt0(xB,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_81]),c_0_57])]) ).
cnf(c_0_195,hypothesis,
smndt0(xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_66]),c_0_61])]) ).
cnf(c_0_196,hypothesis,
( sdtlseqdt0(X1,xR)
| ~ sdtlseqdt0(X1,sdtpldt0(xP,xP))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_186]),c_0_187]),c_0_186]),c_0_187]),c_0_138])]) ).
cnf(c_0_197,hypothesis,
( sdtlseqdt0(xP,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(xH,sdtpldt0(xH,xH))
| ~ sdtlseqdt0(sz0z00,xH) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_157]),c_0_179]),c_0_75])]),c_0_189])]) ).
cnf(c_0_198,hypothesis,
( sdtlseqdt0(X1,xH)
| sdtlseqdt0(xH,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_74]) ).
cnf(c_0_199,hypothesis,
( smndt0(xP) = sz0z00
| ~ sdtlseqdt0(sz0z00,smndt0(xH))
| ~ sdtlseqdt0(sz0z00,xP) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_200,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xH))
| ~ sdtlseqdt0(xH,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_127]),c_0_115])]) ).
cnf(c_0_201,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xB,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_193]),c_0_57])]) ).
cnf(c_0_202,hypothesis,
aScalar0(sdtasdt0(xB,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_194]),c_0_57]),c_0_60])]) ).
cnf(c_0_203,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),xR)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xG)
| ~ sdtlseqdt0(X1,xC)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_204,hypothesis,
xR = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_195]),c_0_187]) ).
cnf(c_0_205,hypothesis,
( sdtlseqdt0(X1,xG)
| sdtlseqdt0(xG,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_60]) ).
cnf(c_0_206,hypothesis,
( sdtlseqdt0(xP,xR)
| ~ sdtlseqdt0(xH,sdtpldt0(xH,xH))
| ~ sdtlseqdt0(sz0z00,xH) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_148])]) ).
cnf(c_0_207,hypothesis,
sdtlseqdt0(xH,xH),
inference(spm,[status(thm)],[c_0_198,c_0_74]) ).
cnf(c_0_208,hypothesis,
( smndt0(xP) = sz0z00
| ~ sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(xH,sz0z00) ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_209,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| ~ sdtlseqdt0(sdtasdt0(xB,xG),sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_201]),c_0_79]),c_0_202])]) ).
cnf(c_0_210,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),sz0z00)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xG)
| ~ sdtlseqdt0(X1,xC)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(rw,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_211,hypothesis,
sdtlseqdt0(xG,xG),
inference(spm,[status(thm)],[c_0_205,c_0_60]) ).
cnf(c_0_212,hypothesis,
( sdtlseqdt0(xP,xR)
| ~ sdtlseqdt0(sz0z00,xH) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_106]),c_0_207]),c_0_74])]) ).
cnf(c_0_213,hypothesis,
( xP = sz0z00
| ~ sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(xH,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_208]),c_0_133]),c_0_148])]) ).
cnf(c_0_214,hypothesis,
( sdtlseqdt0(xH,sz0z00)
| sdtlseqdt0(sz0z00,xH) ),
inference(spm,[status(thm)],[c_0_198,c_0_79]) ).
cnf(c_0_215,hypothesis,
( sdtasdt0(xA,sdtasdt0(xB,X1)) = sdtasdt0(xH,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_216,hypothesis,
sdtasdt0(xH,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_167]),c_0_115])]) ).
cnf(c_0_217,hypothesis,
( sdtlseqdt0(X1,xA)
| sdtlseqdt0(xA,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_58]) ).
cnf(c_0_218,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| ~ sdtlseqdt0(xB,xC) ),
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_209,c_0_210]),c_0_101]),c_0_211]),c_0_60]),c_0_57])]) ).
cnf(c_0_219,hypothesis,
( sdtlseqdt0(X1,xC)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_122]),c_0_61]),c_0_79])]) ).
cnf(c_0_220,hypothesis,
( xR = xP
| ~ sdtlseqdt0(xR,xP)
| ~ sdtlseqdt0(sz0z00,xH) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_212]),c_0_148]),c_0_138])]) ).
cnf(c_0_221,hypothesis,
( xP = sz0z00
| sdtlseqdt0(sz0z00,xH)
| ~ sdtlseqdt0(sz0z00,xP) ),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_222,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),xP)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xH)
| ~ sdtlseqdt0(X1,xE)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_223,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),xH)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xB)
| ~ sdtlseqdt0(X1,xA)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_224,hypothesis,
sdtasdt0(xA,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_98]),c_0_216]),c_0_79]),c_0_57])]) ).
cnf(c_0_225,hypothesis,
sdtlseqdt0(xA,xA),
inference(spm,[status(thm)],[c_0_217,c_0_58]) ).
cnf(c_0_226,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| ~ sdtlseqdt0(xB,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_57])]) ).
cnf(c_0_227,hypothesis,
( sdtlseqdt0(xB,sz0z00)
| sdtlseqdt0(sz0z00,xB) ),
inference(spm,[status(thm)],[c_0_182,c_0_79]) ).
cnf(c_0_228,hypothesis,
sdtasdt0(xB,smndt0(xB)) = smndt0(xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_81]),c_0_57])]) ).
fof(c_0_229,plain,
! [X123,X124] :
( ~ aScalar0(X123)
| ~ aScalar0(X124)
| ~ sdtlseqdt0(sz0z00,X123)
| ~ sdtlseqdt0(sz0z00,X124)
| sdtasdt0(X123,X123) != sdtasdt0(X124,X124)
| X123 = X124 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqrt])]) ).
cnf(c_0_230,plain,
( sdtasdt0(sz0z00,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_78]),c_0_133]),c_0_79])]) ).
cnf(c_0_231,hypothesis,
( xP = sz0z00
| ~ sdtlseqdt0(sz0z00,xP) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_220,c_0_204]),c_0_204]),c_0_221]) ).
cnf(c_0_232,hypothesis,
( sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(sz0z00,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_222,c_0_178]),c_0_99]),c_0_179]),c_0_79]),c_0_75])]) ).
cnf(c_0_233,hypothesis,
( sdtlseqdt0(sz0z00,xH)
| ~ sdtlseqdt0(sz0z00,xB) ),
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_223,c_0_224]),c_0_99]),c_0_225]),c_0_79]),c_0_58])]) ).
cnf(c_0_234,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| sdtlseqdt0(sz0z00,xB) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_235,hypothesis,
smndt0(smndt0(xG)) = xG,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_228]),c_0_81]),c_0_57])]) ).
cnf(c_0_236,hypothesis,
aScalar0(smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_228]),c_0_57])]) ).
cnf(c_0_237,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| sdtasdt0(X1,X1) != sdtasdt0(X2,X2) ),
inference(split_conjunct,[status(thm)],[c_0_229]) ).
cnf(c_0_238,hypothesis,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_133]),c_0_79])]) ).
cnf(c_0_239,hypothesis,
( xP = sz0z00
| ~ sdtlseqdt0(sz0z00,xH) ),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_240,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| sdtlseqdt0(sz0z00,xH) ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_241,hypothesis,
sdtasdt0(xG,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_235]),c_0_236])]) ).
cnf(c_0_242,plain,
( X1 = sz0z00
| sdtasdt0(X1,X1) != sz0z00
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X1) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_127]),c_0_79])]),c_0_238]) ).
cnf(c_0_243,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| xP = sz0z00 ),
inference(spm,[status(thm)],[c_0_239,c_0_240]) ).
cnf(c_0_244,hypothesis,
sdtasdt0(xB,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_98]),c_0_241]),c_0_79]),c_0_57])]) ).
cnf(c_0_245,hypothesis,
( xG = 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_242,c_0_119]),c_0_60]),c_0_99]),c_0_79])]) ).
cnf(c_0_246,hypothesis,
( sdtasdt0(xG,xG) = sz0z00
| xP = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_243]),c_0_244]),c_0_60])]) ).
fof(c_0_247,plain,
! [X96,X97,X98,X99] :
( ~ aScalar0(X96)
| ~ aScalar0(X97)
| ~ aScalar0(X98)
| ~ aScalar0(X99)
| sdtasdt0(sdtpldt0(X96,X97),sdtpldt0(X98,X99)) = sdtpldt0(sdtpldt0(sdtasdt0(X96,X98),sdtasdt0(X96,X99)),sdtpldt0(sdtasdt0(X97,X98),sdtasdt0(X97,X99))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr2])]) ).
cnf(c_0_248,hypothesis,
sdtpldt0(smndt0(xP),xP) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_131]),c_0_132])]) ).
cnf(c_0_249,hypothesis,
sdtpldt0(smndt0(xH),xH) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_167]),c_0_115])]) ).
cnf(c_0_250,hypothesis,
sdtasdt0(xA,xG) = sdtasdt0(xH,xB),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_81]),c_0_57])]) ).
cnf(c_0_251,hypothesis,
( xP = sz0z00
| xG = sz0z00 ),
inference(spm,[status(thm)],[c_0_245,c_0_246]) ).
cnf(c_0_252,hypothesis,
( sdtlseqdt0(X1,xP)
| sdtlseqdt0(xP,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_151,c_0_148]) ).
cnf(c_0_253,hypothesis,
( sdtlseqdt0(X1,xR)
| ~ sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(X1,xP)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_106]),c_0_148])]) ).
cnf(c_0_254,plain,
( sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4)))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_247]) ).
cnf(c_0_255,hypothesis,
sdtpldt0(xP,sz0z00) = sdtpldt0(sz0z00,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_248]),c_0_131]),c_0_148]),c_0_132])]) ).
cnf(c_0_256,hypothesis,
sdtpldt0(xH,sz0z00) = sdtpldt0(sz0z00,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_249]),c_0_167]),c_0_74]),c_0_115])]) ).
cnf(c_0_257,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_258,hypothesis,
( sdtasdt0(xH,xB) = sz0z00
| xP = sz0z00 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_251]),c_0_224]) ).
cnf(c_0_259,hypothesis,
( sdtlseqdt0(xP,sz0z00)
| sdtlseqdt0(sz0z00,xP) ),
inference(spm,[status(thm)],[c_0_252,c_0_79]) ).
cnf(c_0_260,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(X1,xP)
| ~ aScalar0(X1) ),
inference(rw,[status(thm)],[c_0_253,c_0_204]) ).
cnf(c_0_261,hypothesis,
( sdtpldt0(sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,xH)),sdtpldt0(sdtasdt0(xE,X2),xP)) = sdtasdt0(sdtpldt0(X1,xE),sdtpldt0(X2,xH))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_262,hypothesis,
sdtpldt0(sz0z00,xP) = xP,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_255]),c_0_148])]) ).
cnf(c_0_263,hypothesis,
sdtpldt0(sz0z00,xH) = xH,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_256]),c_0_74])]) ).
cnf(c_0_264,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_265,hypothesis,
sdtpldt0(smndt0(xH),sz0z00) = sdtpldt0(sz0z00,smndt0(xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_181]),c_0_115]),c_0_74])]) ).
cnf(c_0_266,hypothesis,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_257,c_0_117]) ).
cnf(c_0_267,hypothesis,
( sdtasdt0(smndt0(xH),xB) = sz0z00
| xP = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_258]),c_0_133]),c_0_57]),c_0_74])]) ).
cnf(c_0_268,hypothesis,
( sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(smndt0(xP),X1)
| ~ sdtlseqdt0(xP,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_147]),c_0_132]),c_0_148])]) ).
cnf(c_0_269,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X1,xP)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_259]),c_0_79]),c_0_148])]),c_0_260]) ).
cnf(c_0_270,hypothesis,
sdtlseqdt0(xP,xP),
inference(spm,[status(thm)],[c_0_252,c_0_148]) ).
cnf(c_0_271,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_272,hypothesis,
sdtpldt0(sdtpldt0(sz0z00,sdtasdt0(xH,xH)),xP) = sdtasdt0(sdtpldt0(xH,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(spm,[status(thm)],[c_0_261,c_0_216]),c_0_178]),c_0_262]),c_0_263]),c_0_79]),c_0_74])]) ).
cnf(c_0_273,plain,
( sdtpldt0(sz0z00,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz0z00,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_98]),c_0_79])]) ).
cnf(c_0_274,plain,
( aScalar0(sdtasdt0(sdtpldt0(X1,X2),X3))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_264]),c_0_50]),c_0_50]) ).
cnf(c_0_275,hypothesis,
sdtpldt0(sz0z00,smndt0(xH)) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_265]),c_0_115])]) ).
cnf(c_0_276,hypothesis,
( sdtasdt0(xB,smndt0(xH)) = sz0z00
| xP = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_267]),c_0_57]),c_0_115])]) ).
cnf(c_0_277,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xP))
| ~ sdtlseqdt0(xP,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_268,c_0_127]),c_0_132])]) ).
cnf(c_0_278,hypothesis,
sdtlseqdt0(xP,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_270]),c_0_148])]) ).
cnf(c_0_279,hypothesis,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_271,c_0_117]) ).
cnf(c_0_280,hypothesis,
sdtpldt0(sdtasdt0(xH,xH),xP) = sdtasdt0(sdtpldt0(xH,xE),xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_273]),c_0_263]),c_0_74])]) ).
cnf(c_0_281,hypothesis,
( aScalar0(sdtasdt0(smndt0(xH),X1))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_275]),c_0_115]),c_0_79])]) ).
cnf(c_0_282,plain,
( sdtasdt0(smndt0(X1),X2) = sdtasdt0(X1,smndt0(X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_44]) ).
cnf(c_0_283,hypothesis,
( sdtasdt0(xB,xH) = sz0z00
| xP = 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_49,c_0_276]),c_0_133]),c_0_167]),c_0_115]),c_0_57])]) ).
cnf(c_0_284,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_277,c_0_278])]) ).
cnf(c_0_285,hypothesis,
( sdtpldt0(xP,sdtasdt0(X1,xH)) = sdtasdt0(sdtpldt0(xE,X1),xH)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_73]),c_0_74]),c_0_75])]) ).
cnf(c_0_286,hypothesis,
( sdtpldt0(xP,sdtasdt0(xH,xH)) = sdtasdt0(sdtpldt0(xH,xE),xH)
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_280]),c_0_148])]) ).
cnf(c_0_287,hypothesis,
( aScalar0(sdtasdt0(xH,smndt0(X1)))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_281,c_0_282]),c_0_74])]) ).
cnf(c_0_288,hypothesis,
( sdtasdt0(xH,xH) = sz0z00
| xP = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_283]),c_0_224]),c_0_74])]) ).
cnf(c_0_289,hypothesis,
( smndt0(xP) = sz0z00
| sdtasdt0(smndt0(xP),smndt0(xP)) != sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_284]),c_0_132])]) ).
fof(c_0_290,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_291,hypothesis,
( sdtasdt0(sdtpldt0(xH,xE),xH) = sdtasdt0(sdtpldt0(xE,xH),xH)
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_286]),c_0_74])]) ).
cnf(c_0_292,hypothesis,
aScalar0(sdtasdt0(xH,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_287,c_0_167]),c_0_115])]) ).
cnf(c_0_293,hypothesis,
( sdtasdt0(xP,xH) = sz0z00
| xP = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_288]),c_0_178]),c_0_74])]) ).
cnf(c_0_294,hypothesis,
( smndt0(xP) = sz0z00
| sdtasdt0(xP,xP) != sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_282]),c_0_131]),c_0_132]),c_0_148])]) ).
fof(c_0_295,plain,
! [X139,X140] :
( ~ aVector0(X139)
| ~ aVector0(X140)
| aDimensionOf0(X139) != aDimensionOf0(X140)
| aDimensionOf0(X140) = sz00
| sdtasasdt0(X139,X140) = sdtpldt0(sdtasasdt0(sziznziztdt0(X139),sziznziztdt0(X140)),sdtasdt0(sdtlbdtrb0(X139,aDimensionOf0(X139)),sdtlbdtrb0(X140,aDimensionOf0(X140)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSPN])]) ).
cnf(c_0_296,hypothesis,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_297,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_298,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH)))),
inference(split_conjunct,[status(thm)],[c_0_290]) ).
cnf(c_0_299,hypothesis,
sdtasdt0(sdtpldt0(xH,xE),xH) = sdtasdt0(sdtpldt0(xE,xH),xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_291,c_0_292])]) ).
cnf(c_0_300,hypothesis,
( sdtasdt0(xH,xP) = sz0z00
| xP = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_293]),c_0_74]),c_0_148])]) ).
cnf(c_0_301,hypothesis,
( xP = sz0z00
| sdtasdt0(xP,xP) != sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_294]),c_0_133]),c_0_148])]) ).
cnf(c_0_302,plain,
( aDimensionOf0(X2) = sz00
| sdtasasdt0(X1,X2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2))))
| ~ aVector0(X1)
| ~ aVector0(X2)
| aDimensionOf0(X1) != aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_295]) ).
cnf(c_0_303,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_304,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_305,hypothesis,
sdtlbdtrb0(xt,aDimensionOf0(xs)) = xB,
inference(rw,[status(thm)],[c_0_296,c_0_297]) ).
cnf(c_0_306,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[m__1692]) ).
cnf(c_0_307,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xH,xH),sdtpldt0(xR,xS))))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(spm,[status(thm)],[c_0_298,c_0_279]) ).
cnf(c_0_308,hypothesis,
sdtpldt0(sdtasdt0(xH,xH),xP) = sdtasdt0(sdtpldt0(xE,xH),xH),
inference(rw,[status(thm)],[c_0_280,c_0_299]) ).
cnf(c_0_309,hypothesis,
xP = sz0z00,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_300]),c_0_178]),c_0_148])]),c_0_301]) ).
fof(c_0_310,plain,
! [X135,X136] :
( ~ aVector0(X135)
| ~ aVector0(X136)
| aDimensionOf0(X135) != aDimensionOf0(X136)
| aScalar0(sdtasasdt0(X135,X136)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScPr])]) ).
cnf(c_0_311,hypothesis,
( sdtpldt0(sdtasasdt0(sziznziztdt0(X1),xq),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),xB)) = sdtasasdt0(X1,xt)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| ~ aVector0(X1) ),
inference(sr,[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_302,c_0_303]),c_0_304]),c_0_297]),c_0_305]),c_0_297]),c_0_297]),c_0_306]) ).
cnf(c_0_312,hypothesis,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_313,hypothesis,
xp = sziznziztdt0(xs),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_314,hypothesis,
xE = sdtasasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_315,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_316,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xH,xH),xR)))
| ~ aScalar0(sdtasdt0(xH,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)],[c_0_307,c_0_186]),c_0_187]),c_0_186]),c_0_187]),c_0_138])]) ).
cnf(c_0_317,hypothesis,
sdtpldt0(sdtasdt0(xH,xH),sz0z00) = sdtasdt0(sdtpldt0(xE,xH),xH),
inference(rw,[status(thm)],[c_0_308,c_0_309]) ).
cnf(c_0_318,plain,
( aScalar0(sdtasasdt0(X1,X2))
| ~ aVector0(X1)
| ~ aVector0(X2)
| aDimensionOf0(X1) != aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_310]) ).
cnf(c_0_319,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_311,c_0_312]),c_0_313]),c_0_314]),c_0_56]),c_0_315])]) ).
cnf(c_0_320,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xH,xH),sz0z00))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_316,c_0_292])]),c_0_204]) ).
cnf(c_0_321,hypothesis,
sdtasdt0(sdtpldt0(xE,xH),xH) = sdtasdt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_317]),c_0_292])]) ).
cnf(c_0_322,hypothesis,
aScalar0(sdtpldt0(xE,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_318,c_0_319]),c_0_297]),c_0_303]),c_0_315])]) ).
cnf(c_0_323,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xH,xH))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_144]),c_0_292])]) ).
cnf(c_0_324,hypothesis,
sdtpldt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_133]),c_0_79])]) ).
cnf(c_0_325,hypothesis,
sdtpldt0(sz0z00,sdtasdt0(xH,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_273,c_0_321]),c_0_263]),c_0_321]),c_0_74]),c_0_322])]) ).
cnf(c_0_326,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xH,xH)),sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xH,xH))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_323,c_0_309]),c_0_309]),c_0_324]),c_0_325]) ).
cnf(c_0_327,hypothesis,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(split_conjunct,[status(thm)],[m__1967]) ).
cnf(c_0_328,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xH,xH),sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_326,c_0_84]),c_0_327]),c_0_292])]) ).
cnf(c_0_329,negated_conjecture,
( ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_328,c_0_127]),c_0_292])]) ).
cnf(c_0_330,negated_conjecture,
~ aScalar0(sdtasdt0(xE,xE)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329,c_0_50]),c_0_46]),c_0_61])]) ).
cnf(c_0_331,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330,c_0_50]),c_0_75])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG076+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n028.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:49:31 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 39.84/23.68 % Version : CSE_E---1.7
% 39.84/23.68 % Problem : theBenchmark.p
% 39.84/23.68 % SZS status Theorem for theBenchmark.p
% 39.84/23.68 % SZS output start CNFRefutation
% See solution above
% 40.04/23.85 % Total time : 17.406s
%------------------------------------------------------------------------------