%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG058+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:06:12 PM UTC 2026
% Result : Theorem 10.82s 2.03s
% Output : CNFRefutation 10.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 177 ( 83 unt; 0 def)
% Number of atoms : 422 ( 114 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 404 ( 159 ~; 159 |; 67 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 131 ( 1 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMNeg,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
& sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(m__1854,hypothesis,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
fof(m__1783,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(mScZero,axiom,
! [X1] :
( aScalar0(X1)
=> ( smndt0(sz0z00) = sz0z00
& smndt0(smndt0(X1)) = X1
& sdtpldt0(smndt0(X1),X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtpldt0(sz0z00,X1) = X1
& sdtpldt0(X1,sz0z00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(m__1837,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__1949,hypothesis,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
fof(m__1726,hypothesis,
( xq = sziznziztdt0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xq,X1) = sdtlbdtrb0(xt,X1) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(m__1709,hypothesis,
( xp = sziznziztdt0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xp,X1) = sdtlbdtrb0(xs,X1) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mLETot,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).
fof(mMDNeg,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMDNeg) ).
fof(mPosMon,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(sz0z00,X1) )
=> ( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtpldt0(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
fof(m__1746,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
fof(m__1766,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
fof(mLEMonM,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X4)
& aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X3,X4)
& sdtlseqdt0(sz0z00,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
fof(mLEMon,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X4)
& aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X3,X4)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
fof(m__1873,hypothesis,
( xH = sdtasdt0(xA,xB)
& aScalar0(xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
fof(mArith,axiom,
! [X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(m__1911,hypothesis,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
fof(m__1820,hypothesis,
( xE = sdtasasdt0(xp,xq)
& aScalar0(xE) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(mLEASm,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEASm) ).
fof(m__,conjecture,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__2004,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2004) ).
fof(c_0_30,plain,
! [X70,X71] :
( ( ~ aScalar0(X71)
| ~ aScalar0(X70)
| sdtasdt0(smndt0(X70),X71) = smndt0(sdtasdt0(X70,X71)) )
& ( ~ aScalar0(X71)
| ~ aScalar0(X70)
| sdtasdt0(X70,smndt0(X71)) = smndt0(sdtasdt0(X70,X71)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])])]) ).
fof(c_0_31,plain,
! [X46,X47] :
( aScalar0(sdtasdt0(X46,X47))
| ~ aScalar0(X47)
| ~ aScalar0(X46) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])])]) ).
cnf(c_0_32,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_34,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_35,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
fof(c_0_36,plain,
! [X33] :
( ( ~ aScalar0(X33)
| smndt0(sz0z00) = sz0z00 )
& ( ~ aScalar0(X33)
| smndt0(smndt0(X33)) = X33 )
& ( ~ aScalar0(X33)
| sdtpldt0(smndt0(X33),X33) = sz0z00 )
& ( ~ aScalar0(X33)
| sdtpldt0(X33,smndt0(X33)) = sz0z00 )
& ( ~ aScalar0(X33)
| sdtasdt0(sz0z00,X33) = sz0z00 )
& ( ~ aScalar0(X33)
| sdtasdt0(X33,sz0z00) = sz0z00 )
& ( ~ aScalar0(X33)
| sdtpldt0(sz0z00,X33) = X33 )
& ( ~ aScalar0(X33)
| sdtpldt0(X33,sz0z00) = X33 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])])]) ).
cnf(c_0_37,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,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_32,c_0_33]),c_0_34]),c_0_35])]) ).
fof(c_0_39,plain,
! [X69] :
( aScalar0(smndt0(X69))
| ~ aScalar0(X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])])]) ).
cnf(c_0_40,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_41,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_42,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_43,plain,
( ~ aScalar0(X1)
| smndt0(sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_45,plain,
( ~ aScalar0(X1)
| smndt0(smndt0(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_47,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_48,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_49,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_50,hypothesis,
( ~ aScalar0(smndt0(xG))
| aScalar0(smndt0(xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_35])]) ).
cnf(c_0_51,plain,
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,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_32,c_0_40]),c_0_41]),c_0_42])]) ).
fof(c_0_53,plain,
! [X28] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X28,X28))
| ~ aVector0(X28) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])])]) ).
fof(c_0_54,hypothesis,
! [X65] :
( xq = sziznziztdt0(xt)
& ( sdtlbdtrb0(xq,X65) = sdtlbdtrb0(xt,X65)
| ~ aNaturalNumber0(X65) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1726])])])]) ).
fof(c_0_55,plain,
! [X25] :
( sdtlseqdt0(sz0z00,sdtasdt0(X25,X25))
| ~ aScalar0(X25) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])])]) ).
fof(c_0_56,hypothesis,
! [X64] :
( xp = sziznziztdt0(xs)
& ( sdtlbdtrb0(xp,X64) = sdtlbdtrb0(xs,X64)
| ~ aNaturalNumber0(X64) )
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& aVector0(xp) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1709])])])]) ).
cnf(c_0_57,plain,
( ~ aScalar0(X1)
| sdtasdt0(X1,sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_58,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_59,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_60,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_32]),c_0_37]) ).
fof(c_0_61,plain,
! [X21,X22] :
( sdtlseqdt0(X22,X21)
| sdtlseqdt0(X21,X22)
| ~ aScalar0(X22)
| ~ aScalar0(X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])])]) ).
fof(c_0_62,plain,
! [X72,X73] :
( sdtasdt0(smndt0(X72),smndt0(X73)) = sdtasdt0(X72,X73)
| ~ aScalar0(X73)
| ~ aScalar0(X72) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMDNeg])])]) ).
cnf(c_0_63,hypothesis,
sdtasdt0(smndt0(xR),xS) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_64,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_34])]) ).
cnf(c_0_65,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_66,hypothesis,
( ~ aScalar0(smndt0(xD))
| aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_52]),c_0_42])]) ).
fof(c_0_67,plain,
! [X23,X24] :
( ( ~ aScalar0(X24)
| ~ aScalar0(X23)
| ~ sdtlseqdt0(sz0z00,X24)
| ~ sdtlseqdt0(sz0z00,X23)
| sdtlseqdt0(sz0z00,sdtasdt0(X23,X24)) )
& ( ~ aScalar0(X24)
| ~ aScalar0(X23)
| ~ sdtlseqdt0(sz0z00,X24)
| ~ sdtlseqdt0(sz0z00,X23)
| sdtlseqdt0(sz0z00,sdtpldt0(X23,X24)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])])]) ).
cnf(c_0_68,plain,
( ~ aVector0(X1)
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_69,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_70,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_71,plain,
( ~ aScalar0(X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_72,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_73,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_74,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_75,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_76,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_77,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_78,plain,
! [X17,X18,X19,X20] :
( sdtlseqdt0(sdtasdt0(X17,X19),sdtasdt0(X18,X20))
| ~ sdtlseqdt0(X19,X20)
| ~ sdtlseqdt0(sz0z00,X19)
| ~ sdtlseqdt0(X17,X18)
| ~ aScalar0(X20)
| ~ aScalar0(X19)
| ~ aScalar0(X18)
| ~ aScalar0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])])]) ).
cnf(c_0_79,plain,
( ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),sz0z00) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_57]),c_0_58]),c_0_59])]) ).
cnf(c_0_80,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_60,c_0_38]),c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_81,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_82,plain,
! [X13,X14,X15,X16] :
( sdtlseqdt0(sdtpldt0(X13,X15),sdtpldt0(X14,X16))
| ~ sdtlseqdt0(X15,X16)
| ~ sdtlseqdt0(X13,X14)
| ~ aScalar0(X16)
| ~ aScalar0(X15)
| ~ aScalar0(X14)
| ~ aScalar0(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])])]) ).
cnf(c_0_83,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(smndt0(xR),smndt0(xS)) = smndt0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_63]),c_0_48]),c_0_64])]) ).
cnf(c_0_85,hypothesis,
( ~ aScalar0(smndt0(xS))
| aScalar0(smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_65]),c_0_49])]) ).
cnf(c_0_86,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_51]),c_0_41])]) ).
cnf(c_0_87,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_88,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_89,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_90,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_74]),c_0_75])]) ).
cnf(c_0_91,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_76]),c_0_77])]) ).
cnf(c_0_92,hypothesis,
xH = sdtasdt0(xA,xB),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_93,plain,
( ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_94,hypothesis,
sdtasdt0(xR,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_64])]) ).
cnf(c_0_95,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(X1,smndt0(xR))
| sdtlseqdt0(smndt0(xR),X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_64]) ).
cnf(c_0_96,plain,
( ~ aScalar0(X1)
| sdtasdt0(sz0z00,X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_97,plain,
( ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_98,plain,
( ~ aScalar0(X1)
| sdtpldt0(sz0z00,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_99,plain,
( ~ aScalar0(X1)
| sdtpldt0(smndt0(X1),X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_100,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_83,c_0_84]),c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_101,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]) ).
cnf(c_0_102,hypothesis,
sdtlseqdt0(sz0z00,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_40]),c_0_88]),c_0_89]),c_0_41]),c_0_42])]) ).
cnf(c_0_103,hypothesis,
sdtlseqdt0(sz0z00,xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_33]),c_0_90]),c_0_91]),c_0_34]),c_0_35])]) ).
fof(c_0_104,plain,
! [X34,X35,X36] :
( ( ~ aScalar0(X36)
| ~ aScalar0(X35)
| ~ aScalar0(X34)
| sdtasdt0(X34,X35) = sdtasdt0(X35,X34) )
& ( ~ aScalar0(X36)
| ~ aScalar0(X35)
| ~ aScalar0(X34)
| sdtasdt0(sdtasdt0(X34,X35),X36) = sdtasdt0(X34,sdtasdt0(X35,X36)) )
& ( ~ aScalar0(X36)
| ~ aScalar0(X35)
| ~ aScalar0(X34)
| sdtpldt0(X34,X35) = sdtpldt0(X35,X34) )
& ( ~ aScalar0(X36)
| ~ aScalar0(X35)
| ~ aScalar0(X34)
| sdtpldt0(sdtpldt0(X34,X35),X36) = sdtpldt0(X34,sdtpldt0(X35,X36)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])])]) ).
cnf(c_0_105,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| aScalar0(sdtasdt0(X1,smndt0(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_32]),c_0_37]) ).
cnf(c_0_106,hypothesis,
sdtasdt0(xA,smndt0(xA)) = smndt0(xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_72]),c_0_73])]) ).
cnf(c_0_107,hypothesis,
xP = sdtasdt0(xE,xH),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_108,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_109,hypothesis,
aScalar0(xE),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_110,hypothesis,
sdtasdt0(xA,smndt0(xB)) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_92]),c_0_75]),c_0_73])]) ).
cnf(c_0_111,hypothesis,
sdtasdt0(xB,smndt0(xB)) = smndt0(xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_74]),c_0_75])]) ).
fof(c_0_112,plain,
! [X8,X9] :
( X8 = X9
| ~ sdtlseqdt0(X9,X8)
| ~ sdtlseqdt0(X8,X9)
| ~ aScalar0(X9)
| ~ aScalar0(X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])])]) ).
cnf(c_0_113,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X2,xS)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X1,smndt0(xR))
| sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_63]),c_0_48]),c_0_64])]) ).
cnf(c_0_114,hypothesis,
sdtasdt0(smndt0(xR),sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_94]),c_0_58]),c_0_59]),c_0_49])]) ).
cnf(c_0_115,hypothesis,
sdtlseqdt0(smndt0(xR),smndt0(xR)),
inference(spm,[status(thm)],[c_0_95,c_0_64]) ).
cnf(c_0_116,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_96]),c_0_59])]) ).
cnf(c_0_117,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X1,X3)
| ~ sdtlseqdt0(sz0z00,X2)
| sdtlseqdt0(X1,sdtpldt0(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_59])]) ).
cnf(c_0_118,hypothesis,
sdtpldt0(xN,smndt0(xN)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101])]) ).
cnf(c_0_119,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_87,c_0_47]),c_0_48]),c_0_49])]),c_0_102]),c_0_103])]) ).
cnf(c_0_120,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(X1,smndt0(xN))
| sdtlseqdt0(smndt0(xN),X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_101]) ).
cnf(c_0_121,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_122,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_123,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_124,hypothesis,
sdtasdt0(smndt0(xF),xD) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_125,hypothesis,
aScalar0(smndt0(xF)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_73])]) ).
cnf(c_0_126,hypothesis,
sdtasdt0(xE,smndt0(xH)) = smndt0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_107]),c_0_108]),c_0_109])]) ).
cnf(c_0_127,hypothesis,
aScalar0(smndt0(xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_110]),c_0_75]),c_0_73])]) ).
cnf(c_0_128,hypothesis,
aScalar0(smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_111]),c_0_75])]) ).
cnf(c_0_129,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_130,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_113,c_0_114]),c_0_115]),c_0_116]),c_0_102]),c_0_59]),c_0_64])]) ).
cnf(c_0_131,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(X1,smndt0(xN))
| sdtlseqdt0(X1,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]),c_0_101]),c_0_44])]) ).
cnf(c_0_132,hypothesis,
sdtlseqdt0(smndt0(xN),smndt0(xN)),
inference(spm,[status(thm)],[c_0_120,c_0_101]) ).
cnf(c_0_133,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_99]),c_0_51]) ).
cnf(c_0_134,hypothesis,
sdtpldt0(smndt0(xN),xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_100]),c_0_101])]) ).
fof(c_0_135,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_136,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| aScalar0(sdtasdt0(X1,sdtasdt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_123]),c_0_37]) ).
cnf(c_0_137,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(smndt0(xF),sdtasdt0(xD,X1)) = sdtasdt0(smndt0(xS),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_41])]),c_0_125])]) ).
cnf(c_0_138,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xE,sdtasdt0(smndt0(xH),X1)) = sdtasdt0(smndt0(xP),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_126]),c_0_109])]),c_0_127])]) ).
cnf(c_0_139,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xC,sdtasdt0(smndt0(xG),X1)) = sdtasdt0(smndt0(xR),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_38]),c_0_35])]),c_0_128])]) ).
cnf(c_0_140,hypothesis,
( ~ sdtlseqdt0(smndt0(xN),sz0z00)
| smndt0(xN) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_59]),c_0_101])]) ).
cnf(c_0_141,hypothesis,
sdtlseqdt0(smndt0(xN),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_101])]) ).
cnf(c_0_142,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,sz0z00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_143,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_133,c_0_134]),c_0_100]),c_0_44]),c_0_101])]) ).
fof(c_0_144,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(fof_simplification,[status(thm)],[c_0_135]) ).
cnf(c_0_145,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(smndt0(xS),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_41]),c_0_125])]) ).
cnf(c_0_146,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),X2) = sdtasdt0(X1,smndt0(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_45]),c_0_51]) ).
cnf(c_0_147,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(smndt0(xP),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_138]),c_0_127]),c_0_109])]) ).
cnf(c_0_148,hypothesis,
aScalar0(xP),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_149,hypothesis,
( ~ aScalar0(smndt0(xH))
| aScalar0(smndt0(xP)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_126]),c_0_109])]) ).
cnf(c_0_150,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(smndt0(xR),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_139]),c_0_128]),c_0_35])]) ).
cnf(c_0_151,hypothesis,
smndt0(xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]) ).
cnf(c_0_152,hypothesis,
sdtpldt0(sz0z00,xN) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_44])]) ).
fof(c_0_153,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(fof_nnf,[status(thm)],[c_0_144]) ).
cnf(c_0_154,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(xS,smndt0(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_48])]) ).
cnf(c_0_155,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_60,c_0_52]),c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_156,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(xP,smndt0(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_146]),c_0_148])]) ).
cnf(c_0_157,hypothesis,
smndt0(smndt0(xP)) = xP,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_126]),c_0_107]),c_0_108]),c_0_109])]) ).
cnf(c_0_158,hypothesis,
aScalar0(smndt0(xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_51]),c_0_108])]) ).
cnf(c_0_159,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(xR,smndt0(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_146]),c_0_49])]) ).
cnf(c_0_160,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(split_conjunct,[status(thm)],[m__2004]) ).
cnf(c_0_161,hypothesis,
xN = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_151]),c_0_143]),c_0_152]) ).
cnf(c_0_162,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,sdtasdt0(X2,sdtasdt0(X1,X2)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_123]),c_0_37]) ).
cnf(c_0_163,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xE,sdtasdt0(xH,X1)) = sdtasdt0(xP,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_107]),c_0_108]),c_0_109])]) ).
cnf(c_0_164,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_165,hypothesis,
aScalar0(sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_86])]) ).
cnf(c_0_166,hypothesis,
aScalar0(sdtasdt0(xP,xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158])]) ).
cnf(c_0_167,hypothesis,
aScalar0(sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_80]),c_0_64])]) ).
cnf(c_0_168,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),sz0z00),
inference(rw,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_169,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xP,xP)),
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_162,c_0_163]),c_0_107]),c_0_108]),c_0_109]),c_0_107]),c_0_148])]) ).
cnf(c_0_170,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xF,sdtasdt0(xD,X1)) = sdtasdt0(xS,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_171,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(xC,sdtasdt0(xG,X1)) = sdtasdt0(xR,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_172,negated_conjecture,
( ~ sdtlseqdt0(sdtasdt0(xP,xP),sdtasdt0(xR,xR))
| ~ sdtlseqdt0(sdtasdt0(xP,xP),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_164,c_0_97]),c_0_165]),c_0_166]),c_0_167])]) ).
cnf(c_0_173,hypothesis,
sdtasdt0(xP,xP) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_168]),c_0_169]),c_0_166]),c_0_59])]) ).
cnf(c_0_174,hypothesis,
sdtlseqdt0(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_170]),c_0_40]),c_0_41]),c_0_42]),c_0_40]),c_0_48])]) ).
cnf(c_0_175,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_162,c_0_171]),c_0_33]),c_0_34]),c_0_35]),c_0_33]),c_0_49])]) ).
cnf(c_0_176,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_173]),c_0_174]),c_0_173]),c_0_175])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG058+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:11:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 10.82/2.03 % Version: 3.5.1
% 10.82/2.03 % Preprocessing class: FSLSSMSMSSSNFFN.
% 10.82/2.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.82/2.03 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 10.82/2.03 % Starting new_bool_3 with 300s (1) cores
% 10.82/2.03 % Starting new_bool_1 with 300s (1) cores
% 10.82/2.03 % Starting sh5l with 300s (1) cores
% 10.82/2.03 % sh5l with pid 1398254 completed with status 0
% 10.82/2.03 % Result found by sh5l
% 10.82/2.03 % Preprocessing class: FSLSSMSMSSSNFFN.
% 10.82/2.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.82/2.03 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 10.82/2.03 % Starting new_bool_3 with 300s (1) cores
% 10.82/2.03 % Starting new_bool_1 with 300s (1) cores
% 10.82/2.03 % Starting sh5l with 300s (1) cores
% 10.82/2.03 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 10.82/2.03 % SinE strategy is gf500_gu_R04_F100_L20000
% 10.82/2.03 % Search class: FGHSF-FFMM21-MFFFFFNN
% 10.82/2.03 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 10.82/2.03 % Starting SubtermCWHack with 28s (1) cores
% 10.82/2.03 % SubtermCWHack with pid 1398262 completed with status 0
% 10.82/2.03 % Result found by SubtermCWHack
% 10.82/2.03 % Preprocessing class: FSLSSMSMSSSNFFN.
% 10.82/2.03 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 10.82/2.03 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 10.82/2.03 % Starting new_bool_3 with 300s (1) cores
% 10.82/2.03 % Starting new_bool_1 with 300s (1) cores
% 10.82/2.03 % Starting sh5l with 300s (1) cores
% 10.82/2.03 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 10.82/2.03 % SinE strategy is gf500_gu_R04_F100_L20000
% 10.82/2.03 % Search class: FGHSF-FFMM21-MFFFFFNN
% 10.82/2.03 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 10.82/2.03 % Starting SubtermCWHack with 28s (1) cores
% 10.82/2.03 % Preprocessing time : 0.003 s
% 10.82/2.03
% 10.82/2.03 % Proof found!
% 10.82/2.03 % SZS status Theorem
% 10.82/2.03 % SZS output start CNFRefutation
% See solution above
% 10.82/2.03 % Parsed axioms : 58
% 10.82/2.03 % Removed by relevancy pruning/SinE : 0
% 10.82/2.03 % Initial clauses : 96
% 10.82/2.03 % Removed in clause preprocessing : 5
% 10.82/2.03 % Initial clauses in saturation : 91
% 10.82/2.03 % Processed clauses : 6715
% 10.82/2.03 % ...of these trivial : 585
% 10.82/2.03 % ...subsumed : 3295
% 10.82/2.03 % ...remaining for further processing : 2835
% 10.82/2.03 % Other redundant clauses eliminated : 7
% 10.82/2.03 % Clauses deleted for lack of memory : 0
% 10.82/2.03 % Backward-subsumed : 94
% 10.82/2.03 % Backward-rewritten : 453
% 10.82/2.03 % Generated clauses : 121287
% 10.82/2.03 % ...of the previous two non-redundant : 103123
% 10.82/2.03 % ...aggressively subsumed : 0
% 10.82/2.03 % Contextual simplify-reflections : 109
% 10.82/2.03 % Paramodulations : 121269
% 10.82/2.03 % Factorizations : 0
% 10.82/2.03 % NegExts : 0
% 10.82/2.03 % Equation resolutions : 18
% 10.82/2.03 % Disequality decompositions : 0
% 10.82/2.03 % Total rewrite steps : 168003
% 10.82/2.03 % ...of those cached : 167212
% 10.82/2.03 % Propositional unsat checks : 0
% 10.82/2.03 % Propositional check models : 0
% 10.82/2.03 % Propositional check unsatisfiable : 0
% 10.82/2.03 % Propositional clauses : 0
% 10.82/2.03 % Propositional clauses after purity: 0
% 10.82/2.03 % Propositional unsat core size : 0
% 10.82/2.03 % Propositional preprocessing time : 0.000
% 10.82/2.03 % Propositional encoding time : 0.000
% 10.82/2.03 % Propositional solver time : 0.000
% 10.82/2.03 % Success case prop preproc time : 0.000
% 10.82/2.03 % Success case prop encoding time : 0.000
% 10.82/2.03 % Success case prop solver time : 0.000
% 10.82/2.03 % Current number of processed clauses : 2285
% 10.82/2.03 % Positive orientable unit clauses : 870
% 10.82/2.03 % Positive unorientable unit clauses: 0
% 10.82/2.03 % Negative unit clauses : 4
% 10.82/2.03 % Non-unit-clauses : 1411
% 10.82/2.03 % Current number of unprocessed clauses: 96197
% 10.82/2.03 % ...number of literals in the above : 421388
% 10.82/2.03 % Current number of archived formulas : 0
% 10.82/2.03 % Current number of archived clauses : 547
% 10.82/2.03 % Clause-clause subsumption calls (NU) : 390644
% 10.82/2.03 % Rec. Clause-clause subsumption calls : 190683
% 10.82/2.03 % Non-unit clause-clause subsumptions : 3479
% 10.82/2.03 % Unit Clause-clause subsumption calls : 32572
% 10.82/2.03 % Rewrite failures with RHS unbound : 0
% 10.82/2.03 % BW rewrite match attempts : 3582
% 10.82/2.03 % BW rewrite match successes : 98
% 10.82/2.03 % Condensation attempts : 0
% 10.82/2.03 % Condensation successes : 0
% 10.82/2.03 % Termbank termtop insertions : 2618629
% 10.82/2.03 % Search garbage collected termcells : 920
% 10.82/2.03
% 10.82/2.03 % -------------------------------------------------
% 10.82/2.03 % User time : 1.288 s
% 10.82/2.03 % System time : 0.087 s
% 10.82/2.03 % Total time : 1.375 s
% 10.82/2.03 % Maximum resident set size: 3960 pages
% 10.82/2.03
% 10.82/2.03 % -------------------------------------------------
% 10.82/2.03 % User time : 1.291 s
% 10.82/2.03 % System time : 0.091 s
% 10.82/2.03 % Total time : 1.383 s
% 10.82/2.03 % Maximum resident set size: 4608 pages
% 10.82/2.03 % E exiting
%------------------------------------------------------------------------------