%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG076+1 : 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 : n008.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 43.01s 26.02s
% Output : CNFRefutation 43.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 41
% Syntax : Number of formulae : 355 ( 148 unt; 0 def)
% Number of atoms : 849 ( 245 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 876 ( 382 ~; 392 |; 74 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 18 con; 0-2 aty)
% Number of variables : 238 ( 3 sgn 88 !; 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(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__1726,hypothesis,
( aVector0(xq)
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
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(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(m__1709,hypothesis,
( aVector0(xp)
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
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(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(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(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__,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(m__1967,hypothesis,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1967) ).
fof(c_0_41,plain,
! [X98,X99] :
( ( sdtasdt0(X98,smndt0(X99)) = smndt0(sdtasdt0(X98,X99))
| ~ aScalar0(X98)
| ~ aScalar0(X99) )
& ( sdtasdt0(smndt0(X98),X99) = smndt0(sdtasdt0(X98,X99))
| ~ aScalar0(X98)
| ~ aScalar0(X99) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])]) ).
fof(c_0_42,plain,
! [X87] :
( ( sdtpldt0(X87,sz0z00) = X87
| ~ aScalar0(X87) )
& ( sdtpldt0(sz0z00,X87) = X87
| ~ aScalar0(X87) )
& ( sdtasdt0(X87,sz0z00) = sz0z00
| ~ aScalar0(X87) )
& ( sdtasdt0(sz0z00,X87) = sz0z00
| ~ aScalar0(X87) )
& ( sdtpldt0(X87,smndt0(X87)) = sz0z00
| ~ aScalar0(X87) )
& ( sdtpldt0(smndt0(X87),X87) = sz0z00
| ~ aScalar0(X87) )
& ( smndt0(smndt0(X87)) = X87
| ~ aScalar0(X87) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])]) ).
fof(c_0_43,plain,
! [X84,X85] :
( ~ aScalar0(X84)
| ~ aScalar0(X85)
| aScalar0(sdtasdt0(X84,X85)) ),
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,
! [X86] :
( ~ aScalar0(X86)
| aScalar0(smndt0(X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])]) ).
fof(c_0_53,plain,
! [X139] :
( ~ aVector0(X139)
| sdtlseqdt0(sz0z00,sdtasasdt0(X139,X139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])]) ).
fof(c_0_54,plain,
! [X120] :
( ~ aScalar0(X120)
| sdtlseqdt0(sz0z00,sdtasdt0(X120,X120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])]) ).
cnf(c_0_55,hypothesis,
xH = sdtasdt0(xA,xB),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_56,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_57,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_58,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_59,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_60,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
fof(c_0_61,plain,
! [X108,X109,X110,X111] :
( ~ aScalar0(X108)
| ~ aScalar0(X109)
| ~ aScalar0(X110)
| ~ aScalar0(X111)
| ~ sdtlseqdt0(X108,X109)
| ~ sdtlseqdt0(X110,X111)
| sdtlseqdt0(sdtpldt0(X108,X110),sdtpldt0(X109,X111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])]) ).
cnf(c_0_62,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_63,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_64,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_65,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_66,plain,
! [X118,X119] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X118,X119))
| ~ sdtlseqdt0(sz0z00,X118)
| ~ sdtlseqdt0(sz0z00,X119)
| ~ aScalar0(X118)
| ~ aScalar0(X119) )
& ( sdtlseqdt0(sz0z00,sdtasdt0(X118,X119))
| ~ sdtlseqdt0(sz0z00,X118)
| ~ sdtlseqdt0(sz0z00,X119)
| ~ aScalar0(X118)
| ~ aScalar0(X119) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])]) ).
cnf(c_0_67,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_68,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_69,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_70,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_71,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_72,hypothesis,
xP = sdtasdt0(xE,xH),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_73,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_74,hypothesis,
aScalar0(xE),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_75,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_55]),c_0_56]),c_0_57])]) ).
fof(c_0_76,plain,
! [X112,X113,X114,X115] :
( ~ aScalar0(X112)
| ~ aScalar0(X113)
| ~ aScalar0(X114)
| ~ aScalar0(X115)
| ~ sdtlseqdt0(X112,X113)
| ~ sdtlseqdt0(sz0z00,X114)
| ~ sdtlseqdt0(X114,X115)
| sdtlseqdt0(sdtasdt0(X112,X114),sdtasdt0(X113,X115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])]) ).
cnf(c_0_77,plain,
( sdtasdt0(sz0z00,X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_78,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
fof(c_0_79,plain,
! [X105,X106,X107] :
( ~ aScalar0(X105)
| ~ aScalar0(X106)
| ~ aScalar0(X107)
| ~ sdtlseqdt0(X105,X106)
| ~ sdtlseqdt0(X106,X107)
| sdtlseqdt0(X105,X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])]) ).
cnf(c_0_80,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_81,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_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_82,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_61]) ).
cnf(c_0_83,plain,
( sdtpldt0(sz0z00,X1) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_84,plain,
( sdtpldt0(smndt0(X1),X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_85,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_62,c_0_63]),c_0_45]),c_0_46]),c_0_47])]) ).
cnf(c_0_86,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_47])]) ).
cnf(c_0_87,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_88,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]) ).
cnf(c_0_89,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_57])]) ).
cnf(c_0_90,plain,
( aScalar0(sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_49]),c_0_50]) ).
cnf(c_0_91,hypothesis,
sdtasdt0(xA,smndt0(xA)) = smndt0(xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_71]),c_0_57])]) ).
fof(c_0_92,plain,
! [X88,X89,X90] :
( ( sdtpldt0(sdtpldt0(X88,X89),X90) = sdtpldt0(X88,sdtpldt0(X89,X90))
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) )
& ( sdtpldt0(X88,X89) = sdtpldt0(X89,X88)
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) )
& ( sdtasdt0(sdtasdt0(X88,X89),X90) = sdtasdt0(X88,sdtasdt0(X89,X90))
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) )
& ( sdtasdt0(X88,X89) = sdtasdt0(X89,X88)
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])]) ).
cnf(c_0_93,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_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_94,hypothesis,
( aScalar0(smndt0(xH))
| ~ aScalar0(smndt0(xB)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_75]),c_0_57])]) ).
cnf(c_0_95,plain,
( sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_96,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_97,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_77]),c_0_78])]) ).
cnf(c_0_98,plain,
( sdtlseqdt0(X1,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_99,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_80]),c_0_56])]) ).
cnf(c_0_100,hypothesis,
( aScalar0(smndt0(xR))
| ~ aScalar0(smndt0(xG)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_81]),c_0_60])]) ).
cnf(c_0_101,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_102,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[m__1709]) ).
fof(c_0_103,plain,
! [X91,X92,X93] :
( ( sdtasdt0(X91,sdtpldt0(X92,X93)) = sdtpldt0(sdtasdt0(X91,X92),sdtasdt0(X91,X93))
| ~ aScalar0(X91)
| ~ aScalar0(X92)
| ~ aScalar0(X93) )
& ( sdtasdt0(sdtpldt0(X91,X92),X93) = sdtpldt0(sdtasdt0(X91,X93),sdtasdt0(X92,X93))
| ~ aScalar0(X91)
| ~ aScalar0(X92)
| ~ aScalar0(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])]) ).
cnf(c_0_104,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_82,c_0_83]),c_0_78])]) ).
cnf(c_0_105,hypothesis,
sdtpldt0(xS,smndt0(xS)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
cnf(c_0_106,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_87,c_0_45]),c_0_88]),c_0_89]),c_0_46]),c_0_47])]) ).
cnf(c_0_107,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
fof(c_0_108,plain,
! [X102] :
( ~ aScalar0(X102)
| sdtlseqdt0(X102,X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])]) ).
cnf(c_0_109,hypothesis,
aScalar0(smndt0(xF)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_57])]) ).
cnf(c_0_110,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_111,plain,
( sdtpldt0(X1,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_112,hypothesis,
( aScalar0(smndt0(xP))
| ~ aScalar0(smndt0(xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_93]),c_0_74])]) ).
cnf(c_0_113,hypothesis,
aScalar0(smndt0(xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_65]),c_0_56])]) ).
cnf(c_0_114,plain,
( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_115,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_116,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_95,c_0_96]),c_0_97]),c_0_78])]) ).
cnf(c_0_117,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_98,c_0_99]),c_0_59]),c_0_78])]) ).
cnf(c_0_118,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_62,c_0_81]),c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_119,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_65]),c_0_59])]) ).
cnf(c_0_120,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_101]),c_0_102])]) ).
fof(c_0_121,plain,
! [X82,X83] :
( ~ aScalar0(X82)
| ~ aScalar0(X83)
| aScalar0(sdtpldt0(X82,X83)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])]) ).
cnf(c_0_122,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_103]) ).
fof(c_0_123,plain,
! [X103,X104] :
( ~ aScalar0(X103)
| ~ aScalar0(X104)
| ~ sdtlseqdt0(X103,X104)
| ~ sdtlseqdt0(X104,X103)
| X103 = X104 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])]) ).
cnf(c_0_124,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_104,c_0_105]),c_0_106]),c_0_86]),c_0_107])]) ).
cnf(c_0_125,plain,
( sdtlseqdt0(X1,X1)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_126,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xS))
| ~ sdtlseqdt0(X1,smndt0(xF))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xD)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_51]),c_0_46])]),c_0_109])]) ).
cnf(c_0_127,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_84]),c_0_65]) ).
cnf(c_0_128,hypothesis,
sdtpldt0(smndt0(xS),xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_85]),c_0_86])]) ).
fof(c_0_129,plain,
! [X116,X117] :
( ~ aScalar0(X116)
| ~ aScalar0(X117)
| sdtlseqdt0(X116,X117)
| sdtlseqdt0(X117,X116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])]) ).
cnf(c_0_130,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_62,c_0_93]),c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_131,hypothesis,
aScalar0(smndt0(xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_113])]) ).
cnf(c_0_132,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_133,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_116,c_0_117]),c_0_59]),c_0_97]),c_0_78])]) ).
cnf(c_0_134,hypothesis,
sdtpldt0(xR,smndt0(xR)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_118]),c_0_119])]) ).
cnf(c_0_135,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_87,c_0_58]),c_0_99]),c_0_120]),c_0_59]),c_0_60])]) ).
cnf(c_0_136,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_137,plain,
( aScalar0(sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_138,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_122,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_139,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_140,hypothesis,
sdtlseqdt0(smndt0(xS),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_86])]) ).
cnf(c_0_141,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_126,c_0_96]),c_0_97]),c_0_88]),c_0_78])]) ).
cnf(c_0_142,plain,
( sdtpldt0(X1,sz0z00) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_143,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_127,c_0_128]),c_0_85]),c_0_107]),c_0_86])]) ).
cnf(c_0_144,hypothesis,
sdtpldt0(smndt0(xR),xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_118]),c_0_119])]) ).
cnf(c_0_145,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_146,hypothesis,
sdtpldt0(xP,smndt0(xP)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_130]),c_0_131])]) ).
cnf(c_0_147,hypothesis,
aScalar0(xP),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_148,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_149,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_96]),c_0_132]),c_0_78])]) ).
cnf(c_0_150,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,xG))
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_125]) ).
cnf(c_0_151,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_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_152,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_104,c_0_134]),c_0_135]),c_0_119]),c_0_136])]) ).
cnf(c_0_153,hypothesis,
sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
inference(split_conjunct,[status(thm)],[m__1983]) ).
cnf(c_0_154,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_137,c_0_122]),c_0_50]),c_0_50]) ).
cnf(c_0_155,hypothesis,
sdtasdt0(xE,sdtpldt0(xH,xH)) = sdtpldt0(xP,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_72]),c_0_73])]) ).
cnf(c_0_156,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_139,c_0_140]),c_0_86]),c_0_78])]) ).
cnf(c_0_157,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_125]),c_0_109])]) ).
cnf(c_0_158,hypothesis,
sdtpldt0(sz0z00,xS) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_107])]) ).
cnf(c_0_159,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_127,c_0_144]),c_0_118]),c_0_136]),c_0_119])]) ).
cnf(c_0_160,hypothesis,
( sdtlseqdt0(X1,xE)
| sdtlseqdt0(xE,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_74]) ).
cnf(c_0_161,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_122,c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_162,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_104,c_0_146]),c_0_131]),c_0_147])]) ).
cnf(c_0_163,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_148,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_164,hypothesis,
sdtasdt0(xP,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_130]),c_0_131])]) ).
cnf(c_0_165,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_62,c_0_75]),c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_166,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xR))
| ~ aScalar0(smndt0(xC)) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_167,hypothesis,
sdtlseqdt0(smndt0(xR),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_125]),c_0_119])]) ).
cnf(c_0_168,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_98,c_0_153]) ).
cnf(c_0_169,hypothesis,
aScalar0(sdtpldt0(xP,xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_73]),c_0_74])]) ).
cnf(c_0_170,hypothesis,
smndt0(xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_156,c_0_157])]) ).
cnf(c_0_171,hypothesis,
sdtpldt0(xS,sz0z00) = xS,
inference(rw,[status(thm)],[c_0_143,c_0_158]) ).
cnf(c_0_172,hypothesis,
sdtpldt0(sz0z00,xR) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_159]),c_0_136])]) ).
cnf(c_0_173,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_95,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_174,hypothesis,
sdtlseqdt0(xE,xE),
inference(spm,[status(thm)],[c_0_160,c_0_74]) ).
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_161,c_0_55]),c_0_56])]) ).
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_162,c_0_125]),c_0_131])]) ).
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_95,c_0_93]),c_0_74])]),c_0_113])]) ).
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_163,c_0_96]),c_0_164]),c_0_78]),c_0_73])]) ).
cnf(c_0_179,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_82,c_0_83]),c_0_78])]) ).
cnf(c_0_180,hypothesis,
sdtpldt0(xH,smndt0(xH)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_165]),c_0_113])]) ).
cnf(c_0_181,hypothesis,
( sdtlseqdt0(X1,xB)
| sdtlseqdt0(xB,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_56]) ).
cnf(c_0_182,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_148,c_0_80]),c_0_56])]) ).
cnf(c_0_183,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_139,c_0_166]),c_0_167]),c_0_78]),c_0_119])]) ).
cnf(c_0_184,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_168,c_0_169])]) ).
cnf(c_0_185,hypothesis,
xS = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_170]),c_0_171]) ).
cnf(c_0_186,hypothesis,
sdtpldt0(xR,sz0z00) = xR,
inference(rw,[status(thm)],[c_0_159,c_0_172]) ).
cnf(c_0_187,hypothesis,
( sdtlseqdt0(xP,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(xH,sdtpldt0(xH,xH))
| ~ sdtlseqdt0(sz0z00,xH)
| ~ aScalar0(sdtpldt0(xH,xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_155]),c_0_174]),c_0_74])]) ).
cnf(c_0_188,hypothesis,
aScalar0(sdtpldt0(xH,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_175]),c_0_56]),c_0_57])]) ).
cnf(c_0_189,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_139,c_0_176]),c_0_131]),c_0_78])]) ).
cnf(c_0_190,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_97]),c_0_174]),c_0_78]),c_0_74])]) ).
cnf(c_0_191,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_179,c_0_180]),c_0_113]),c_0_73])]) ).
cnf(c_0_192,hypothesis,
sdtlseqdt0(xB,xB),
inference(spm,[status(thm)],[c_0_181,c_0_56]) ).
cnf(c_0_193,hypothesis,
sdtasdt0(xG,xB) = sdtasdt0(xB,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_80]),c_0_56])]) ).
cnf(c_0_194,hypothesis,
smndt0(xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_65]),c_0_60])]) ).
cnf(c_0_195,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_184,c_0_185]),c_0_186]),c_0_185]),c_0_186]),c_0_136])]) ).
cnf(c_0_196,hypothesis,
( sdtlseqdt0(xP,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(xH,sdtpldt0(xH,xH))
| ~ sdtlseqdt0(sz0z00,xH) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_187,c_0_188])]) ).
cnf(c_0_197,hypothesis,
( sdtlseqdt0(X1,xH)
| sdtlseqdt0(xH,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_73]) ).
cnf(c_0_198,hypothesis,
( smndt0(xP) = sz0z00
| ~ sdtlseqdt0(sz0z00,smndt0(xH))
| ~ sdtlseqdt0(sz0z00,xP) ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_199,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xH))
| ~ sdtlseqdt0(xH,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_125]),c_0_113])]) ).
cnf(c_0_200,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xB,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_192]),c_0_56])]) ).
cnf(c_0_201,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_193]),c_0_56]),c_0_59])]) ).
cnf(c_0_202,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_95,c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_203,hypothesis,
xR = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_194]),c_0_186]) ).
cnf(c_0_204,hypothesis,
( sdtlseqdt0(X1,xG)
| sdtlseqdt0(xG,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_59]) ).
cnf(c_0_205,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_195,c_0_196]),c_0_147])]) ).
cnf(c_0_206,hypothesis,
sdtlseqdt0(xH,xH),
inference(spm,[status(thm)],[c_0_197,c_0_73]) ).
cnf(c_0_207,hypothesis,
( smndt0(xP) = sz0z00
| ~ sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(xH,sz0z00) ),
inference(spm,[status(thm)],[c_0_198,c_0_199]) ).
cnf(c_0_208,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_139,c_0_200]),c_0_78]),c_0_201])]) ).
cnf(c_0_209,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_202,c_0_203]) ).
cnf(c_0_210,hypothesis,
sdtlseqdt0(xG,xG),
inference(spm,[status(thm)],[c_0_204,c_0_59]) ).
cnf(c_0_211,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_205,c_0_104]),c_0_206]),c_0_73])]) ).
cnf(c_0_212,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_207]),c_0_132]),c_0_147])]) ).
cnf(c_0_213,hypothesis,
( sdtlseqdt0(xH,sz0z00)
| sdtlseqdt0(sz0z00,xH) ),
inference(spm,[status(thm)],[c_0_197,c_0_78]) ).
cnf(c_0_214,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_148,c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_215,hypothesis,
sdtasdt0(xH,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_165]),c_0_113])]) ).
cnf(c_0_216,hypothesis,
( sdtlseqdt0(X1,xA)
| sdtlseqdt0(xA,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_57]) ).
cnf(c_0_217,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_208,c_0_209]),c_0_99]),c_0_210]),c_0_59]),c_0_56])]) ).
cnf(c_0_218,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_98,c_0_120]),c_0_60]),c_0_78])]) ).
cnf(c_0_219,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_139,c_0_211]),c_0_147]),c_0_136])]) ).
cnf(c_0_220,hypothesis,
( xP = sz0z00
| sdtlseqdt0(sz0z00,xH)
| ~ sdtlseqdt0(sz0z00,xP) ),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_221,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_95,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_222,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_95,c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_223,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_214,c_0_96]),c_0_215]),c_0_78]),c_0_56])]) ).
cnf(c_0_224,hypothesis,
sdtlseqdt0(xA,xA),
inference(spm,[status(thm)],[c_0_216,c_0_57]) ).
cnf(c_0_225,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| ~ sdtlseqdt0(xB,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_56])]) ).
cnf(c_0_226,hypothesis,
( sdtlseqdt0(xB,sz0z00)
| sdtlseqdt0(sz0z00,xB) ),
inference(spm,[status(thm)],[c_0_181,c_0_78]) ).
cnf(c_0_227,hypothesis,
sdtasdt0(xB,smndt0(xB)) = smndt0(xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_80]),c_0_56])]) ).
fof(c_0_228,plain,
! [X94,X95,X96,X97] :
( ~ aScalar0(X94)
| ~ aScalar0(X95)
| ~ aScalar0(X96)
| ~ aScalar0(X97)
| sdtasdt0(sdtpldt0(X94,X95),sdtpldt0(X96,X97)) = sdtpldt0(sdtpldt0(sdtasdt0(X94,X96),sdtasdt0(X94,X97)),sdtpldt0(sdtasdt0(X95,X96),sdtasdt0(X95,X97))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr2])]) ).
cnf(c_0_229,hypothesis,
sdtpldt0(smndt0(xP),xP) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_130]),c_0_131])]) ).
cnf(c_0_230,hypothesis,
sdtpldt0(smndt0(xH),xH) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_165]),c_0_113])]) ).
fof(c_0_231,plain,
! [X121,X122] :
( ~ aScalar0(X121)
| ~ aScalar0(X122)
| ~ sdtlseqdt0(sz0z00,X121)
| ~ sdtlseqdt0(sz0z00,X122)
| sdtasdt0(X121,X121) != sdtasdt0(X122,X122)
| X121 = X122 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqrt])]) ).
cnf(c_0_232,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_77]),c_0_132]),c_0_78])]) ).
cnf(c_0_233,hypothesis,
( xP = sz0z00
| ~ sdtlseqdt0(sz0z00,xP) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_219,c_0_203]),c_0_203]),c_0_220]) ).
cnf(c_0_234,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_221,c_0_178]),c_0_97]),c_0_174]),c_0_78]),c_0_74])]) ).
cnf(c_0_235,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_222,c_0_223]),c_0_97]),c_0_224]),c_0_78]),c_0_57])]) ).
cnf(c_0_236,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| sdtlseqdt0(sz0z00,xB) ),
inference(spm,[status(thm)],[c_0_225,c_0_226]) ).
cnf(c_0_237,hypothesis,
smndt0(smndt0(xG)) = xG,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_227]),c_0_80]),c_0_56])]) ).
cnf(c_0_238,hypothesis,
aScalar0(smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_227]),c_0_56])]) ).
cnf(c_0_239,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_228]) ).
cnf(c_0_240,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_127,c_0_229]),c_0_130]),c_0_147]),c_0_131])]) ).
cnf(c_0_241,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_127,c_0_230]),c_0_165]),c_0_73]),c_0_113])]) ).
cnf(c_0_242,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_231]) ).
cnf(c_0_243,hypothesis,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_132]),c_0_78])]) ).
cnf(c_0_244,hypothesis,
( xP = sz0z00
| ~ sdtlseqdt0(sz0z00,xH) ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_245,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| sdtlseqdt0(sz0z00,xH) ),
inference(spm,[status(thm)],[c_0_235,c_0_236]) ).
cnf(c_0_246,hypothesis,
sdtasdt0(xG,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_237]),c_0_238])]) ).
cnf(c_0_247,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_239,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_248,hypothesis,
sdtpldt0(sz0z00,xP) = xP,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_240]),c_0_147])]) ).
cnf(c_0_249,hypothesis,
sdtpldt0(sz0z00,xH) = xH,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_241]),c_0_73])]) ).
cnf(c_0_250,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_242,c_0_125]),c_0_78])]),c_0_243]) ).
cnf(c_0_251,hypothesis,
( sdtasdt0(xB,xG) = sz0z00
| xP = sz0z00 ),
inference(spm,[status(thm)],[c_0_244,c_0_245]) ).
cnf(c_0_252,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_182,c_0_96]),c_0_246]),c_0_78]),c_0_56])]) ).
cnf(c_0_253,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_254,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_247,c_0_215]),c_0_178]),c_0_248]),c_0_249]),c_0_78]),c_0_73])]) ).
cnf(c_0_255,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_122,c_0_96]),c_0_78])]) ).
cnf(c_0_256,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_103]) ).
cnf(c_0_257,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_127,c_0_180]),c_0_113]),c_0_73])]) ).
cnf(c_0_258,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_250,c_0_117]),c_0_59]),c_0_97]),c_0_78])]) ).
cnf(c_0_259,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_182,c_0_251]),c_0_252]),c_0_59])]) ).
cnf(c_0_260,hypothesis,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_253,c_0_115]) ).
cnf(c_0_261,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_254,c_0_255]),c_0_249]),c_0_73])]) ).
cnf(c_0_262,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_137,c_0_256]),c_0_50]),c_0_50]) ).
cnf(c_0_263,hypothesis,
sdtpldt0(sz0z00,smndt0(xH)) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_257]),c_0_113])]) ).
fof(c_0_264,plain,
! [X137,X138] :
( ~ aVector0(X137)
| ~ aVector0(X138)
| aDimensionOf0(X137) != aDimensionOf0(X138)
| aDimensionOf0(X138) = sz00
| sdtasasdt0(X137,X138) = sdtpldt0(sdtasasdt0(sziznziztdt0(X137),sziznziztdt0(X138)),sdtasdt0(sdtlbdtrb0(X137,aDimensionOf0(X137)),sdtlbdtrb0(X138,aDimensionOf0(X138)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefSPN])]) ).
cnf(c_0_265,hypothesis,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_266,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_267,hypothesis,
sdtasdt0(xA,xG) = sdtasdt0(xH,xB),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_80]),c_0_56])]) ).
cnf(c_0_268,hypothesis,
( xP = sz0z00
| xG = sz0z00 ),
inference(spm,[status(thm)],[c_0_258,c_0_259]) ).
cnf(c_0_269,hypothesis,
( sdtlseqdt0(X1,xP)
| sdtlseqdt0(xP,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_145,c_0_147]) ).
cnf(c_0_270,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_195,c_0_104]),c_0_147])]) ).
cnf(c_0_271,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_272,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_256,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_273,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_260,c_0_261]),c_0_147])]) ).
cnf(c_0_274,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_262,c_0_263]),c_0_113]),c_0_78])]) ).
cnf(c_0_275,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_276,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_264]) ).
cnf(c_0_277,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_278,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_279,hypothesis,
sdtlbdtrb0(xt,aDimensionOf0(xs)) = xB,
inference(rw,[status(thm)],[c_0_265,c_0_266]) ).
cnf(c_0_280,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[m__1692]) ).
cnf(c_0_281,hypothesis,
( sdtasdt0(xH,xB) = sz0z00
| xP = sz0z00 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267,c_0_268]),c_0_223]) ).
cnf(c_0_282,hypothesis,
( sdtlseqdt0(xP,sz0z00)
| sdtlseqdt0(sz0z00,xP) ),
inference(spm,[status(thm)],[c_0_269,c_0_78]) ).
cnf(c_0_283,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(sz0z00,xP)
| ~ sdtlseqdt0(X1,xP)
| ~ aScalar0(X1) ),
inference(rw,[status(thm)],[c_0_270,c_0_203]) ).
cnf(c_0_284,hypothesis,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_271,c_0_115]) ).
cnf(c_0_285,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_272,c_0_273]),c_0_73])]) ).
cnf(c_0_286,hypothesis,
( aScalar0(sdtasdt0(xH,smndt0(X1)))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_275]),c_0_73])]) ).
fof(c_0_287,plain,
! [X133,X134] :
( ~ aVector0(X133)
| ~ aVector0(X134)
| aDimensionOf0(X133) != aDimensionOf0(X134)
| aScalar0(sdtasasdt0(X133,X134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScPr])]) ).
cnf(c_0_288,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_276,c_0_277]),c_0_278]),c_0_266]),c_0_279]),c_0_266]),c_0_266]),c_0_280]) ).
cnf(c_0_289,hypothesis,
xA = sdtlbdtrb0(xs,aDimensionOf0(xs)),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_290,hypothesis,
xp = sziznziztdt0(xs),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_291,hypothesis,
xE = sdtasasdt0(xp,xq),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_292,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_293,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_281]),c_0_132]),c_0_56]),c_0_73])]) ).
cnf(c_0_294,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_179,c_0_146]),c_0_131]),c_0_147])]) ).
cnf(c_0_295,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_98,c_0_282]),c_0_78]),c_0_147])]),c_0_283]) ).
cnf(c_0_296,hypothesis,
sdtlseqdt0(xP,xP),
inference(spm,[status(thm)],[c_0_269,c_0_147]) ).
cnf(c_0_297,hypothesis,
( sdtasdt0(sdtpldt0(xE,xH),xH) = sdtasdt0(xH,sdtpldt0(xH,xE))
| ~ aScalar0(sdtpldt0(xH,xE))
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_285]),c_0_73])]) ).
cnf(c_0_298,hypothesis,
aScalar0(sdtasdt0(xH,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_165]),c_0_113])]) ).
cnf(c_0_299,plain,
( aScalar0(sdtasasdt0(X1,X2))
| ~ aVector0(X1)
| ~ aVector0(X2)
| aDimensionOf0(X1) != aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_287]) ).
cnf(c_0_300,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_288,c_0_289]),c_0_290]),c_0_291]),c_0_55]),c_0_292])]) ).
fof(c_0_301,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_302,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_284,c_0_293]),c_0_56]),c_0_113])]) ).
cnf(c_0_303,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xP))
| ~ sdtlseqdt0(xP,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_125]),c_0_131])]) ).
cnf(c_0_304,hypothesis,
sdtlseqdt0(xP,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_295,c_0_296]),c_0_147])]) ).
cnf(c_0_305,hypothesis,
( sdtpldt0(sdtasdt0(X1,xH),xP) = sdtasdt0(sdtpldt0(X1,xE),xH)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_306,hypothesis,
( sdtasdt0(sdtpldt0(xE,xH),xH) = sdtasdt0(xH,sdtpldt0(xH,xE))
| ~ aScalar0(sdtpldt0(xH,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_297,c_0_298])]) ).
cnf(c_0_307,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_299,c_0_300]),c_0_266]),c_0_277]),c_0_292])]) ).
cnf(c_0_308,hypothesis,
sdtasdt0(sdtpldt0(xH,xE),xH) = sdtasdt0(sdtpldt0(xE,xH),xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_285,c_0_298])]) ).
cnf(c_0_309,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_301]) ).
cnf(c_0_310,hypothesis,
( sdtpldt0(sdtpldt0(sdtasdt0(xE,X1),xP),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X2,xH))) = sdtasdt0(sdtpldt0(xE,X2),sdtpldt0(X1,xH))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_72]),c_0_73]),c_0_74])]) ).
cnf(c_0_311,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_302]),c_0_132]),c_0_165]),c_0_113]),c_0_56])]) ).
cnf(c_0_312,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_303,c_0_304])]) ).
cnf(c_0_313,hypothesis,
( sdtpldt0(sdtasdt0(xH,sdtpldt0(xH,xE)),xP) = sdtasdt0(sdtpldt0(sdtpldt0(xE,xH),xE),xH)
| ~ aScalar0(sdtpldt0(xH,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_306]),c_0_307])]) ).
cnf(c_0_314,hypothesis,
aScalar0(sdtasdt0(sdtpldt0(xE,xH),xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_308]),c_0_73]),c_0_74])]) ).
cnf(c_0_315,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH)))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtpldt0(xR,xS),sdtasdt0(xH,xH))))
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_110]),c_0_147])]) ).
cnf(c_0_316,hypothesis,
sdtpldt0(xP,sdtpldt0(sz0z00,sdtasdt0(xH,xH))) = sdtasdt0(sdtpldt0(xE,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)],[inference(spm,[status(thm)],[c_0_310,c_0_215]),c_0_178]),c_0_248]),c_0_249]),c_0_78]),c_0_73])]) ).
cnf(c_0_317,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_214,c_0_311]),c_0_223]),c_0_73])]) ).
cnf(c_0_318,hypothesis,
( smndt0(xP) = sz0z00
| sdtasdt0(smndt0(xP),smndt0(xP)) != sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_312]),c_0_131])]) ).
cnf(c_0_319,hypothesis,
sdtpldt0(sdtasdt0(xH,sdtpldt0(xE,xH)),xP) = sdtasdt0(sdtpldt0(sdtpldt0(xE,xH),xE),xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_260]),c_0_307]),c_0_74]),c_0_73])]) ).
cnf(c_0_320,hypothesis,
aScalar0(sdtasdt0(xH,sdtpldt0(xE,xH))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_284]),c_0_73]),c_0_307])]) ).
cnf(c_0_321,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH)))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xH,xH),sdtpldt0(xR,xS))))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(spm,[status(thm)],[c_0_315,c_0_260]) ).
cnf(c_0_322,hypothesis,
sdtpldt0(xP,sdtasdt0(xH,xH)) = sdtasdt0(sdtpldt0(xE,xH),xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_255]),c_0_249]),c_0_73])]) ).
cnf(c_0_323,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_163,c_0_317]),c_0_178]),c_0_73])]) ).
cnf(c_0_324,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_318,c_0_275]),c_0_130]),c_0_131]),c_0_147])]) ).
cnf(c_0_325,hypothesis,
( sdtpldt0(xP,sdtasdt0(xH,sdtpldt0(xH,xE))) = sdtasdt0(sdtpldt0(xE,sdtpldt0(xE,xH)),xH)
| ~ aScalar0(sdtpldt0(xH,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_306]),c_0_307])]) ).
cnf(c_0_326,hypothesis,
sdtpldt0(xP,sdtasdt0(xH,sdtpldt0(xE,xH))) = sdtasdt0(sdtpldt0(sdtpldt0(xE,xH),xE),xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_319]),c_0_147]),c_0_320])]) ).
cnf(c_0_327,plain,
( sdtpldt0(sz0z00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_83]),c_0_78])]) ).
cnf(c_0_328,hypothesis,
sdtpldt0(sdtasdt0(xH,xH),xP) = sdtasdt0(sdtpldt0(xE,xH),xH),
inference(rw,[status(thm)],[c_0_261,c_0_308]) ).
cnf(c_0_329,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(xP,sdtasdt0(sdtpldt0(xE,xH),xH))),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xH,xH),sdtpldt0(xR,xS))))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(rw,[status(thm)],[c_0_321,c_0_322]) ).
cnf(c_0_330,hypothesis,
( sdtpldt0(sdtasdt0(sdtpldt0(xE,xH),xH),xP) = sdtasdt0(sdtpldt0(sdtpldt0(xH,xE),xE),xH)
| ~ aScalar0(sdtpldt0(xH,xE)) ),
inference(spm,[status(thm)],[c_0_305,c_0_308]) ).
cnf(c_0_331,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_284,c_0_323]),c_0_73]),c_0_147])]) ).
cnf(c_0_332,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_324]),c_0_132]),c_0_147])]) ).
cnf(c_0_333,hypothesis,
sdtasdt0(sdtpldt0(sdtpldt0(xE,xH),xE),xH) = sdtasdt0(sdtpldt0(xE,sdtpldt0(xE,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_325,c_0_260]),c_0_326]),c_0_307]),c_0_74]),c_0_73])]) ).
cnf(c_0_334,hypothesis,
sdtpldt0(sz0z00,sdtasdt0(sdtpldt0(xE,xH),xH)) = sdtasdt0(sdtpldt0(xE,xH),xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_327,c_0_328]),c_0_147]),c_0_298])]) ).
cnf(c_0_335,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtpldt0(xP,sdtasdt0(sdtpldt0(xE,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_329,c_0_185]),c_0_186]),c_0_185]),c_0_186]),c_0_136])]) ).
cnf(c_0_336,hypothesis,
( sdtpldt0(xP,sdtasdt0(sdtpldt0(xE,xH),xH)) = sdtasdt0(sdtpldt0(sdtpldt0(xH,xE),xE),xH)
| ~ aScalar0(sdtpldt0(xH,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_330]),c_0_147]),c_0_314])]) ).
cnf(c_0_337,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_163,c_0_331]),c_0_178]),c_0_147])]),c_0_332]) ).
cnf(c_0_338,hypothesis,
sdtpldt0(xP,sdtasdt0(xH,sdtpldt0(xE,xH))) = sdtasdt0(sdtpldt0(xE,sdtpldt0(xE,xH)),xH),
inference(rw,[status(thm)],[c_0_326,c_0_333]) ).
cnf(c_0_339,hypothesis,
sdtpldt0(sz0z00,sdtasdt0(xH,sdtpldt0(xE,xH))) = sdtasdt0(xH,sdtpldt0(xE,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_334,c_0_284]),c_0_73]),c_0_307])]) ).
cnf(c_0_340,hypothesis,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(sdtpldt0(xE,sdtpldt0(xE,xH)),xH)),sdtpldt0(sdtasdt0(xC,xD),sdtpldt0(sdtasdt0(xH,xH),xR)))
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_335,c_0_272]),c_0_307])]) ).
cnf(c_0_341,hypothesis,
( sdtasdt0(sdtpldt0(sdtpldt0(xH,xE),xE),xH) = sdtasdt0(sdtpldt0(xE,xH),xH)
| ~ aScalar0(sdtpldt0(xH,xE)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_336,c_0_337]),c_0_334]) ).
cnf(c_0_342,hypothesis,
sdtasdt0(sdtpldt0(xE,sdtpldt0(xE,xH)),xH) = sdtasdt0(xH,sdtpldt0(xE,xH)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_338,c_0_337]),c_0_339]) ).
cnf(c_0_343,hypothesis,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(sdtpldt0(xE,sdtpldt0(xE,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_340,c_0_298])]),c_0_203]) ).
cnf(c_0_344,hypothesis,
sdtasdt0(sdtpldt0(xE,xH),xH) = sdtasdt0(xH,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(spm,[status(thm)],[c_0_341,c_0_260]),c_0_333]),c_0_342]),c_0_307]),c_0_74]),c_0_73])]) ).
cnf(c_0_345,hypothesis,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(sdtpldt0(xE,sdtpldt0(xE,xH)),xH)),sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xH,xH))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_142]),c_0_298])]) ).
cnf(c_0_346,hypothesis,
sdtpldt0(sdtasdt0(xH,xH),sz0z00) = sdtasdt0(xH,sdtpldt0(xE,xH)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_328,c_0_337]),c_0_344]) ).
cnf(c_0_347,hypothesis,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xH,sdtpldt0(xE,xH))),sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xH,xH))),
inference(rw,[status(thm)],[c_0_345,c_0_342]) ).
cnf(c_0_348,hypothesis,
sdtasdt0(xH,sdtpldt0(xE,xH)) = sdtasdt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_346]),c_0_298])]) ).
cnf(c_0_349,hypothesis,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xE,xE),sdtasdt0(xH,xH)),sdtpldt0(sdtasdt0(xC,xD),sdtasdt0(xH,xH))),
inference(rw,[status(thm)],[c_0_347,c_0_348]) ).
cnf(c_0_350,hypothesis,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(split_conjunct,[status(thm)],[m__1967]) ).
cnf(c_0_351,hypothesis,
( ~ 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_349,c_0_82]),c_0_350]),c_0_298])]) ).
cnf(c_0_352,hypothesis,
( ~ aScalar0(sdtasdt0(xC,xD))
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_351,c_0_125]),c_0_298])]) ).
cnf(c_0_353,hypothesis,
~ aScalar0(sdtasdt0(xE,xE)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_352,c_0_50]),c_0_46]),c_0_60])]) ).
cnf(c_0_354,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_353,c_0_50]),c_0_74])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG076+1 : 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
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:49:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 43.01/26.02 % Version : CSE_E---1.7
% 43.01/26.02 % Problem : theBenchmark.p
% 43.01/26.02 % SZS status Theorem for theBenchmark.p
% 43.01/26.02 % SZS output start CNFRefutation
% See solution above
% 43.31/26.21 % Total time : 18.403s
%------------------------------------------------------------------------------