%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG067+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:05:12 PM UTC 2026
% Result : Theorem 14.49s 9.21s
% Output : CNFRefutation 14.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 36
% Syntax : Number of formulae : 197 ( 87 unt; 0 def)
% Number of atoms : 508 ( 133 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 529 ( 218 ~; 217 |; 70 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 17 con; 0-2 aty)
% Number of variables : 166 ( 2 sgn 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMNeg,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
& sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1930,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
fof(m__1800,hypothesis,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(m__1837,hypothesis,
( aScalar0(xF)
& xF = sdtasdt0(xA,xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mScZero,axiom,
! [X1] :
( aScalar0(X1)
=> ( sdtpldt0(X1,sz0z00) = X1
& sdtpldt0(sz0z00,X1) = X1
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtpldt0(smndt0(X1),X1) = sz0z00
& smndt0(smndt0(X1)) = X1
& smndt0(sz0z00) = sz0z00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScSqPos) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(m__1949,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(m__1892,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
fof(mPosMon,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X2) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
fof(m__1726,hypothesis,
( aVector0(xq)
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
fof(m__1746,hypothesis,
( aScalar0(xA)
& xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
fof(m__1854,hypothesis,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1854) ).
fof(m__1766,hypothesis,
( aScalar0(xB)
& xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(m__1709,hypothesis,
( aVector0(xp)
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mLEMon) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mLEMonM,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3)
& aScalar0(X4) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(sz0z00,X3)
& sdtlseqdt0(X3,X4) )
=> sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEMonM) ).
fof(mArith,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(mLERef,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLERef) ).
fof(mLEASm,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEASm) ).
fof(mLETrn,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETrn) ).
fof(m__1911,hypothesis,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
fof(m__1873,hypothesis,
( aScalar0(xH)
& xH = sdtasdt0(xA,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
fof(m__1820,hypothesis,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(m__2004,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2004) ).
fof(mSqrt,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X2)
& sdtasdt0(X1,X1) = sdtasdt0(X2,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqrt) ).
fof(mLETot,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).
fof(mDistr2,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3)
& aScalar0(X4) )
=> sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
fof(m__,conjecture,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDistr,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).
fof(m__2104,hypothesis,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2104) ).
fof(c_0_36,plain,
! [X98,X99] :
( ( sdtasdt0(X98,smndt0(X99)) = smndt0(sdtasdt0(X98,X99))
| ~ aScalar0(X98)
| ~ aScalar0(X99) )
& ( sdtasdt0(smndt0(X98),X99) = smndt0(sdtasdt0(X98,X99))
| ~ aScalar0(X98)
| ~ aScalar0(X99) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])]) ).
fof(c_0_37,plain,
! [X84,X85] :
( ~ aScalar0(X84)
| ~ aScalar0(X85)
| aScalar0(sdtasdt0(X84,X85)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])]) ).
cnf(c_0_38,plain,
( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_40,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_41,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_42,plain,
! [X87] :
( ( sdtpldt0(X87,sz0z00) = X87
| ~ aScalar0(X87) )
& ( sdtpldt0(sz0z00,X87) = X87
| ~ aScalar0(X87) )
& ( sdtasdt0(X87,sz0z00) = sz0z00
| ~ aScalar0(X87) )
& ( sdtasdt0(sz0z00,X87) = sz0z00
| ~ aScalar0(X87) )
& ( sdtpldt0(X87,smndt0(X87)) = sz0z00
| ~ aScalar0(X87) )
& ( sdtpldt0(smndt0(X87),X87) = sz0z00
| ~ aScalar0(X87) )
& ( smndt0(smndt0(X87)) = X87
| ~ aScalar0(X87) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])]) ).
cnf(c_0_43,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,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_38,c_0_39]),c_0_40]),c_0_41])]) ).
fof(c_0_45,plain,
! [X86] :
( ~ aScalar0(X86)
| aScalar0(smndt0(X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])]) ).
fof(c_0_46,plain,
! [X139] :
( ~ aVector0(X139)
| sdtlseqdt0(sz0z00,sdtasasdt0(X139,X139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])]) ).
fof(c_0_47,plain,
! [X120] :
( ~ aScalar0(X120)
| sdtlseqdt0(sz0z00,sdtasdt0(X120,X120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])]) ).
cnf(c_0_48,plain,
( smndt0(smndt0(X1)) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_50,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_51,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_52,hypothesis,
( aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xD)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_41])]) ).
cnf(c_0_53,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_54,plain,
! [X118,X119] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X118,X119))
| ~ sdtlseqdt0(sz0z00,X118)
| ~ sdtlseqdt0(sz0z00,X119)
| ~ aScalar0(X118)
| ~ aScalar0(X119) )
& ( sdtlseqdt0(sz0z00,sdtasdt0(X118,X119))
| ~ sdtlseqdt0(sz0z00,X118)
| ~ sdtlseqdt0(sz0z00,X119)
| ~ aScalar0(X118)
| ~ aScalar0(X119) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])]) ).
cnf(c_0_55,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_57,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_58,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_60,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_61,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_62,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_63,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_64,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_65,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_66,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_67,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
fof(c_0_68,plain,
! [X108,X109,X110,X111] :
( ~ aScalar0(X108)
| ~ aScalar0(X109)
| ~ aScalar0(X110)
| ~ aScalar0(X111)
| ~ sdtlseqdt0(X108,X109)
| ~ sdtlseqdt0(X110,X111)
| sdtlseqdt0(sdtpldt0(X108,X110),sdtpldt0(X109,X111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])]) ).
cnf(c_0_69,plain,
( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_38]),c_0_43]) ).
cnf(c_0_70,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_38,c_0_49]),c_0_50]),c_0_51])]) ).
cnf(c_0_71,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_40])]) ).
cnf(c_0_72,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_73,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_74,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
cnf(c_0_75,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_61]),c_0_62])]) ).
cnf(c_0_76,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_63]),c_0_64])]) ).
cnf(c_0_77,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_38,c_0_65]),c_0_66]),c_0_67])]) ).
cnf(c_0_78,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_68]) ).
cnf(c_0_79,plain,
( sdtpldt0(sz0z00,X1) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_80,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_81,plain,
( sdtpldt0(smndt0(X1),X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_82,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_69,c_0_70]),c_0_49]),c_0_50]),c_0_51])]) ).
cnf(c_0_83,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_70]),c_0_51])]),c_0_71])]) ).
cnf(c_0_84,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_72,c_0_39]),c_0_73]),c_0_74]),c_0_40]),c_0_41])]) ).
cnf(c_0_85,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_72,c_0_65]),c_0_75]),c_0_76]),c_0_66]),c_0_67])]) ).
fof(c_0_86,plain,
! [X112,X113,X114,X115] :
( ~ aScalar0(X112)
| ~ aScalar0(X113)
| ~ aScalar0(X114)
| ~ aScalar0(X115)
| ~ sdtlseqdt0(X112,X113)
| ~ sdtlseqdt0(sz0z00,X114)
| ~ sdtlseqdt0(X114,X115)
| sdtlseqdt0(sdtasdt0(X112,X114),sdtasdt0(X113,X115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])]) ).
cnf(c_0_87,plain,
( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_88,hypothesis,
( aScalar0(smndt0(xR))
| ~ aScalar0(smndt0(xG)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_77]),c_0_67])]) ).
fof(c_0_89,plain,
! [X88,X89,X90] :
( ( sdtpldt0(sdtpldt0(X88,X89),X90) = sdtpldt0(X88,sdtpldt0(X89,X90))
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) )
& ( sdtpldt0(X88,X89) = sdtpldt0(X89,X88)
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) )
& ( sdtasdt0(sdtasdt0(X88,X89),X90) = sdtasdt0(X88,sdtasdt0(X89,X90))
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) )
& ( sdtasdt0(X88,X89) = sdtasdt0(X89,X88)
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])]) ).
cnf(c_0_90,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_78,c_0_79]),c_0_80])]) ).
cnf(c_0_91,hypothesis,
sdtpldt0(xN,smndt0(xN)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_92,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_72,c_0_49]),c_0_50]),c_0_51])]),c_0_84]),c_0_85])]) ).
cnf(c_0_93,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
fof(c_0_94,plain,
! [X102] :
( ~ aScalar0(X102)
| sdtlseqdt0(X102,X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])]) ).
cnf(c_0_95,plain,
( sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_96,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_87,c_0_49]),c_0_50]),c_0_51])]) ).
cnf(c_0_97,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_53]),c_0_66])]) ).
cnf(c_0_98,plain,
( sdtasdt0(sz0z00,X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_99,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_100,plain,
( sdtpldt0(X1,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_101,plain,
! [X103,X104] :
( ~ aScalar0(X103)
| ~ aScalar0(X104)
| ~ sdtlseqdt0(X103,X104)
| ~ sdtlseqdt0(X104,X103)
| X103 = X104 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])]) ).
cnf(c_0_102,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_90,c_0_91]),c_0_92]),c_0_83]),c_0_93])]) ).
cnf(c_0_103,plain,
( sdtlseqdt0(X1,X1)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_104,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xN))
| ~ sdtlseqdt0(X1,smndt0(xR))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xS)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_50])]),c_0_97])]) ).
cnf(c_0_105,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_106,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_98]),c_0_80])]) ).
cnf(c_0_107,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_81]),c_0_53]) ).
cnf(c_0_108,hypothesis,
sdtpldt0(smndt0(xN),xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_82]),c_0_83])]) ).
fof(c_0_109,plain,
! [X105,X106,X107] :
( ~ aScalar0(X105)
| ~ aScalar0(X106)
| ~ aScalar0(X107)
| ~ sdtlseqdt0(X105,X106)
| ~ sdtlseqdt0(X106,X107)
| sdtlseqdt0(X105,X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])]) ).
cnf(c_0_110,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_111,hypothesis,
sdtlseqdt0(smndt0(xN),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_83])]) ).
cnf(c_0_112,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xN))
| ~ sdtlseqdt0(X1,smndt0(xR))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]),c_0_84]),c_0_80])]) ).
cnf(c_0_113,plain,
( sdtpldt0(X1,sz0z00) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_114,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_107,c_0_108]),c_0_82]),c_0_93]),c_0_83])]) ).
cnf(c_0_115,hypothesis,
xP = sdtasdt0(xE,xH),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_116,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_117,hypothesis,
aScalar0(xE),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_118,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(split_conjunct,[status(thm)],[m__2004]) ).
cnf(c_0_119,plain,
( sdtlseqdt0(X1,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_120,hypothesis,
( smndt0(xN) = sz0z00
| ~ sdtlseqdt0(sz0z00,smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_83]),c_0_80])]) ).
cnf(c_0_121,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_103]),c_0_97])]) ).
cnf(c_0_122,hypothesis,
sdtpldt0(sz0z00,xN) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_93])]) ).
cnf(c_0_123,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_38,c_0_115]),c_0_116]),c_0_117])]) ).
cnf(c_0_124,hypothesis,
( sdtasdt0(xP,xP) = xN
| ~ sdtlseqdt0(xN,sdtasdt0(xP,xP))
| ~ aScalar0(sdtasdt0(xP,xP)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_118]),c_0_93])]) ).
cnf(c_0_125,plain,
( sdtlseqdt0(X1,sdtasdt0(X2,X2))
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(sdtasdt0(X2,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_58]),c_0_80])]) ).
cnf(c_0_126,hypothesis,
aScalar0(xP),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_127,hypothesis,
smndt0(xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]) ).
cnf(c_0_128,hypothesis,
sdtpldt0(xN,sz0z00) = xN,
inference(rw,[status(thm)],[c_0_114,c_0_122]) ).
cnf(c_0_129,plain,
( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_130,hypothesis,
( aScalar0(smndt0(xP))
| ~ aScalar0(smndt0(xH)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_123]),c_0_117])]) ).
cnf(c_0_131,hypothesis,
( sdtasdt0(xP,xP) = xN
| ~ sdtlseqdt0(xN,sz0z00)
| ~ aScalar0(sdtasdt0(xP,xP)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_93]),c_0_126])]) ).
cnf(c_0_132,hypothesis,
xN = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_127]),c_0_128]) ).
cnf(c_0_133,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_129,c_0_93]) ).
cnf(c_0_134,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_69,c_0_123]),c_0_115]),c_0_116]),c_0_117])]) ).
cnf(c_0_135,hypothesis,
aScalar0(smndt0(xP)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_53]),c_0_116])]) ).
cnf(c_0_136,hypothesis,
( sdtasdt0(xP,xP) = sz0z00
| ~ aScalar0(sdtasdt0(xP,xP)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_132]),c_0_132]),c_0_106])]) ).
fof(c_0_137,plain,
! [X121,X122] :
( ~ aScalar0(X121)
| ~ aScalar0(X122)
| ~ sdtlseqdt0(sz0z00,X121)
| ~ sdtlseqdt0(sz0z00,X122)
| sdtasdt0(X121,X121) != sdtasdt0(X122,X122)
| X121 = X122 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqrt])]) ).
cnf(c_0_138,plain,
( sdtasdt0(sz0z00,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_98]),c_0_133]),c_0_80])]) ).
cnf(c_0_139,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_78,c_0_79]),c_0_80])]) ).
cnf(c_0_140,hypothesis,
sdtpldt0(xP,smndt0(xP)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_134]),c_0_135])]) ).
cnf(c_0_141,hypothesis,
sdtasdt0(xP,xP) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_43]),c_0_126])]) ).
cnf(c_0_142,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_143,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_137]) ).
cnf(c_0_144,hypothesis,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_133]),c_0_80])]) ).
cnf(c_0_145,hypothesis,
( sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(smndt0(xP),X1)
| ~ sdtlseqdt0(xP,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_135]),c_0_126])]) ).
cnf(c_0_146,hypothesis,
sdtasdt0(xP,smndt0(xP)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_141]),c_0_133]),c_0_126])]) ).
fof(c_0_147,plain,
! [X116,X117] :
( ~ aScalar0(X116)
| ~ aScalar0(X117)
| sdtlseqdt0(X116,X117)
| sdtlseqdt0(X117,X116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])]) ).
fof(c_0_148,plain,
! [X94,X95,X96,X97] :
( ~ aScalar0(X94)
| ~ aScalar0(X95)
| ~ aScalar0(X96)
| ~ aScalar0(X97)
| sdtasdt0(sdtpldt0(X94,X95),sdtpldt0(X96,X97)) = sdtpldt0(sdtpldt0(sdtasdt0(X94,X96),sdtasdt0(X94,X97)),sdtpldt0(sdtasdt0(X95,X96),sdtasdt0(X95,X97))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr2])]) ).
cnf(c_0_149,hypothesis,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_142,c_0_93]) ).
cnf(c_0_150,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_69,c_0_44]),c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_151,plain,
( X1 = sz0z00
| sdtasdt0(X1,X1) != sz0z00
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X1) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_103]),c_0_80])]),c_0_144]) ).
cnf(c_0_152,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xP))
| ~ sdtlseqdt0(xP,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_103]),c_0_135])]) ).
cnf(c_0_153,hypothesis,
sdtasdt0(smndt0(xP),smndt0(xP)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_146]),c_0_133]),c_0_135]),c_0_126])]) ).
cnf(c_0_154,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_147]) ).
cnf(c_0_155,plain,
( sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4)))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_148]) ).
cnf(c_0_156,hypothesis,
sdtasdt0(xS,smndt0(xR)) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_149]),c_0_97]),c_0_50])]) ).
cnf(c_0_157,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_69,c_0_77]),c_0_65]),c_0_66]),c_0_67])]) ).
cnf(c_0_158,hypothesis,
sdtpldt0(smndt0(xS),xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_150]),c_0_71])]) ).
fof(c_0_159,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_160,plain,
! [X91,X92,X93] :
( ( sdtasdt0(X91,sdtpldt0(X92,X93)) = sdtpldt0(sdtasdt0(X91,X92),sdtasdt0(X91,X93))
| ~ aScalar0(X91)
| ~ aScalar0(X92)
| ~ aScalar0(X93) )
& ( sdtasdt0(sdtpldt0(X91,X92),X93) = sdtpldt0(sdtasdt0(X91,X93),sdtasdt0(X92,X93))
| ~ aScalar0(X91)
| ~ aScalar0(X92)
| ~ aScalar0(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])]) ).
cnf(c_0_161,hypothesis,
( smndt0(xP) = sz0z00
| ~ sdtlseqdt0(xP,sz0z00) ),
inference(cn,[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_135])]) ).
cnf(c_0_162,hypothesis,
( sdtlseqdt0(X1,xP)
| sdtlseqdt0(xP,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_154,c_0_126]) ).
cnf(c_0_163,hypothesis,
( sdtpldt0(sdtpldt0(xN,sdtasdt0(xR,X1)),sdtpldt0(sdtasdt0(X2,xS),sdtasdt0(X2,X1))) = sdtasdt0(sdtpldt0(xR,X2),sdtpldt0(xS,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_49]),c_0_50]),c_0_51])]) ).
cnf(c_0_164,hypothesis,
sdtasdt0(xS,xR) = xN,
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_38,c_0_156]),c_0_82]),c_0_157]),c_0_97]),c_0_50])]) ).
cnf(c_0_165,hypothesis,
sdtpldt0(xS,sz0z00) = sdtpldt0(sz0z00,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_158]),c_0_150]),c_0_50]),c_0_71])]) ).
cnf(c_0_166,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_167,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_168,hypothesis,
( xP = sz0z00
| ~ sdtlseqdt0(xP,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_161]),c_0_133]),c_0_126])]) ).
cnf(c_0_169,hypothesis,
( sdtlseqdt0(xP,sz0z00)
| sdtlseqdt0(sz0z00,xP) ),
inference(spm,[status(thm)],[c_0_162,c_0_80]) ).
cnf(c_0_170,hypothesis,
sdtpldt0(sdtpldt0(xN,sdtasdt0(xR,xR)),sdtpldt0(sdtasdt0(xS,xS),xN)) = sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xS,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_51]),c_0_50])]) ).
cnf(c_0_171,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_160]) ).
cnf(c_0_172,hypothesis,
sdtpldt0(sz0z00,xS) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_165]),c_0_50])]) ).
cnf(c_0_173,hypothesis,
sdtpldt0(smndt0(xR),xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_157]),c_0_97])]) ).
cnf(c_0_174,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(sdtpldt0(xP,xP),xP),sdtasdt0(xP,xP)),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN),xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_126])]) ).
cnf(c_0_175,hypothesis,
( xP = sz0z00
| sdtlseqdt0(sz0z00,xP) ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
fof(c_0_176,plain,
! [X82,X83] :
( ~ aScalar0(X82)
| ~ aScalar0(X83)
| aScalar0(sdtpldt0(X82,X83)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])]) ).
cnf(c_0_177,hypothesis,
sdtpldt0(sdtpldt0(sz0z00,sdtasdt0(xR,xR)),sdtpldt0(sdtasdt0(xS,xS),sz0z00)) = sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xS,xR)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_132]),c_0_132]) ).
cnf(c_0_178,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_171,c_0_105]),c_0_80])]) ).
cnf(c_0_179,hypothesis,
sdtpldt0(xS,sz0z00) = xS,
inference(rw,[status(thm)],[c_0_165,c_0_172]) ).
cnf(c_0_180,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_107,c_0_173]),c_0_157]),c_0_51]),c_0_97])]) ).
cnf(c_0_181,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(sdtasdt0(sdtpldt0(xP,xP),xP),sdtasdt0(xP,xP)),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),xN))
| ~ aScalar0(sdtpldt0(sdtasdt0(sdtpldt0(xP,xP),xP),sdtasdt0(xP,xP)))
| ~ aScalar0(sdtasdt0(xP,xP)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_78]),c_0_118]),c_0_93])]) ).
cnf(c_0_182,hypothesis,
xP = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_175]),c_0_141]),c_0_126])]) ).
cnf(c_0_183,hypothesis,
sdtpldt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_133]),c_0_80])]) ).
cnf(c_0_184,hypothesis,
sdtlseqdt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(split_conjunct,[status(thm)],[m__2104]) ).
cnf(c_0_185,plain,
( aScalar0(sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_176]) ).
cnf(c_0_186,hypothesis,
sdtpldt0(sdtpldt0(sz0z00,sdtasdt0(xR,xR)),sdtasdt0(xS,xS)) = sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xS,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179]),c_0_50])]) ).
cnf(c_0_187,plain,
( sdtpldt0(sz0z00,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz0z00,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_105]),c_0_80])]) ).
cnf(c_0_188,hypothesis,
sdtpldt0(sz0z00,xR) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_180]),c_0_51])]) ).
cnf(c_0_189,negated_conjecture,
( ~ sdtlseqdt0(sz0z00,sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),sz0z00))
| ~ aScalar0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,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(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_132]),c_0_132]),c_0_182]),c_0_182]),c_0_183]),c_0_182]),c_0_144]),c_0_182]),c_0_182]),c_0_144]),c_0_183]),c_0_182]),c_0_182]),c_0_183]),c_0_182]),c_0_144]),c_0_182]),c_0_182]),c_0_144]),c_0_183]),c_0_80]),c_0_182]),c_0_182]),c_0_144]),c_0_80])]) ).
cnf(c_0_190,hypothesis,
sdtlseqdt0(sz0z00,sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_141]),c_0_141]),c_0_183]) ).
cnf(c_0_191,plain,
( aScalar0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_171]),c_0_43]),c_0_43]) ).
cnf(c_0_192,hypothesis,
sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xS,xR)) = sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_188]),c_0_51])]) ).
cnf(c_0_193,negated_conjecture,
~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_113]),c_0_190])]) ).
cnf(c_0_194,hypothesis,
( aScalar0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_192]),c_0_51]),c_0_50])]) ).
cnf(c_0_195,hypothesis,
~ aScalar0(sdtpldt0(xR,xS)),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_196,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_185]),c_0_50]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG067+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n002.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:49:31 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 14.49/9.21 % Version : CSE_E---1.7
% 14.49/9.21 % Problem : theBenchmark.p
% 14.49/9.21 % SZS status Theorem for theBenchmark.p
% 14.49/9.21 % SZS output start CNFRefutation
% See solution above
% 14.49/9.28 % Total time : 6.384s
%------------------------------------------------------------------------------