TSTP Solution File: RNG060+2 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : RNG060+2 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n012.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 02:36:06 EDT 2024
% Result : Theorem 8.43s 1.55s
% Output : CNFRefutation 8.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 36
% Syntax : Number of formulae : 251 ( 104 unt; 0 def)
% Number of atoms : 632 ( 210 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 652 ( 271 ~; 271 |; 80 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 15 con; 0-2 aty)
% Number of variables : 195 ( 3 sgn 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mDefSPN) ).
fof(m__1692,hypothesis,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1692) ).
fof(m__1726,hypothesis,
( aVector0(xq)
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xq,X1) = sdtlbdtrb0(xt,X1) )
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
fof(m__1766,hypothesis,
( aScalar0(xB)
& xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).
fof(m__1678_01,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678_01) ).
fof(m__1678,hypothesis,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
fof(mScPr,axiom,
! [X1,X2] :
( ( aVector0(X1)
& aVector0(X2) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> aScalar0(sdtasasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).
fof(m__1800,hypothesis,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
fof(m__1854,hypothesis,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
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/sandbox/benchmark/theBenchmark.p',mArith) ).
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/sandbox/benchmark/theBenchmark.p',mMNeg) ).
fof(m__1930,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(m__1837,hypothesis,
( aScalar0(xF)
& xF = sdtasdt0(xA,xA) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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/sandbox/benchmark/theBenchmark.p',mScZero) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1892,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
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/sandbox/benchmark/theBenchmark.p',m__2144) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
fof(mMDNeg,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).
fof(m__1949,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
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/sandbox/benchmark/theBenchmark.p',mPosMon) ).
fof(m__1746,hypothesis,
( aScalar0(xA)
& xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
fof(m__1709,hypothesis,
( aVector0(xp)
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xp,X1) = sdtlbdtrb0(xs,X1) )
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).
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/sandbox/benchmark/theBenchmark.p',mLEMon) ).
fof(mLETot,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
fof(mLEASm,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
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/sandbox/benchmark/theBenchmark.p',mDistr) ).
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/sandbox/benchmark/theBenchmark.p',mLEMonM) ).
fof(m__,conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',mSqrt) ).
fof(mLERef,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
fof(c_0_36,plain,
! [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)))) ) ),
inference(fof_simplification,[status(thm)],[mDefSPN]) ).
fof(c_0_37,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1692]) ).
fof(c_0_38,plain,
! [X73,X74] :
( ~ aVector0(X73)
| ~ aVector0(X74)
| aDimensionOf0(X73) != aDimensionOf0(X74)
| aDimensionOf0(X74) = sz00
| sdtasasdt0(X73,X74) = sdtpldt0(sdtasasdt0(sziznziztdt0(X73),sziznziztdt0(X74)),sdtasdt0(sdtlbdtrb0(X73,aDimensionOf0(X73)),sdtlbdtrb0(X74,aDimensionOf0(X74)))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])])]) ).
fof(c_0_39,hypothesis,
! [X79] :
( aVector0(xq)
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& ( ~ aNaturalNumber0(X79)
| sdtlbdtrb0(xq,X79) = sdtlbdtrb0(xt,X79) )
& xq = sziznziztdt0(xt) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1726])])])]) ).
cnf(c_0_40,hypothesis,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_41,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
fof(c_0_42,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_37]) ).
cnf(c_0_43,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_38]) ).
cnf(c_0_44,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,hypothesis,
sdtlbdtrb0(xt,aDimensionOf0(xs)) = xB,
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_47,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_48,plain,
! [X69,X70] :
( ~ aVector0(X69)
| ~ aVector0(X70)
| aDimensionOf0(X69) != aDimensionOf0(X70)
| aScalar0(sdtasasdt0(X69,X70)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScPr])])]) ).
cnf(c_0_49,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_41]),c_0_44]),c_0_45]),c_0_46])]),c_0_47]) ).
cnf(c_0_50,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_51,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
fof(c_0_52,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_53,plain,
( aScalar0(sdtasasdt0(X1,X2))
| ~ aVector0(X1)
| ~ aVector0(X2)
| aDimensionOf0(X1) != aDimensionOf0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,hypothesis,
sdtasasdt0(xt,xt) = sdtpldt0(xD,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_44]),c_0_50]),c_0_45]),c_0_51]),c_0_46])]) ).
cnf(c_0_55,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_56,hypothesis,
aScalar0(sdtpldt0(xD,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_46])]) ).
fof(c_0_57,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])])])]) ).
cnf(c_0_58,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_59,hypothesis,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_61,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
fof(c_0_62,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])])])]) ).
fof(c_0_63,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_64,plain,
( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,hypothesis,
sdtasdt0(xD,xF) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_61])]) ).
cnf(c_0_66,plain,
( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_68,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_69,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_70,plain,
( smndt0(smndt0(X1)) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_73,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_74,hypothesis,
sdtasdt0(xD,smndt0(xF)) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_60]),c_0_61])]) ).
fof(c_0_75,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_76,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])])]) ).
cnf(c_0_77,hypothesis,
sdtasdt0(smndt0(xC),xG) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69])]) ).
cnf(c_0_78,plain,
( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_64]),c_0_71]) ).
cnf(c_0_79,hypothesis,
sdtasdt0(xC,smndt0(xG)) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_67]),c_0_68]),c_0_69])]) ).
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),smndt0(xS)) = sdtasdt0(xS,xS),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_82,hypothesis,
( sdtasdt0(xR,smndt0(smndt0(xS))) = smndt0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_72]),c_0_73])]) ).
cnf(c_0_83,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_84,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_85,hypothesis,
( aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xF)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_74]),c_0_61])]) ).
cnf(c_0_86,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_87,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])])])]) ).
cnf(c_0_88,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_89,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_90,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
fof(c_0_91,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])])]) ).
cnf(c_0_92,hypothesis,
( sdtasdt0(xG,smndt0(xC)) = smndt0(xR)
| ~ aScalar0(smndt0(xC)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_77]),c_0_68])]) ).
cnf(c_0_93,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_78,c_0_79]),c_0_67]),c_0_68]),c_0_69])]) ).
fof(c_0_94,hypothesis,
! [X78] :
( aVector0(xp)
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& ( ~ aNaturalNumber0(X78)
| sdtlbdtrb0(xp,X78) = sdtlbdtrb0(xs,X78) )
& xp = sziznziztdt0(xs) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1709])])])]) ).
cnf(c_0_95,plain,
( sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_96,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(smndt0(xS))) = smndt0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(spm,[status(thm)],[c_0_64,c_0_81]) ).
cnf(c_0_97,hypothesis,
( smndt0(smndt0(xN)) = xN
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_70]),c_0_83]),c_0_84])]) ).
cnf(c_0_98,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_60])]) ).
cnf(c_0_99,hypothesis,
( aScalar0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_100,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_101,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).
cnf(c_0_102,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_103,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_104,hypothesis,
( sdtasdt0(xG,xC) = xR
| ~ 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_78,c_0_92]),c_0_93]),c_0_69]),c_0_68])]) ).
cnf(c_0_105,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_106,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_107,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_108,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_95,c_0_96]),c_0_84])]) ).
cnf(c_0_109,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_110,plain,
( sdtpldt0(smndt0(X1),X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_111,hypothesis,
smndt0(smndt0(xN)) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_112,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_98])]) ).
fof(c_0_113,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_114,hypothesis,
( sdtlseqdt0(sz0z00,xS)
| ~ sdtlseqdt0(sz0z00,xD) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_65]),c_0_101]),c_0_60]),c_0_61])]) ).
cnf(c_0_115,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_50]),c_0_103])]) ).
cnf(c_0_116,hypothesis,
sdtasdt0(xG,xC) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_86]),c_0_69])]) ).
cnf(c_0_117,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_105]),c_0_106])]) ).
cnf(c_0_118,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_51]),c_0_107])]) ).
fof(c_0_119,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_120,plain,
( sdtpldt0(X1,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_121,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_66,c_0_108]),c_0_84])]) ).
cnf(c_0_122,hypothesis,
sdtasdt0(xF,smndt0(xD)) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_58]),c_0_61]),c_0_60])]) ).
fof(c_0_123,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_124,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_125,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_86]) ).
cnf(c_0_126,hypothesis,
sdtpldt0(xN,smndt0(xN)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112])]) ).
cnf(c_0_127,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_128,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_113]) ).
cnf(c_0_129,plain,
( sdtpldt0(sz0z00,X1) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_130,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_131,hypothesis,
sdtlseqdt0(sz0z00,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_132,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_100,c_0_116]),c_0_117]),c_0_118]),c_0_69]),c_0_68])]) ).
cnf(c_0_133,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
fof(c_0_134,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_135,plain,
( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,smndt0(X2))) = sz0z00
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_64]),c_0_71]) ).
cnf(c_0_136,hypothesis,
sdtasdt0(smndt0(xS),xS) = sdtasdt0(xS,smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_98])]) ).
cnf(c_0_137,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_78,c_0_122]),c_0_58]),c_0_61]),c_0_60])]) ).
cnf(c_0_138,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_139,plain,
( aScalar0(sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_64]),c_0_71]) ).
cnf(c_0_140,hypothesis,
sdtasdt0(xB,smndt0(xB)) = smndt0(xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_51]),c_0_107])]) ).
cnf(c_0_141,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_142,plain,
( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_143,plain,
( aScalar0(sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_144,plain,
( sdtpldt0(X1,sz0z00) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_145,hypothesis,
sdtpldt0(smndt0(xN),sz0z00) = sdtpldt0(sz0z00,smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_112]),c_0_127])]) ).
cnf(c_0_146,plain,
( sdtasdt0(sz0z00,X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_147,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_128,c_0_129]),c_0_130])]) ).
cnf(c_0_148,hypothesis,
sdtlseqdt0(sz0z00,xN),
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_100,c_0_83]),c_0_84]),c_0_73])]),c_0_131]),c_0_132])]) ).
cnf(c_0_149,hypothesis,
( sdtlseqdt0(X1,smndt0(xN))
| sdtlseqdt0(smndt0(xN),X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_112]) ).
fof(c_0_150,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_151,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_134]) ).
cnf(c_0_152,hypothesis,
sdtpldt0(sdtasdt0(xS,smndt0(xS)),sdtasdt0(xS,xS)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_81]),c_0_136]),c_0_84]),c_0_98])]) ).
cnf(c_0_153,hypothesis,
sdtpldt0(smndt0(xS),xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_137]),c_0_98])]) ).
cnf(c_0_154,plain,
( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_155,plain,
( aScalar0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_138]),c_0_71]) ).
cnf(c_0_156,hypothesis,
sdtasdt0(smndt0(xG),xC) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_116]),c_0_69]),c_0_68])]) ).
cnf(c_0_157,hypothesis,
aScalar0(smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_107])]) ).
cnf(c_0_158,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_141,c_0_142]),c_0_130])]),c_0_143]) ).
cnf(c_0_159,hypothesis,
sdtpldt0(sz0z00,smndt0(xN)) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_112])]) ).
cnf(c_0_160,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_146]),c_0_130])]) ).
cnf(c_0_161,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X1,smndt0(xN))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_126]),c_0_148]),c_0_112]),c_0_127])]) ).
cnf(c_0_162,hypothesis,
sdtlseqdt0(smndt0(xN),smndt0(xN)),
inference(spm,[status(thm)],[c_0_149,c_0_112]) ).
cnf(c_0_163,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_150]) ).
cnf(c_0_164,hypothesis,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_165,hypothesis,
sdtasdt0(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_151,c_0_152]),c_0_153]),c_0_84]),c_0_98])]) ).
cnf(c_0_166,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_154,c_0_127]) ).
cnf(c_0_167,hypothesis,
( sdtlseqdt0(X1,smndt0(xS))
| sdtlseqdt0(smndt0(xS),X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_98]) ).
cnf(c_0_168,hypothesis,
( aScalar0(sdtasdt0(X1,smndt0(xR)))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_69]),c_0_157])]) ).
cnf(c_0_169,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_79]),c_0_68]),c_0_69])]) ).
cnf(c_0_170,hypothesis,
( smndt0(xN) = sz0z00
| ~ sdtlseqdt0(smndt0(xN),sz0z00)
| ~ sdtlseqdt0(sz0z00,smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_160]),c_0_112]),c_0_130])]) ).
cnf(c_0_171,hypothesis,
sdtlseqdt0(smndt0(xN),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_112])]) ).
cnf(c_0_172,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xN))
| ~ sdtlseqdt0(X1,smndt0(xS))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xR)
| ~ 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_163,c_0_164]),c_0_73])]),c_0_98])]) ).
cnf(c_0_173,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_66,c_0_165]),c_0_166]),c_0_130]),c_0_84])]) ).
cnf(c_0_174,hypothesis,
sdtlseqdt0(smndt0(xS),smndt0(xS)),
inference(spm,[status(thm)],[c_0_167,c_0_98]) ).
cnf(c_0_175,hypothesis,
sdtpldt0(smndt0(xN),xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_111]),c_0_112])]) ).
cnf(c_0_176,hypothesis,
smndt0(sdtasdt0(xS,smndt0(xS))) = sdtasdt0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_136]),c_0_81]),c_0_84]),c_0_98])]) ).
cnf(c_0_177,hypothesis,
( aScalar0(sdtasdt0(smndt0(xR),X1))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_59]),c_0_169])]) ).
cnf(c_0_178,plain,
( sdtasdt0(smndt0(X1),X2) = sdtasdt0(X1,smndt0(X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_66]) ).
cnf(c_0_179,hypothesis,
( smndt0(xN) = sz0z00
| ~ sdtlseqdt0(sz0z00,smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171])]) ).
cnf(c_0_180,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_174]),c_0_160]),c_0_132]),c_0_130]),c_0_98])]) ).
cnf(c_0_181,hypothesis,
sdtpldt0(xN,sz0z00) = sdtpldt0(sz0z00,xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_175]),c_0_111]),c_0_127]),c_0_112])]) ).
cnf(c_0_182,hypothesis,
sdtasdt0(xS,smndt0(smndt0(xS))) = sdtasdt0(xS,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_176]),c_0_98]),c_0_84])]) ).
cnf(c_0_183,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,sdtasdt0(X2,sdtasdt0(X1,X2))))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_138]),c_0_71]) ).
cnf(c_0_184,hypothesis,
( sdtasdt0(xC,sdtasdt0(xG,X1)) = sdtasdt0(xR,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_67]),c_0_68]),c_0_69])]) ).
cnf(c_0_185,hypothesis,
( aScalar0(sdtasdt0(xR,smndt0(X1)))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_73])]) ).
cnf(c_0_186,hypothesis,
smndt0(xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_180])]) ).
cnf(c_0_187,hypothesis,
sdtpldt0(sz0z00,xN) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_181]),c_0_127])]) ).
cnf(c_0_188,hypothesis,
( aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(smndt0(xS))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_182]),c_0_84])]) ).
cnf(c_0_189,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xR,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_183,c_0_184]),c_0_67]),c_0_68]),c_0_69]),c_0_67]),c_0_73])]) ).
cnf(c_0_190,hypothesis,
aScalar0(sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_93]),c_0_169])]) ).
cnf(c_0_191,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),xN)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xS)
| ~ sdtlseqdt0(X1,xR)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_83]),c_0_84]),c_0_73])]) ).
cnf(c_0_192,hypothesis,
xN = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_186]),c_0_181]),c_0_187]) ).
cnf(c_0_193,hypothesis,
( sdtlseqdt0(X1,xR)
| sdtlseqdt0(xR,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_73]) ).
fof(c_0_194,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_195,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_196,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_81]),c_0_98])]) ).
cnf(c_0_197,hypothesis,
aScalar0(sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_70]),c_0_84])]) ).
cnf(c_0_198,hypothesis,
( sdtlseqdt0(X1,xS)
| sdtlseqdt0(xS,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_84]) ).
cnf(c_0_199,hypothesis,
( sdtasdt0(xR,xR) = sz0z00
| ~ sdtlseqdt0(sdtasdt0(xR,xR),sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_189]),c_0_130]),c_0_190])]) ).
cnf(c_0_200,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),sz0z00)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xS)
| ~ sdtlseqdt0(X1,xR)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(rw,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_201,hypothesis,
sdtlseqdt0(xR,xR),
inference(spm,[status(thm)],[c_0_193,c_0_73]) ).
fof(c_0_202,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(fof_nnf,[status(thm)],[c_0_194]) ).
cnf(c_0_203,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_204,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_128,c_0_129]),c_0_130])]) ).
cnf(c_0_205,hypothesis,
sdtpldt0(xS,smndt0(xS)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_137]),c_0_98])]) ).
fof(c_0_206,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_207,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_195]) ).
cnf(c_0_208,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_64,c_0_146]),c_0_130])]),c_0_166]) ).
cnf(c_0_209,hypothesis,
( sdtasdt0(xS,xS) = sz0z00
| ~ sdtlseqdt0(sdtasdt0(xS,xS),sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_196]),c_0_130]),c_0_197])]) ).
cnf(c_0_210,hypothesis,
sdtlseqdt0(xS,xS),
inference(spm,[status(thm)],[c_0_198,c_0_84]) ).
cnf(c_0_211,hypothesis,
( sdtasdt0(xR,xR) = sz0z00
| ~ sdtlseqdt0(xR,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_132]),c_0_201]),c_0_73])]) ).
cnf(c_0_212,hypothesis,
( sdtlseqdt0(xS,xR)
| sdtlseqdt0(xR,xS) ),
inference(spm,[status(thm)],[c_0_198,c_0_73]) ).
cnf(c_0_213,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(split_conjunct,[status(thm)],[c_0_202]) ).
cnf(c_0_214,hypothesis,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_203,c_0_56]) ).
cnf(c_0_215,hypothesis,
( sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(smndt0(xS),X1)
| ~ sdtlseqdt0(xS,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_98]),c_0_84])]) ).
cnf(c_0_216,plain,
( sdtlseqdt0(X1,X1)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_206]) ).
cnf(c_0_217,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_147,c_0_205]),c_0_131]),c_0_98]),c_0_84])]) ).
cnf(c_0_218,hypothesis,
sdtpldt0(smndt0(xR),xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_93]),c_0_169])]) ).
cnf(c_0_219,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_220,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_125,c_0_205]),c_0_98]),c_0_84])]) ).
cnf(c_0_221,hypothesis,
( X1 = xS
| sdtasdt0(X1,X1) != sdtasdt0(xS,xS)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_131]),c_0_84])]) ).
cnf(c_0_222,hypothesis,
( X1 = xR
| sdtasdt0(X1,X1) != sdtasdt0(xR,xR)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_132]),c_0_73])]) ).
cnf(c_0_223,hypothesis,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_166]),c_0_130])]) ).
cnf(c_0_224,hypothesis,
( sdtasdt0(xS,xS) = sz0z00
| ~ sdtlseqdt0(xS,xR) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_200]),c_0_131]),c_0_210]),c_0_84])]) ).
cnf(c_0_225,hypothesis,
( sdtasdt0(xR,xR) = sz0z00
| sdtlseqdt0(xS,xR) ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_226,negated_conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_112]),c_0_197])]) ).
cnf(c_0_227,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_151,c_0_72]),c_0_73])]),c_0_98])]) ).
cnf(c_0_228,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xS))
| ~ sdtlseqdt0(xS,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_98])]) ).
cnf(c_0_229,hypothesis,
sdtlseqdt0(smndt0(xS),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_174]),c_0_98])]) ).
cnf(c_0_230,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_125,c_0_218]),c_0_93]),c_0_73]),c_0_169])]) ).
cnf(c_0_231,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_151,c_0_219]),c_0_130])]) ).
cnf(c_0_232,hypothesis,
sdtpldt0(sz0z00,smndt0(xS)) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_220]),c_0_98])]) ).
cnf(c_0_233,hypothesis,
( sdtasdt0(xS,xS) = xS
| sdtasdt0(sdtasdt0(xS,xS),sdtasdt0(xS,xS)) != sdtasdt0(xS,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_196]),c_0_197])]) ).
cnf(c_0_234,hypothesis,
( xR = sz0z00
| sdtasdt0(xR,xR) != sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_216]),c_0_223]),c_0_130])]) ).
cnf(c_0_235,hypothesis,
( sdtasdt0(xR,xR) = sz0z00
| sdtasdt0(xS,xS) = sz0z00 ),
inference(spm,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_236,negated_conjecture,
sdtpldt0(sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_73])]) ).
cnf(c_0_237,hypothesis,
( smndt0(xS) = sz0z00
| ~ sdtlseqdt0(xS,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_228]),c_0_229]),c_0_130]),c_0_98])]) ).
cnf(c_0_238,hypothesis,
sdtpldt0(sz0z00,xR) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_230]),c_0_73])]) ).
cnf(c_0_239,hypothesis,
sdtpldt0(sdtasdt0(xS,xS),sz0z00) = 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_231,c_0_81]),c_0_220]),c_0_232]),c_0_81]),c_0_98])]) ).
cnf(c_0_240,hypothesis,
( sdtasdt0(xS,xS) = xS
| sdtasdt0(xS,sdtasdt0(xS,sdtasdt0(xS,xS))) != sdtasdt0(xS,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_138]),c_0_197]),c_0_84])]) ).
cnf(c_0_241,hypothesis,
( sdtasdt0(xS,xS) = sz0z00
| xR = sz0z00 ),
inference(spm,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_242,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_151,c_0_81]),c_0_98])]) ).
cnf(c_0_243,negated_conjecture,
( sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)) != sdtasdt0(xR,xR)
| ~ sdtlseqdt0(xS,sz0z00) ),
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_236,c_0_237]),c_0_230]),c_0_238]),c_0_192]),c_0_166]),c_0_239]),c_0_230]),c_0_238]),c_0_230]),c_0_238]) ).
cnf(c_0_244,hypothesis,
( xR = sz0z00
| xS = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_241]),c_0_165]),c_0_165])]) ).
cnf(c_0_245,hypothesis,
sdtpldt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_166]),c_0_130])]) ).
cnf(c_0_246,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_242,c_0_129]),c_0_81]),c_0_173]),c_0_130]),c_0_98])]) ).
cnf(c_0_247,hypothesis,
( sdtpldt0(sdtasdt0(xS,xS),sdtasdt0(xR,xR)) != sdtasdt0(xR,xR)
| ~ sdtlseqdt0(xS,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_214]),c_0_197]),c_0_190])]) ).
cnf(c_0_248,negated_conjecture,
xS = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_226,c_0_244]),c_0_223]),c_0_192]),c_0_166]),c_0_245]),c_0_192]),c_0_166]),c_0_239]),c_0_246]),c_0_232]),c_0_232]),c_0_81])]) ).
cnf(c_0_249,hypothesis,
sdtpldt0(sz0z00,sdtasdt0(xR,xR)) != sdtasdt0(xR,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)],[c_0_247,c_0_248]),c_0_248]),c_0_223]),c_0_248]),c_0_160])]) ).
cnf(c_0_250,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_129]),c_0_190])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG060+2 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat May 18 11:59:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.43/1.55 # Version: 3.1.0
% 8.43/1.55 # Preprocessing class: FSLSSMSMSSSNFFN.
% 8.43/1.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.43/1.55 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 8.43/1.55 # Starting new_bool_3 with 300s (1) cores
% 8.43/1.55 # Starting new_bool_1 with 300s (1) cores
% 8.43/1.55 # Starting sh5l with 300s (1) cores
% 8.43/1.55 # C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 26355 completed with status 0
% 8.43/1.55 # Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 8.43/1.55 # Preprocessing class: FSLSSMSMSSSNFFN.
% 8.43/1.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.43/1.55 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 8.43/1.55 # No SInE strategy applied
% 8.43/1.55 # Search class: FGHSF-FFMM21-MFFFFFNN
% 8.43/1.55 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 8.43/1.55 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 8.43/1.55 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 8.43/1.55 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 8.43/1.55 # Starting new_bool_3 with 136s (1) cores
% 8.43/1.55 # Starting new_bool_1 with 136s (1) cores
% 8.43/1.55 # G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 26362 completed with status 0
% 8.43/1.55 # Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 8.43/1.55 # Preprocessing class: FSLSSMSMSSSNFFN.
% 8.43/1.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.43/1.55 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 8.43/1.55 # No SInE strategy applied
% 8.43/1.55 # Search class: FGHSF-FFMM21-MFFFFFNN
% 8.43/1.55 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 8.43/1.55 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 8.43/1.55 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 8.43/1.55 # Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 8.43/1.55 # Preprocessing time : 0.002 s
% 8.43/1.55 # Presaturation interreduction done
% 8.43/1.55
% 8.43/1.55 # Proof found!
% 8.43/1.55 # SZS status Theorem
% 8.43/1.55 # SZS output start CNFRefutation
% See solution above
% 8.43/1.55 # Parsed axioms : 59
% 8.43/1.55 # Removed by relevancy pruning/SinE : 0
% 8.43/1.55 # Initial clauses : 99
% 8.43/1.55 # Removed in clause preprocessing : 5
% 8.43/1.55 # Initial clauses in saturation : 94
% 8.43/1.55 # Processed clauses : 4963
% 8.43/1.55 # ...of these trivial : 1225
% 8.43/1.55 # ...subsumed : 1447
% 8.43/1.55 # ...remaining for further processing : 2291
% 8.43/1.55 # Other redundant clauses eliminated : 6
% 8.43/1.55 # Clauses deleted for lack of memory : 0
% 8.43/1.55 # Backward-subsumed : 29
% 8.43/1.55 # Backward-rewritten : 1234
% 8.43/1.55 # Generated clauses : 96556
% 8.43/1.55 # ...of the previous two non-redundant : 84221
% 8.43/1.55 # ...aggressively subsumed : 0
% 8.43/1.55 # Contextual simplify-reflections : 94
% 8.43/1.55 # Paramodulations : 96543
% 8.43/1.55 # Factorizations : 0
% 8.43/1.55 # NegExts : 0
% 8.43/1.55 # Equation resolutions : 13
% 8.43/1.55 # Disequality decompositions : 0
% 8.43/1.55 # Total rewrite steps : 198795
% 8.43/1.55 # ...of those cached : 197664
% 8.43/1.55 # Propositional unsat checks : 0
% 8.43/1.55 # Propositional check models : 0
% 8.43/1.55 # Propositional check unsatisfiable : 0
% 8.43/1.55 # Propositional clauses : 0
% 8.43/1.55 # Propositional clauses after purity: 0
% 8.43/1.55 # Propositional unsat core size : 0
% 8.43/1.55 # Propositional preprocessing time : 0.000
% 8.43/1.55 # Propositional encoding time : 0.000
% 8.43/1.55 # Propositional solver time : 0.000
% 8.43/1.55 # Success case prop preproc time : 0.000
% 8.43/1.55 # Success case prop encoding time : 0.000
% 8.43/1.55 # Success case prop solver time : 0.000
% 8.43/1.55 # Current number of processed clauses : 931
% 8.43/1.55 # Positive orientable unit clauses : 536
% 8.43/1.55 # Positive unorientable unit clauses: 0
% 8.43/1.55 # Negative unit clauses : 6
% 8.43/1.55 # Non-unit-clauses : 389
% 8.43/1.55 # Current number of unprocessed clauses: 78041
% 8.43/1.55 # ...number of literals in the above : 278790
% 8.43/1.55 # Current number of archived formulas : 0
% 8.43/1.55 # Current number of archived clauses : 1357
% 8.43/1.55 # Clause-clause subsumption calls (NU) : 71542
% 8.43/1.55 # Rec. Clause-clause subsumption calls : 35013
% 8.43/1.55 # Non-unit clause-clause subsumptions : 1535
% 8.43/1.55 # Unit Clause-clause subsumption calls : 16004
% 8.43/1.55 # Rewrite failures with RHS unbound : 0
% 8.43/1.55 # BW rewrite match attempts : 3116
% 8.43/1.55 # BW rewrite match successes : 216
% 8.43/1.55 # Condensation attempts : 0
% 8.43/1.55 # Condensation successes : 0
% 8.43/1.55 # Termbank termtop insertions : 2575041
% 8.43/1.55 # Search garbage collected termcells : 911
% 8.43/1.55
% 8.43/1.55 # -------------------------------------------------
% 8.43/1.55 # User time : 0.980 s
% 8.43/1.55 # System time : 0.044 s
% 8.43/1.55 # Total time : 1.024 s
% 8.43/1.55 # Maximum resident set size: 1980 pages
% 8.43/1.55
% 8.43/1.55 # -------------------------------------------------
% 8.43/1.55 # User time : 4.979 s
% 8.43/1.55 # System time : 0.130 s
% 8.43/1.55 # Total time : 5.109 s
% 8.43/1.55 # Maximum resident set size: 1768 pages
% 8.43/1.55 % E---3.1 exiting
% 8.43/1.55 % E exiting
%------------------------------------------------------------------------------