TSTP Solution File: RNG063+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : RNG063+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.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 21 02:36:07 EDT 2024
% Result : Theorem 28.57s 4.10s
% Output : CNFRefutation 28.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 42
% Syntax : Number of formulae : 312 ( 149 unt; 0 def)
% Number of atoms : 758 ( 276 equ)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 770 ( 324 ~; 328 |; 81 &)
% ( 2 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-2 aty)
% Number of variables : 256 ( 13 sgn 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefInit,axiom,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( aVector0(X2)
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
fof(mSuccEqu,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( szszuzczcdt0(X1) = szszuzczcdt0(X2)
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
fof(m__1726,hypothesis,
( aVector0(xq)
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1678,hypothesis,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(mElmSc,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aNaturalNumber0(X2) )
=> aScalar0(sdtlbdtrb0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
fof(m__1709,hypothesis,
( aVector0(xp)
& 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(mDimNat,axiom,
! [X1] :
( aVector0(X1)
=> aNaturalNumber0(aDimensionOf0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
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(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(mMDNeg,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMDNeg) ).
fof(m__2144,hypothesis,
( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).
fof(m__1892,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
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(m__1949,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
fof(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(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(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
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(m__1746,hypothesis,
( aScalar0(xA)
& xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
fof(m__1854,hypothesis,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
fof(m__1766,hypothesis,
( aScalar0(xB)
& xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
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(mLERef,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
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(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(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(mLETot,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).
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__2221,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2221) ).
fof(m__,conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),xN),xN) = sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2262,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2262) ).
fof(c_0_42,plain,
! [X1] :
( aVector0(X1)
=> ( aDimensionOf0(X1) != sz00
=> ! [X2] :
( X2 = sziznziztdt0(X1)
<=> ( aVector0(X2)
& szszuzczcdt0(aDimensionOf0(X2)) = aDimensionOf0(X1)
& ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(X1,X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefInit]) ).
fof(c_0_43,plain,
! [X62,X63,X64,X65] :
( ( aVector0(X63)
| X63 != sziznziztdt0(X62)
| aDimensionOf0(X62) = sz00
| ~ aVector0(X62) )
& ( szszuzczcdt0(aDimensionOf0(X63)) = aDimensionOf0(X62)
| X63 != sziznziztdt0(X62)
| aDimensionOf0(X62) = sz00
| ~ aVector0(X62) )
& ( ~ aNaturalNumber0(X64)
| sdtlbdtrb0(X63,X64) = sdtlbdtrb0(X62,X64)
| X63 != sziznziztdt0(X62)
| aDimensionOf0(X62) = sz00
| ~ aVector0(X62) )
& ( aNaturalNumber0(esk2_2(X62,X65))
| ~ aVector0(X65)
| szszuzczcdt0(aDimensionOf0(X65)) != aDimensionOf0(X62)
| X65 = sziznziztdt0(X62)
| aDimensionOf0(X62) = sz00
| ~ aVector0(X62) )
& ( sdtlbdtrb0(X65,esk2_2(X62,X65)) != sdtlbdtrb0(X62,esk2_2(X62,X65))
| ~ aVector0(X65)
| szszuzczcdt0(aDimensionOf0(X65)) != aDimensionOf0(X62)
| X65 = sziznziztdt0(X62)
| aDimensionOf0(X62) = sz00
| ~ aVector0(X62) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_42])])])])])])]) ).
fof(c_0_44,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1692]) ).
cnf(c_0_45,plain,
( szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X2)
| aDimensionOf0(X2) = sz00
| X1 != sziznziztdt0(X2)
| ~ aVector0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_46,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_44]) ).
cnf(c_0_47,plain,
( sdtlbdtrb0(X2,X1) = sdtlbdtrb0(X3,X1)
| aDimensionOf0(X3) = sz00
| ~ aNaturalNumber0(X1)
| X2 != sziznziztdt0(X3)
| ~ aVector0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_48,plain,
! [X9,X10] :
( ~ aNaturalNumber0(X9)
| ~ aNaturalNumber0(X10)
| szszuzczcdt0(X9) != szszuzczcdt0(X10)
| X9 = X10 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSuccEqu])])]) ).
cnf(c_0_49,plain,
( szszuzczcdt0(aDimensionOf0(sziznziztdt0(X1))) = aDimensionOf0(X1)
| aDimensionOf0(X1) = sz00
| ~ aVector0(X1) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_50,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_51,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
cnf(c_0_52,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_53,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_54,plain,
! [X60,X61] :
( ~ aVector0(X60)
| ~ aNaturalNumber0(X61)
| aScalar0(sdtlbdtrb0(X60,X61)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mElmSc])])]) ).
cnf(c_0_55,plain,
( sdtlbdtrb0(sziznziztdt0(X1),X2) = sdtlbdtrb0(X1,X2)
| aDimensionOf0(X1) = sz00
| ~ aVector0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_56,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| szszuzczcdt0(X1) != szszuzczcdt0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,hypothesis,
szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xs),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_51]),c_0_52])]),c_0_53]) ).
cnf(c_0_58,hypothesis,
xp = sziznziztdt0(xs),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_59,hypothesis,
aVector0(xs),
inference(split_conjunct,[status(thm)],[m__1678]) ).
fof(c_0_60,plain,
! [X21,X22,X23] :
( ( sdtpldt0(sdtpldt0(X21,X22),X23) = sdtpldt0(X21,sdtpldt0(X22,X23))
| ~ aScalar0(X21)
| ~ aScalar0(X22)
| ~ aScalar0(X23) )
& ( sdtpldt0(X21,X22) = sdtpldt0(X22,X21)
| ~ aScalar0(X21)
| ~ aScalar0(X22)
| ~ aScalar0(X23) )
& ( sdtasdt0(sdtasdt0(X21,X22),X23) = sdtasdt0(X21,sdtasdt0(X22,X23))
| ~ aScalar0(X21)
| ~ aScalar0(X22)
| ~ aScalar0(X23) )
& ( sdtasdt0(X21,X22) = sdtasdt0(X22,X21)
| ~ aScalar0(X21)
| ~ aScalar0(X22)
| ~ aScalar0(X23) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])])]) ).
cnf(c_0_61,plain,
( aScalar0(sdtlbdtrb0(X1,X2))
| ~ aVector0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,hypothesis,
( sdtlbdtrb0(xt,X1) = sdtlbdtrb0(xq,X1)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_50]),c_0_51]),c_0_52])]),c_0_53]) ).
cnf(c_0_63,hypothesis,
( aDimensionOf0(xq) = X1
| szszuzczcdt0(X1) != aDimensionOf0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xq))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,hypothesis,
szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_58]),c_0_59])]),c_0_53]) ).
fof(c_0_65,plain,
! [X59] :
( ~ aVector0(X59)
| aNaturalNumber0(aDimensionOf0(X59)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDimNat])])]) ).
fof(c_0_66,plain,
! [X19] :
( ~ aScalar0(X19)
| aScalar0(smndt0(X19)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])])]) ).
fof(c_0_67,plain,
! [X31,X32] :
( ( sdtasdt0(X31,smndt0(X32)) = smndt0(sdtasdt0(X31,X32))
| ~ aScalar0(X31)
| ~ aScalar0(X32) )
& ( sdtasdt0(smndt0(X31),X32) = smndt0(sdtasdt0(X31,X32))
| ~ aScalar0(X31)
| ~ aScalar0(X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])])]) ).
fof(c_0_68,plain,
! [X17,X18] :
( ~ aScalar0(X17)
| ~ aScalar0(X18)
| aScalar0(sdtasdt0(X17,X18)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])])]) ).
cnf(c_0_69,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_70,hypothesis,
( aScalar0(sdtlbdtrb0(xq,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_52])]) ).
cnf(c_0_71,hypothesis,
( aDimensionOf0(xp) = aDimensionOf0(xq)
| ~ aNaturalNumber0(aDimensionOf0(xq))
| ~ aNaturalNumber0(aDimensionOf0(xp)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
( aNaturalNumber0(aDimensionOf0(X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_74,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_76,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_78,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_79,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_80,plain,
! [X33,X34] :
( ~ aScalar0(X33)
| ~ aScalar0(X34)
| sdtasdt0(smndt0(X33),smndt0(X34)) = sdtasdt0(X33,X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMDNeg])])]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_82,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_83,hypothesis,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X3) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_84,hypothesis,
( aDimensionOf0(xp) = aDimensionOf0(xq)
| ~ aNaturalNumber0(aDimensionOf0(xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_85,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_86,plain,
( aScalar0(sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
cnf(c_0_87,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_75,c_0_77]),c_0_78]),c_0_79])]) ).
fof(c_0_88,plain,
! [X20] :
( ( sdtpldt0(X20,sz0z00) = X20
| ~ aScalar0(X20) )
& ( sdtpldt0(sz0z00,X20) = X20
| ~ aScalar0(X20) )
& ( sdtasdt0(X20,sz0z00) = sz0z00
| ~ aScalar0(X20) )
& ( sdtasdt0(sz0z00,X20) = sz0z00
| ~ aScalar0(X20) )
& ( sdtpldt0(X20,smndt0(X20)) = sz0z00
| ~ aScalar0(X20) )
& ( sdtpldt0(smndt0(X20),X20) = sz0z00
| ~ aScalar0(X20) )
& ( smndt0(smndt0(X20)) = X20
| ~ aScalar0(X20) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])])]) ).
cnf(c_0_89,plain,
( sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_90,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(xR)) = smndt0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_81]),c_0_82])]) ).
cnf(c_0_91,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_92,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_93,hypothesis,
( sdtpldt0(X1,xR) = sdtpldt0(xR,X1)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_82]) ).
cnf(c_0_94,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_95,hypothesis,
aDimensionOf0(xp) = aDimensionOf0(xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_72]),c_0_85])]) ).
cnf(c_0_96,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_97,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_98,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_78]),c_0_79])]) ).
cnf(c_0_99,plain,
( smndt0(smndt0(X1)) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_100,hypothesis,
( smndt0(smndt0(xN)) = sdtasdt0(xS,xR)
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_82]),c_0_91])]) ).
cnf(c_0_101,hypothesis,
( sdtpldt0(X1,xN) = sdtpldt0(xN,X1)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_92]) ).
cnf(c_0_102,hypothesis,
( sdtpldt0(xR,sz0z00) = sdtpldt0(sz0z00,xR)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_103,hypothesis,
aNaturalNumber0(aDimensionOf0(xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_95]),c_0_73])]) ).
cnf(c_0_104,plain,
( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_105,hypothesis,
( sdtasdt0(xR,sdtasdt0(smndt0(xS),X1)) = sdtasdt0(smndt0(xN),X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_82])]),c_0_98])]) ).
cnf(c_0_106,hypothesis,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_107,plain,
( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_75]),c_0_76]) ).
cnf(c_0_108,hypothesis,
( sdtasdt0(xS,xR) = xN
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_92])]) ).
cnf(c_0_109,hypothesis,
( sdtpldt0(xN,sz0z00) = sdtpldt0(sz0z00,xN)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_94]) ).
cnf(c_0_110,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_111,plain,
! [X55] :
( ~ aScalar0(X55)
| sdtlseqdt0(sz0z00,sdtasdt0(X55,X55)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])])]) ).
fof(c_0_112,plain,
! [X75] :
( ~ aVector0(X75)
| sdtlseqdt0(sz0z00,sdtasasdt0(X75,X75)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])])]) ).
fof(c_0_113,plain,
! [X40,X41,X42] :
( ~ aScalar0(X40)
| ~ aScalar0(X41)
| ~ aScalar0(X42)
| ~ sdtlseqdt0(X40,X41)
| ~ sdtlseqdt0(X41,X42)
| sdtlseqdt0(X40,X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])])]) ).
fof(c_0_114,plain,
! [X53,X54] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X53,X54))
| ~ sdtlseqdt0(sz0z00,X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ aScalar0(X53)
| ~ aScalar0(X54) )
& ( sdtlseqdt0(sz0z00,sdtasdt0(X53,X54))
| ~ sdtlseqdt0(sz0z00,X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ aScalar0(X53)
| ~ aScalar0(X54) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])])]) ).
fof(c_0_115,plain,
! [X15,X16] :
( ~ aScalar0(X15)
| ~ aScalar0(X16)
| aScalar0(sdtpldt0(X15,X16)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])])]) ).
cnf(c_0_116,plain,
( sdtpldt0(X1,sz0z00) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_117,hypothesis,
sdtpldt0(xR,sz0z00) = sdtpldt0(sz0z00,xR),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_118,plain,
( sdtasdt0(smndt0(X1),X2) = sdtasdt0(X1,smndt0(X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_104]) ).
cnf(c_0_119,hypothesis,
sdtasdt0(smndt0(xN),smndt0(xS)) = sdtasdt0(xR,sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_98])]) ).
cnf(c_0_120,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_107,c_0_87]),c_0_77]),c_0_78]),c_0_79])]) ).
cnf(c_0_121,hypothesis,
sdtasdt0(xS,xR) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_74]),c_0_91])]) ).
fof(c_0_122,plain,
! [X24,X25,X26] :
( ( sdtasdt0(X24,sdtpldt0(X25,X26)) = sdtpldt0(sdtasdt0(X24,X25),sdtasdt0(X24,X26))
| ~ aScalar0(X24)
| ~ aScalar0(X25)
| ~ aScalar0(X26) )
& ( sdtasdt0(sdtpldt0(X24,X25),X26) = sdtpldt0(sdtasdt0(X24,X26),sdtasdt0(X25,X26))
| ~ aScalar0(X24)
| ~ aScalar0(X25)
| ~ aScalar0(X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])])]) ).
cnf(c_0_123,hypothesis,
sdtpldt0(xN,sz0z00) = sdtpldt0(sz0z00,xN),
inference(spm,[status(thm)],[c_0_109,c_0_103]) ).
cnf(c_0_124,hypothesis,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_92]) ).
cnf(c_0_125,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_126,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_127,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_128,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_129,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_130,plain,
( sdtlseqdt0(X1,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_131,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_132,plain,
( aScalar0(sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_133,hypothesis,
sdtpldt0(sz0z00,xR) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_82])]) ).
cnf(c_0_134,plain,
( sdtasdt0(sz0z00,X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_135,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_136,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_137,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_138,hypothesis,
sdtasdt0(xR,sdtasdt0(xS,xS)) = sdtasdt0(xN,xS),
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_120]),c_0_98]),c_0_92])]) ).
cnf(c_0_139,hypothesis,
sdtasdt0(xS,smndt0(xR)) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_121]),c_0_82]),c_0_91])]) ).
cnf(c_0_140,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_122]) ).
cnf(c_0_141,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_122]) ).
cnf(c_0_142,hypothesis,
( sdtpldt0(smndt0(xS),xR) = sdtpldt0(xR,smndt0(xS))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_98]) ).
cnf(c_0_143,hypothesis,
sdtpldt0(sz0z00,xN) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_123]),c_0_92])]) ).
cnf(c_0_144,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_145,hypothesis,
sdtasdt0(xD,xF) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_124]),c_0_79]),c_0_78])]) ).
cnf(c_0_146,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127])]) ).
cnf(c_0_147,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_85])]) ).
fof(c_0_148,plain,
! [X47,X48,X49,X50] :
( ~ aScalar0(X47)
| ~ aScalar0(X48)
| ~ aScalar0(X49)
| ~ aScalar0(X50)
| ~ sdtlseqdt0(X47,X48)
| ~ sdtlseqdt0(sz0z00,X49)
| ~ sdtlseqdt0(X49,X50)
| sdtlseqdt0(sdtasdt0(X47,X49),sdtasdt0(X48,X50)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])])]) ).
cnf(c_0_149,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X3))
| ~ sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X3)
| ~ aScalar0(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_94])]),c_0_132]) ).
cnf(c_0_150,hypothesis,
sdtpldt0(xR,sz0z00) = xR,
inference(rw,[status(thm)],[c_0_117,c_0_133]) ).
cnf(c_0_151,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_134]),c_0_94])]) ).
cnf(c_0_152,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_153,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_154,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_155,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_135]),c_0_136])]) ).
cnf(c_0_156,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_137]),c_0_73])]) ).
cnf(c_0_157,hypothesis,
sdtasdt0(smndt0(xN),smndt0(xS)) = sdtasdt0(xN,xS),
inference(rw,[status(thm)],[c_0_119,c_0_138]) ).
cnf(c_0_158,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_139]),c_0_82]),c_0_91])]) ).
cnf(c_0_159,hypothesis,
( sdtpldt0(sdtasdt0(xR,X1),smndt0(xN)) = sdtasdt0(xR,sdtpldt0(X1,smndt0(xS)))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_97]),c_0_82])]),c_0_98])]) ).
cnf(c_0_160,hypothesis,
( sdtpldt0(sdtasdt0(X1,xR),smndt0(xN)) = sdtasdt0(sdtpldt0(X1,smndt0(xS)),xR)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_81]),c_0_82])]),c_0_98])]) ).
cnf(c_0_161,hypothesis,
sdtpldt0(smndt0(xS),xR) = sdtpldt0(xR,smndt0(xS)),
inference(spm,[status(thm)],[c_0_142,c_0_103]) ).
cnf(c_0_162,hypothesis,
sdtpldt0(xN,sz0z00) = xN,
inference(rw,[status(thm)],[c_0_123,c_0_143]) ).
cnf(c_0_163,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_164,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_144,c_0_145]),c_0_146]),c_0_147]),c_0_79]),c_0_78])]) ).
cnf(c_0_165,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_148]) ).
cnf(c_0_166,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_167,hypothesis,
( sdtlseqdt0(X1,xR)
| ~ sdtlseqdt0(sz0z00,xR)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151]),c_0_94]),c_0_82])]) ).
cnf(c_0_168,hypothesis,
sdtlseqdt0(sz0z00,xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_152]),c_0_153]),c_0_154])]),c_0_155]),c_0_156])]) ).
cnf(c_0_169,hypothesis,
sdtasdt0(smndt0(xS),smndt0(xN)) = sdtasdt0(xN,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_157]),c_0_98]),c_0_158])]) ).
cnf(c_0_170,hypothesis,
smndt0(smndt0(xN)) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_139]),c_0_121]),c_0_82]),c_0_91])]) ).
cnf(c_0_171,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),xR) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_82])]) ).
cnf(c_0_172,hypothesis,
aScalar0(sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_161]),c_0_82]),c_0_98])]) ).
cnf(c_0_173,hypothesis,
( sdtlseqdt0(X1,xN)
| ~ sdtlseqdt0(sz0z00,xN)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_162]),c_0_151]),c_0_94]),c_0_92])]) ).
cnf(c_0_174,hypothesis,
( sdtlseqdt0(sz0z00,xN)
| ~ sdtlseqdt0(sz0z00,xR) ),
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_144,c_0_163]),c_0_91]),c_0_82])]),c_0_164])]) ).
cnf(c_0_175,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_94])]),c_0_151])]) ).
cnf(c_0_176,hypothesis,
( sdtlseqdt0(X1,xR)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_167,c_0_168])]) ).
fof(c_0_177,plain,
! [X37] :
( ~ aScalar0(X37)
| sdtlseqdt0(X37,X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])])]) ).
cnf(c_0_178,hypothesis,
sdtasdt0(xN,xS) = sdtasdt0(xS,xN),
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_169]),c_0_170]),c_0_158]),c_0_91])]) ).
cnf(c_0_179,hypothesis,
smndt0(sdtasdt0(xR,sdtpldt0(xR,smndt0(xS)))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_171]),c_0_82]),c_0_172])]) ).
cnf(c_0_180,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_75,c_0_152]),c_0_153]),c_0_154])]) ).
fof(c_0_181,plain,
! [X56,X57] :
( ~ aScalar0(X56)
| ~ aScalar0(X57)
| ~ sdtlseqdt0(sz0z00,X56)
| ~ sdtlseqdt0(sz0z00,X57)
| sdtasdt0(X56,X56) != sdtasdt0(X57,X57)
| X56 = X57 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqrt])])]) ).
cnf(c_0_182,hypothesis,
( sdtlseqdt0(X1,xN)
| ~ sdtlseqdt0(sz0z00,xR)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_183,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,xR))
| ~ 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_175,c_0_176]),c_0_82]),c_0_151]),c_0_94])]) ).
cnf(c_0_184,plain,
( sdtlseqdt0(X1,X1)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_185,hypothesis,
sdtasdt0(smndt0(xS),smndt0(xN)) = sdtasdt0(xS,xN),
inference(rw,[status(thm)],[c_0_169,c_0_178]) ).
cnf(c_0_186,plain,
( sdtpldt0(sdtasdt0(X1,smndt0(X2)),sdtasdt0(X3,X2)) = sdtasdt0(sdtpldt0(X1,smndt0(X3)),smndt0(X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_89]),c_0_74]),c_0_74]) ).
cnf(c_0_187,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),smndt0(xR)) = sdtasdt0(xR,smndt0(sdtpldt0(xR,smndt0(xS)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_179]),c_0_172]),c_0_82])]) ).
cnf(c_0_188,hypothesis,
( sdtpldt0(X1,xS) = sdtpldt0(xS,X1)
| ~ aScalar0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_91]) ).
cnf(c_0_189,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_180]),c_0_153]),c_0_154])]) ).
cnf(c_0_190,plain,
( sdtpldt0(smndt0(X1),X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_191,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_181]) ).
cnf(c_0_192,hypothesis,
( sdtlseqdt0(X1,xN)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_168])]) ).
cnf(c_0_193,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,xR))
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_194,hypothesis,
sdtasdt0(smndt0(xN),smndt0(xN)) = sdtasdt0(xR,sdtasdt0(xS,xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_185]),c_0_158])]) ).
cnf(c_0_195,hypothesis,
sdtasdt0(xR,smndt0(sdtpldt0(xR,smndt0(xS)))) = sdtpldt0(sdtasdt0(xR,smndt0(xR)),xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_121]),c_0_82]),c_0_91])]) ).
cnf(c_0_196,hypothesis,
( sdtpldt0(smndt0(xR),xS) = sdtpldt0(xS,smndt0(xR))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_188,c_0_189]) ).
fof(c_0_197,plain,
! [X38,X39] :
( ~ aScalar0(X38)
| ~ aScalar0(X39)
| ~ sdtlseqdt0(X38,X39)
| ~ sdtlseqdt0(X39,X38)
| X38 = X39 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])])]) ).
fof(c_0_198,plain,
! [X43,X44,X45,X46] :
( ~ aScalar0(X43)
| ~ aScalar0(X44)
| ~ aScalar0(X45)
| ~ aScalar0(X46)
| ~ sdtlseqdt0(X43,X44)
| ~ sdtlseqdt0(X45,X46)
| sdtlseqdt0(sdtpldt0(X43,X45),sdtpldt0(X44,X46)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])])]) ).
cnf(c_0_199,hypothesis,
( sdtpldt0(xN,smndt0(xN)) = sz0z00
| ~ aScalar0(smndt0(xN)) ),
inference(spm,[status(thm)],[c_0_190,c_0_170]) ).
cnf(c_0_200,hypothesis,
( X1 = xN
| sdtasdt0(X1,X1) != sdtasdt0(xN,xN)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_92]),c_0_151]),c_0_94])]) ).
cnf(c_0_201,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_81]),c_0_98])]) ).
cnf(c_0_202,hypothesis,
sdtasdt0(xR,sdtasdt0(xS,xN)) = sdtasdt0(xN,xN),
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_194]),c_0_170]),c_0_158]),c_0_92])]) ).
fof(c_0_203,plain,
! [X51,X52] :
( ~ aScalar0(X51)
| ~ aScalar0(X52)
| sdtlseqdt0(X51,X52)
| sdtlseqdt0(X52,X51) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])])]) ).
cnf(c_0_204,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(smndt0(xS))) = smndt0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(spm,[status(thm)],[c_0_75,c_0_106]) ).
cnf(c_0_205,hypothesis,
smndt0(sdtpldt0(sdtasdt0(xR,smndt0(xR)),xN)) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_195]),c_0_172]),c_0_82])]) ).
cnf(c_0_206,hypothesis,
( sdtpldt0(sdtasdt0(xR,X1),xN) = sdtasdt0(xR,sdtpldt0(X1,xS))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_163]),c_0_91]),c_0_82])]) ).
cnf(c_0_207,hypothesis,
sdtpldt0(smndt0(xR),xS) = sdtpldt0(xS,smndt0(xR)),
inference(spm,[status(thm)],[c_0_196,c_0_103]) ).
cnf(c_0_208,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_197]) ).
cnf(c_0_209,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_198]) ).
cnf(c_0_210,plain,
( sdtpldt0(sz0z00,X1) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_211,hypothesis,
sdtpldt0(xN,smndt0(xN)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_158])]) ).
cnf(c_0_212,hypothesis,
smndt0(xN) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_194]),c_0_202]),c_0_158])]) ).
cnf(c_0_213,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_203]) ).
cnf(c_0_214,hypothesis,
( smndt0(sdtasdt0(xS,xS)) = sdtasdt0(xS,smndt0(xS))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_204]),c_0_91])]) ).
cnf(c_0_215,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),smndt0(xR)) = sdtpldt0(sdtasdt0(xR,smndt0(xR)),xN),
inference(rw,[status(thm)],[c_0_187,c_0_195]) ).
cnf(c_0_216,hypothesis,
smndt0(sdtasdt0(xR,sdtpldt0(xS,smndt0(xR)))) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_207]),c_0_189])]) ).
cnf(c_0_217,hypothesis,
aScalar0(sdtpldt0(xS,smndt0(xR))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_207]),c_0_91]),c_0_189])]) ).
cnf(c_0_218,plain,
( sdtpldt0(X1,X2) = sz0z00
| ~ sdtlseqdt0(sdtpldt0(X1,X2),sz0z00)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_131]),c_0_94])]),c_0_132]) ).
cnf(c_0_219,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_209,c_0_210]),c_0_94])]) ).
cnf(c_0_220,hypothesis,
sdtpldt0(xN,xN) = sz0z00,
inference(rw,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_221,hypothesis,
sdtlseqdt0(sz0z00,xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_168])]) ).
cnf(c_0_222,hypothesis,
( sdtlseqdt0(X1,xN)
| sdtlseqdt0(xN,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_213,c_0_92]) ).
cnf(c_0_223,hypothesis,
( sdtasdt0(smndt0(xS),xS) = sdtasdt0(xS,smndt0(xS))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_214]),c_0_91])]) ).
cnf(c_0_224,plain,
( sdtpldt0(sdtasdt0(smndt0(X1),X2),sdtasdt0(X1,X3)) = sdtasdt0(smndt0(X1),sdtpldt0(X2,smndt0(X3)))
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_89]),c_0_74]),c_0_74]) ).
cnf(c_0_225,hypothesis,
sdtasdt0(smndt0(xR),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtasdt0(xR,smndt0(xR)),xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_215]),c_0_189]),c_0_172])]) ).
cnf(c_0_226,hypothesis,
sdtasdt0(xR,smndt0(sdtpldt0(xS,smndt0(xR)))) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_216]),c_0_217]),c_0_82])]) ).
cnf(c_0_227,hypothesis,
( xN = sz0z00
| ~ sdtlseqdt0(xN,sz0z00)
| ~ sdtlseqdt0(sz0z00,xN) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_162]),c_0_151]),c_0_94]),c_0_92])]) ).
cnf(c_0_228,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X1,xN)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_221]),c_0_92])]) ).
cnf(c_0_229,hypothesis,
sdtlseqdt0(xN,xN),
inference(spm,[status(thm)],[c_0_222,c_0_92]) ).
cnf(c_0_230,hypothesis,
( sdtpldt0(xN,xR) = sdtpldt0(xR,xN)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_82]) ).
cnf(c_0_231,hypothesis,
( smndt0(sdtasdt0(xS,xS)) = sdtasdt0(smndt0(xS),xS)
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_99]),c_0_91])]) ).
cnf(c_0_232,hypothesis,
sdtasdt0(smndt0(xS),xS) = sdtasdt0(xS,smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_223,c_0_98])]) ).
cnf(c_0_233,hypothesis,
( aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(spm,[status(thm)],[c_0_76,c_0_106]) ).
cnf(c_0_234,hypothesis,
sdtpldt0(sdtasdt0(smndt0(xR),xR),xN) = sdtpldt0(sdtasdt0(xR,smndt0(xR)),xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_163]),c_0_82]),c_0_91])]) ).
cnf(c_0_235,hypothesis,
sdtpldt0(sdtasdt0(xR,smndt0(xR)),xN) = sdtasdt0(xR,sdtpldt0(xS,smndt0(xR))),
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_107,c_0_226]),c_0_179]),c_0_187]),c_0_195]),c_0_217]),c_0_82])]) ).
cnf(c_0_236,hypothesis,
( xN = sz0z00
| ~ sdtlseqdt0(xN,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_227,c_0_221])]) ).
cnf(c_0_237,hypothesis,
sdtlseqdt0(xN,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_229]),c_0_92])]) ).
cnf(c_0_238,plain,
( sdtpldt0(X1,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_239,hypothesis,
sdtpldt0(xN,xR) = sdtpldt0(xR,xN),
inference(spm,[status(thm)],[c_0_230,c_0_103]) ).
cnf(c_0_240,plain,
( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_241,hypothesis,
( sdtpldt0(sdtasdt0(smndt0(xS),X1),smndt0(xN)) = sdtasdt0(smndt0(xS),sdtpldt0(X1,xR))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_81]),c_0_82])]),c_0_98])]) ).
cnf(c_0_242,hypothesis,
smndt0(sdtasdt0(xS,xS)) = sdtasdt0(xS,smndt0(xS)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_231,c_0_98])]),c_0_232]) ).
cnf(c_0_243,hypothesis,
aScalar0(sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_74]),c_0_91])]) ).
cnf(c_0_244,hypothesis,
sdtpldt0(sdtasdt0(smndt0(xR),xR),xN) = sdtasdt0(xR,sdtpldt0(xS,smndt0(xR))),
inference(rw,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_245,hypothesis,
xN = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_236,c_0_237])]) ).
cnf(c_0_246,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_247,plain,
( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,smndt0(X2))) = sz0z00
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_75]),c_0_76]) ).
cnf(c_0_248,hypothesis,
aScalar0(sdtpldt0(xR,xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_239]),c_0_82]),c_0_92])]) ).
cnf(c_0_249,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_240,c_0_92]) ).
cnf(c_0_250,hypothesis,
sdtasdt0(xR,sdtpldt0(smndt0(xS),smndt0(xS))) = sdtpldt0(smndt0(xN),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_97]),c_0_98])]) ).
cnf(c_0_251,hypothesis,
sdtpldt0(smndt0(xN),smndt0(xN)) = sdtasdt0(smndt0(xS),sdtpldt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_81]),c_0_82])]) ).
cnf(c_0_252,hypothesis,
sdtpldt0(sdtasdt0(xS,xS),sdtasdt0(xS,smndt0(xS))) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_242]),c_0_243])]) ).
cnf(c_0_253,plain,
( sdtpldt0(sdtasdt0(X1,X2),sz0z00) = sdtasdt0(X1,sdtpldt0(X2,sz0z00))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_166]),c_0_94])]) ).
cnf(c_0_254,hypothesis,
sdtpldt0(sdtasdt0(smndt0(xR),xR),sz0z00) = sdtasdt0(xR,sdtpldt0(xS,smndt0(xR))),
inference(rw,[status(thm)],[c_0_244,c_0_245]) ).
cnf(c_0_255,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_190]),c_0_74]) ).
cnf(c_0_256,hypothesis,
sdtpldt0(xR,smndt0(xR)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_180]),c_0_152]),c_0_153]),c_0_154])]) ).
cnf(c_0_257,hypothesis,
( sdtpldt0(sdtpldt0(xR,xN),xR) = sdtpldt0(xR,sdtpldt0(xR,xN))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_248]) ).
cnf(c_0_258,plain,
( sdtasdt0(sz0z00,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_134]),c_0_94])]),c_0_249]) ).
cnf(c_0_259,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_107,c_0_180]),c_0_152]),c_0_153]),c_0_154])]) ).
cnf(c_0_260,hypothesis,
sdtasdt0(xR,sdtpldt0(smndt0(xS),smndt0(xS))) = sdtasdt0(smndt0(xS),sdtpldt0(xR,xR)),
inference(rw,[status(thm)],[c_0_250,c_0_251]) ).
cnf(c_0_261,plain,
( sdtasdt0(sdtpldt0(X1,X1),X2) = sdtasdt0(X1,sdtpldt0(X2,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_262,hypothesis,
sdtasdt0(xS,sdtpldt0(xS,smndt0(xS))) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_252]),c_0_98]),c_0_91])]) ).
cnf(c_0_263,hypothesis,
sdtasdt0(xR,sdtpldt0(xS,smndt0(xR))) = sdtasdt0(smndt0(xR),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_253,c_0_254]),c_0_117]),c_0_133]),c_0_82]),c_0_189])]) ).
cnf(c_0_264,hypothesis,
sdtpldt0(smndt0(xR),sz0z00) = sdtpldt0(sz0z00,smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_256]),c_0_189]),c_0_82])]) ).
fof(c_0_265,plain,
! [X27,X28,X29,X30] :
( ~ aScalar0(X27)
| ~ aScalar0(X28)
| ~ aScalar0(X29)
| ~ aScalar0(X30)
| sdtasdt0(sdtpldt0(X27,X28),sdtpldt0(X29,X30)) = sdtpldt0(sdtpldt0(sdtasdt0(X27,X29),sdtasdt0(X27,X30)),sdtpldt0(sdtasdt0(X28,X29),sdtasdt0(X28,X30))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr2])])]) ).
cnf(c_0_266,plain,
( sdtpldt0(sz0z00,sdtasdt0(sz0z00,X1)) = sdtasdt0(sz0z00,sdtpldt0(X2,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_134]),c_0_94])]) ).
cnf(c_0_267,hypothesis,
sdtpldt0(sdtpldt0(xR,xN),xR) = sdtpldt0(xR,sdtpldt0(xR,xN)),
inference(spm,[status(thm)],[c_0_257,c_0_103]) ).
cnf(c_0_268,hypothesis,
sdtasdt0(sz0z00,xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_189])]) ).
cnf(c_0_269,hypothesis,
sdtpldt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_249]),c_0_94])]) ).
cnf(c_0_270,hypothesis,
sdtasdt0(smndt0(xS),sdtpldt0(xR,xR)) = sdtasdt0(sdtpldt0(xR,xR),smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_98]),c_0_82])]) ).
cnf(c_0_271,hypothesis,
sdtasdt0(xS,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_238]),c_0_91])]) ).
cnf(c_0_272,hypothesis,
sdtpldt0(xS,smndt0(xS)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_87]),c_0_77]),c_0_78]),c_0_79])]) ).
cnf(c_0_273,hypothesis,
sdtpldt0(sdtasdt0(xR,smndt0(xR)),sz0z00) = sdtasdt0(smndt0(xR),xR),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_235,c_0_245]),c_0_263]) ).
cnf(c_0_274,hypothesis,
sdtpldt0(sz0z00,smndt0(xR)) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_264]),c_0_189])]) ).
cnf(c_0_275,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(split_conjunct,[status(thm)],[m__2221]) ).
cnf(c_0_276,hypothesis,
sdtasdt0(smndt0(xS),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_106]),c_0_161]),c_0_98])]) ).
cnf(c_0_277,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_265]) ).
cnf(c_0_278,hypothesis,
sdtasdt0(sz0z00,sdtpldt0(xR,sdtpldt0(xR,xN))) = 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_266,c_0_267]),c_0_268]),c_0_269]),c_0_82]),c_0_248])]) ).
cnf(c_0_279,hypothesis,
sdtasdt0(sz0z00,xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_120]),c_0_98])]) ).
cnf(c_0_280,hypothesis,
sdtpldt0(smndt0(xN),smndt0(xN)) = sdtasdt0(sdtpldt0(xR,xR),smndt0(xS)),
inference(rw,[status(thm)],[c_0_251,c_0_270]) ).
cnf(c_0_281,hypothesis,
( sdtasdt0(smndt0(xS),sdtpldt0(X1,smndt0(xS))) = sdtpldt0(sdtasdt0(smndt0(xS),X1),sdtasdt0(xS,xS))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_106]),c_0_98])]) ).
cnf(c_0_282,hypothesis,
sdtasdt0(smndt0(xS),sz0z00) = sz0z00,
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_271]),c_0_249]),c_0_94]),c_0_91])]) ).
cnf(c_0_283,hypothesis,
sdtpldt0(smndt0(xS),sz0z00) = sdtpldt0(sz0z00,smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_272]),c_0_98]),c_0_91])]) ).
cnf(c_0_284,hypothesis,
aScalar0(sdtpldt0(xR,sdtpldt0(xR,xN))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_267]),c_0_82]),c_0_248])]) ).
cnf(c_0_285,hypothesis,
sdtasdt0(smndt0(xR),xR) = sdtasdt0(xR,smndt0(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_253,c_0_273]),c_0_264]),c_0_274]),c_0_189]),c_0_82])]) ).
fof(c_0_286,negated_conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),xN),xN) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_287,hypothesis,
( sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(smndt0(xN),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_246]),c_0_158])]) ).
cnf(c_0_288,hypothesis,
aScalar0(sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_276]),c_0_172]),c_0_98])]) ).
cnf(c_0_289,hypothesis,
( sdtpldt0(smndt0(xN),sdtasdt0(smndt0(xS),X1)) = sdtasdt0(smndt0(xS),sdtpldt0(xR,X1))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_81]),c_0_82])]),c_0_98])]) ).
cnf(c_0_290,hypothesis,
( sdtpldt0(sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),X2),sdtasdt0(xS,xS))) = sdtasdt0(sdtpldt0(X1,smndt0(xS)),sdtpldt0(X2,smndt0(xS)))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_106]),c_0_98])]) ).
cnf(c_0_291,hypothesis,
sdtasdt0(sz0z00,sdtpldt0(xR,xR)) = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_245]),c_0_117]),c_0_133]) ).
cnf(c_0_292,hypothesis,
sdtasdt0(sz0z00,smndt0(xS)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_279]),c_0_249]),c_0_91]),c_0_94])]) ).
cnf(c_0_293,hypothesis,
sdtasdt0(sdtpldt0(xR,xR),smndt0(xS)) = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_280,c_0_212]),c_0_212]),c_0_245]),c_0_245]),c_0_269]) ).
cnf(c_0_294,hypothesis,
sdtpldt0(sz0z00,sdtasdt0(xS,xS)) = sdtasdt0(xS,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_281,c_0_210]),c_0_106]),c_0_282]),c_0_94]),c_0_98])]) ).
cnf(c_0_295,hypothesis,
sdtpldt0(sz0z00,smndt0(xS)) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_283]),c_0_98])]) ).
cnf(c_0_296,hypothesis,
aScalar0(sdtpldt0(xR,xR)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_245]),c_0_117]),c_0_133]) ).
cnf(c_0_297,hypothesis,
smndt0(sdtasdt0(xR,smndt0(xR))) = sdtasdt0(xR,xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_285]),c_0_259]),c_0_82]),c_0_189])]) ).
fof(c_0_298,negated_conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),xN),xN) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
inference(fof_nnf,[status(thm)],[c_0_286]) ).
cnf(c_0_299,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(split_conjunct,[status(thm)],[m__2262]) ).
cnf(c_0_300,hypothesis,
( sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(smndt0(xN),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_287,c_0_288])]) ).
cnf(c_0_301,hypothesis,
sdtpldt0(smndt0(xN),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) = sdtasdt0(smndt0(xS),sdtpldt0(xR,sdtpldt0(xR,smndt0(xS)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_276]),c_0_172])]) ).
cnf(c_0_302,hypothesis,
sdtasdt0(smndt0(xS),sdtpldt0(sdtpldt0(xR,xR),smndt0(xS))) = sdtasdt0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_290,c_0_291]),c_0_292]),c_0_269]),c_0_270]),c_0_293]),c_0_294]),c_0_294]),c_0_295]),c_0_296]),c_0_94])]) ).
cnf(c_0_303,hypothesis,
sdtasdt0(smndt0(xR),smndt0(xR)) = sdtasdt0(xR,xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_297]),c_0_189]),c_0_82])]) ).
cnf(c_0_304,negated_conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),xN),xN) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
inference(split_conjunct,[status(thm)],[c_0_298]) ).
cnf(c_0_305,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),sz0z00),sz0z00),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_299,c_0_212]),c_0_212]),c_0_245]),c_0_245]) ).
cnf(c_0_306,hypothesis,
( sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(smndt0(xS),sdtpldt0(xR,sdtpldt0(xR,smndt0(xS))))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(rw,[status(thm)],[c_0_300,c_0_301]) ).
cnf(c_0_307,hypothesis,
sdtasdt0(smndt0(xS),sdtpldt0(xR,sdtpldt0(xR,smndt0(xS)))) = sdtasdt0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_302,c_0_246]),c_0_98]),c_0_82])]) ).
cnf(c_0_308,hypothesis,
aScalar0(sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_303]),c_0_189])]) ).
cnf(c_0_309,negated_conjecture,
sdtpldt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),sz0z00),sz0z00),sz0z00),sz0z00) != sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_304,c_0_245]),c_0_245]),c_0_305]) ).
cnf(c_0_310,hypothesis,
sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),sz0z00),sz0z00) = sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_306,c_0_307]),c_0_305]),c_0_308])]) ).
cnf(c_0_311,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_310]),c_0_310])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG063+1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 12:21:07 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.57/4.10 # Version: 3.1.0
% 28.57/4.10 # Preprocessing class: FSLSSMSMSSSNFFN.
% 28.57/4.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.57/4.10 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 28.57/4.10 # Starting new_bool_3 with 300s (1) cores
% 28.57/4.10 # Starting new_bool_1 with 300s (1) cores
% 28.57/4.10 # Starting sh5l with 300s (1) cores
% 28.57/4.10 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 1612 completed with status 0
% 28.57/4.10 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 28.57/4.10 # Preprocessing class: FSLSSMSMSSSNFFN.
% 28.57/4.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.57/4.10 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 28.57/4.10 # No SInE strategy applied
% 28.57/4.10 # Search class: FGHSF-FFMM21-MFFFFFNN
% 28.57/4.10 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 28.57/4.10 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 28.57/4.10 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 28.57/4.10 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 28.57/4.10 # Starting new_bool_3 with 136s (1) cores
% 28.57/4.10 # Starting new_bool_1 with 136s (1) cores
% 28.57/4.10 # G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 1620 completed with status 0
% 28.57/4.10 # Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 28.57/4.10 # Preprocessing class: FSLSSMSMSSSNFFN.
% 28.57/4.10 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 28.57/4.10 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 28.57/4.10 # No SInE strategy applied
% 28.57/4.10 # Search class: FGHSF-FFMM21-MFFFFFNN
% 28.57/4.10 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 28.57/4.10 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 28.57/4.10 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 28.57/4.10 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 28.57/4.10 # Preprocessing time : 0.002 s
% 28.57/4.10 # Presaturation interreduction done
% 28.57/4.10
% 28.57/4.10 # Proof found!
% 28.57/4.10 # SZS status Theorem
% 28.57/4.10 # SZS output start CNFRefutation
% See solution above
% 28.57/4.10 # Parsed axioms : 62
% 28.57/4.10 # Removed by relevancy pruning/SinE : 0
% 28.57/4.10 # Initial clauses : 98
% 28.57/4.10 # Removed in clause preprocessing : 5
% 28.57/4.10 # Initial clauses in saturation : 93
% 28.57/4.10 # Processed clauses : 7453
% 28.57/4.10 # ...of these trivial : 1507
% 28.57/4.10 # ...subsumed : 1961
% 28.57/4.10 # ...remaining for further processing : 3985
% 28.57/4.10 # Other redundant clauses eliminated : 7
% 28.57/4.10 # Clauses deleted for lack of memory : 0
% 28.57/4.10 # Backward-subsumed : 26
% 28.57/4.10 # Backward-rewritten : 1543
% 28.57/4.10 # Generated clauses : 226685
% 28.57/4.10 # ...of the previous two non-redundant : 207999
% 28.57/4.10 # ...aggressively subsumed : 0
% 28.57/4.10 # Contextual simplify-reflections : 104
% 28.57/4.10 # Paramodulations : 226669
% 28.57/4.10 # Factorizations : 0
% 28.57/4.10 # NegExts : 0
% 28.57/4.10 # Equation resolutions : 16
% 28.57/4.10 # Disequality decompositions : 0
% 28.57/4.10 # Total rewrite steps : 449928
% 28.57/4.10 # ...of those cached : 447873
% 28.57/4.10 # Propositional unsat checks : 0
% 28.57/4.10 # Propositional check models : 0
% 28.57/4.10 # Propositional check unsatisfiable : 0
% 28.57/4.10 # Propositional clauses : 0
% 28.57/4.10 # Propositional clauses after purity: 0
% 28.57/4.10 # Propositional unsat core size : 0
% 28.57/4.10 # Propositional preprocessing time : 0.000
% 28.57/4.10 # Propositional encoding time : 0.000
% 28.57/4.10 # Propositional solver time : 0.000
% 28.57/4.10 # Success case prop preproc time : 0.000
% 28.57/4.10 # Success case prop encoding time : 0.000
% 28.57/4.10 # Success case prop solver time : 0.000
% 28.57/4.10 # Current number of processed clauses : 2320
% 28.57/4.10 # Positive orientable unit clauses : 1573
% 28.57/4.10 # Positive unorientable unit clauses: 0
% 28.57/4.10 # Negative unit clauses : 2
% 28.57/4.10 # Non-unit-clauses : 745
% 28.57/4.10 # Current number of unprocessed clauses: 198423
% 28.57/4.10 # ...number of literals in the above : 818632
% 28.57/4.10 # Current number of archived formulas : 0
% 28.57/4.10 # Current number of archived clauses : 1662
% 28.57/4.10 # Clause-clause subsumption calls (NU) : 118268
% 28.57/4.10 # Rec. Clause-clause subsumption calls : 55273
% 28.57/4.10 # Non-unit clause-clause subsumptions : 2080
% 28.57/4.10 # Unit Clause-clause subsumption calls : 30402
% 28.57/4.10 # Rewrite failures with RHS unbound : 0
% 28.57/4.10 # BW rewrite match attempts : 5077
% 28.57/4.10 # BW rewrite match successes : 431
% 28.57/4.10 # Condensation attempts : 0
% 28.57/4.10 # Condensation successes : 0
% 28.57/4.10 # Termbank termtop insertions : 7599091
% 28.57/4.10 # Search garbage collected termcells : 885
% 28.57/4.10
% 28.57/4.10 # -------------------------------------------------
% 28.57/4.10 # User time : 3.331 s
% 28.57/4.10 # System time : 0.161 s
% 28.57/4.10 # Total time : 3.491 s
% 28.57/4.10 # Maximum resident set size: 1980 pages
% 28.57/4.10
% 28.57/4.10 # -------------------------------------------------
% 28.57/4.10 # User time : 17.272 s
% 28.57/4.10 # System time : 0.451 s
% 28.57/4.10 # Total time : 17.724 s
% 28.57/4.10 # Maximum resident set size: 1764 pages
% 28.57/4.10 % E---3.1 exiting
% 28.57/4.10 % E exiting
%------------------------------------------------------------------------------