%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG068+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 02:06:16 PM UTC 2026
% Result : Theorem 14.14s 17.55s
% Output : CNFRefutation 14.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 35
% Syntax : Number of formulae : 181 ( 83 unt; 0 def)
% Number of atoms : 473 ( 138 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 486 ( 194 ~; 187 |; 77 &)
% ( 0 <=>; 28 =>; 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 : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 154 ( 2 sgn 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSPN,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> 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,
( xq = sziznziztdt0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xq,X1) = sdtlbdtrb0(xt,X1) )
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& aVector0(xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
fof(m__1766,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
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(xt)
& aVector0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1678) ).
fof(mScPr,axiom,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( aDimensionOf0(X1) = aDimensionOf0(X2)
=> aScalar0(sdtasasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScPr) ).
fof(m__1800,hypothesis,
( xD = sdtasasdt0(xq,xq)
& aScalar0(xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
fof(m__1854,hypothesis,
( xG = sdtasdt0(xB,xB)
& aScalar0(xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
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/sandbox/benchmark/theBenchmark.p',mArith) ).
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/sandbox/benchmark/theBenchmark.p',mMNeg) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(m__1783,hypothesis,
( xC = sdtasasdt0(xp,xp)
& aScalar0(xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1949,hypothesis,
( xN = sdtasdt0(xR,xS)
& aScalar0(xN) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
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/sandbox/benchmark/theBenchmark.p',mScZero) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
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/sandbox/benchmark/theBenchmark.p',mPosMon) ).
fof(m__1837,hypothesis,
( xF = sdtasdt0(xA,xA)
& aScalar0(xF) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__1746,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).
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/sandbox/benchmark/theBenchmark.p',m__1709) ).
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/sandbox/benchmark/theBenchmark.p',mLEMon) ).
fof(mLETot,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
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/sandbox/benchmark/theBenchmark.p',mLEMonM) ).
fof(mLEASm,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
fof(m__,conjecture,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mLETrn,axiom,
! [X1,X2,X3] :
( ( aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).
fof(m__2004,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2004) ).
fof(mDistr2,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X4)
& aScalar0(X3)
& aScalar0(X2)
& aScalar0(X1) )
=> 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/sandbox/benchmark/theBenchmark.p',mDistr2) ).
fof(m__1911,hypothesis,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(c_0_35,plain,
! [X1,X2] :
( ( aVector0(X2)
& aVector0(X1) )
=> ( ( aDimensionOf0(X2) != sz00
& aDimensionOf0(X1) = aDimensionOf0(X2) )
=> 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_36,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_simplification,[status(thm)],[m__1692]) ).
fof(c_0_37,plain,
! [X73,X74] :
( sdtasasdt0(X73,X74) = sdtpldt0(sdtasasdt0(sziznziztdt0(X73),sziznziztdt0(X74)),sdtasdt0(sdtlbdtrb0(X73,aDimensionOf0(X73)),sdtlbdtrb0(X74,aDimensionOf0(X74))))
| aDimensionOf0(X74) = sz00
| aDimensionOf0(X73) != aDimensionOf0(X74)
| ~ aVector0(X74)
| ~ aVector0(X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
fof(c_0_38,hypothesis,
! [X79] :
( xq = sziznziztdt0(xt)
& ( sdtlbdtrb0(xq,X79) = sdtlbdtrb0(xt,X79)
| ~ aNaturalNumber0(X79) )
& 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])])])]) ).
cnf(c_0_39,hypothesis,
xB = sdtlbdtrb0(xt,aDimensionOf0(xt)),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_40,hypothesis,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(split_conjunct,[status(thm)],[m__1678_01]) ).
fof(c_0_41,hypothesis,
aDimensionOf0(xs) != sz00,
inference(fof_nnf,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| sdtasasdt0(X1,X2) = sdtpldt0(sdtasasdt0(sziznziztdt0(X1),sziznziztdt0(X2)),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),sdtlbdtrb0(X2,aDimensionOf0(X2))))
| aDimensionOf0(X2) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,hypothesis,
xq = sziznziztdt0(xt),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,hypothesis,
sdtlbdtrb0(xt,aDimensionOf0(xs)) = xB,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,hypothesis,
aVector0(xt),
inference(split_conjunct,[status(thm)],[m__1678]) ).
cnf(c_0_46,hypothesis,
aDimensionOf0(xs) != sz00,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_47,plain,
! [X69,X70] :
( aScalar0(sdtasasdt0(X69,X70))
| aDimensionOf0(X69) != aDimensionOf0(X70)
| ~ aVector0(X70)
| ~ aVector0(X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScPr])])]) ).
cnf(c_0_48,hypothesis,
( ~ aVector0(X1)
| aDimensionOf0(X1) != aDimensionOf0(xs)
| sdtpldt0(sdtasasdt0(sziznziztdt0(X1),xq),sdtasdt0(sdtlbdtrb0(X1,aDimensionOf0(X1)),xB)) = sdtasasdt0(X1,xt) ),
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_42,c_0_40]),c_0_43]),c_0_44]),c_0_45])]),c_0_46]) ).
cnf(c_0_49,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_50,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
fof(c_0_51,plain,
! [X21,X22,X23] :
( ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtasdt0(X21,X22) = sdtasdt0(X22,X21) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtasdt0(sdtasdt0(X21,X22),X23) = sdtasdt0(X21,sdtasdt0(X22,X23)) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtpldt0(X21,X22) = sdtpldt0(X22,X21) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ aScalar0(X21)
| sdtpldt0(sdtpldt0(X21,X22),X23) = sdtpldt0(X21,sdtpldt0(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])])]) ).
cnf(c_0_52,plain,
( aDimensionOf0(X1) != aDimensionOf0(X2)
| ~ aVector0(X2)
| ~ aVector0(X1)
| aScalar0(sdtasasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,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_48,c_0_40]),c_0_43]),c_0_49]),c_0_44]),c_0_50]),c_0_45])]) ).
fof(c_0_54,plain,
! [X31,X32] :
( ( ~ aScalar0(X32)
| ~ aScalar0(X31)
| sdtasdt0(smndt0(X31),X32) = smndt0(sdtasdt0(X31,X32)) )
& ( ~ aScalar0(X32)
| ~ aScalar0(X31)
| sdtasdt0(X31,smndt0(X32)) = smndt0(sdtasdt0(X31,X32)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])])]) ).
cnf(c_0_55,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,hypothesis,
aScalar0(sdtpldt0(xD,xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_45])]) ).
cnf(c_0_57,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_58,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_59,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_60,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
fof(c_0_61,plain,
! [X17,X18] :
( aScalar0(sdtasdt0(X17,X18))
| ~ aScalar0(X18)
| ~ aScalar0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])])]) ).
cnf(c_0_62,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,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_57,c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_64,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_65,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_66,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_67,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_68,hypothesis,
( ~ aScalar0(smndt0(xC))
| sdtasdt0(xG,smndt0(xC)) = smndt0(xR) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_59])]) ).
fof(c_0_69,plain,
! [X19] :
( aScalar0(smndt0(X19))
| ~ aScalar0(X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])])]) ).
cnf(c_0_70,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_57,c_0_64]),c_0_65]),c_0_66])]) ).
cnf(c_0_71,hypothesis,
( ~ aScalar0(smndt0(xC))
| aScalar0(smndt0(xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_59])]) ).
cnf(c_0_72,plain,
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_73,hypothesis,
( ~ aScalar0(smndt0(xR))
| sdtasdt0(xS,smndt0(xR)) = smndt0(xN) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_62]),c_0_65])]) ).
cnf(c_0_74,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_60])]) ).
fof(c_0_75,plain,
! [X20] :
( ( ~ aScalar0(X20)
| smndt0(sz0z00) = sz0z00 )
& ( ~ aScalar0(X20)
| smndt0(smndt0(X20)) = X20 )
& ( ~ aScalar0(X20)
| sdtpldt0(smndt0(X20),X20) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtpldt0(X20,smndt0(X20)) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtasdt0(sz0z00,X20) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtasdt0(X20,sz0z00) = sz0z00 )
& ( ~ aScalar0(X20)
| sdtpldt0(sz0z00,X20) = X20 )
& ( ~ aScalar0(X20)
| sdtpldt0(X20,sz0z00) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])])]) ).
cnf(c_0_76,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_77,hypothesis,
sdtasdt0(xS,smndt0(xR)) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).
fof(c_0_78,plain,
! [X55] :
( sdtlseqdt0(sz0z00,sdtasdt0(X55,X55))
| ~ aScalar0(X55) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])])]) ).
fof(c_0_79,plain,
! [X75] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X75,X75))
| ~ aVector0(X75) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])])]) ).
cnf(c_0_80,plain,
( ~ aScalar0(X1)
| smndt0(smndt0(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(xS,smndt0(smndt0(xR))) = smndt0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_74]),c_0_65])]) ).
fof(c_0_82,plain,
! [X53,X54] :
( ( ~ aScalar0(X54)
| ~ aScalar0(X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ sdtlseqdt0(sz0z00,X53)
| sdtlseqdt0(sz0z00,sdtasdt0(X53,X54)) )
& ( ~ aScalar0(X54)
| ~ aScalar0(X53)
| ~ sdtlseqdt0(sz0z00,X54)
| ~ sdtlseqdt0(sz0z00,X53)
| sdtlseqdt0(sz0z00,sdtpldt0(X53,X54)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])])]) ).
cnf(c_0_83,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_84,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_85,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_86,plain,
( ~ aScalar0(X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_87,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_88,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_89,plain,
( ~ aVector0(X1)
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_90,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_91,hypothesis,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| smndt0(sdtasdt0(X1,X2)) = sdtasdt0(X2,smndt0(X1)) ),
inference(spm,[status(thm)],[c_0_76,c_0_62]) ).
cnf(c_0_92,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_76]),c_0_67]) ).
cnf(c_0_93,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_76,c_0_58]),c_0_59]),c_0_60])]) ).
fof(c_0_94,hypothesis,
! [X78] :
( xp = sziznziztdt0(xs)
& ( sdtlbdtrb0(xp,X78) = sdtlbdtrb0(xs,X78)
| ~ aNaturalNumber0(X78) )
& 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_95,hypothesis,
smndt0(smndt0(xN)) = sdtasdt0(xS,xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_80]),c_0_66])]) ).
cnf(c_0_96,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_97,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_98,hypothesis,
sdtasdt0(xD,xF) = xS,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_62]),c_0_84]),c_0_85])]) ).
cnf(c_0_99,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]) ).
cnf(c_0_100,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_49]),c_0_90])]) ).
cnf(c_0_101,hypothesis,
sdtasdt0(xG,smndt0(xC)) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_58]),c_0_60]),c_0_59])]) ).
cnf(c_0_102,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_92,c_0_93]),c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_103,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_104,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_105,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_106,plain,
( ~ aScalar0(X1)
| smndt0(sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_107,plain,
! [X43,X44,X45,X46] :
( sdtlseqdt0(sdtpldt0(X43,X45),sdtpldt0(X44,X46))
| ~ sdtlseqdt0(X45,X46)
| ~ sdtlseqdt0(X43,X44)
| ~ aScalar0(X46)
| ~ aScalar0(X45)
| ~ aScalar0(X44)
| ~ aScalar0(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])])]) ).
cnf(c_0_108,hypothesis,
sdtasdt0(xS,xR) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_95]),c_0_96])]) ).
cnf(c_0_109,hypothesis,
( ~ aScalar0(smndt0(xR))
| aScalar0(smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_73]),c_0_65])]) ).
cnf(c_0_110,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_97,c_0_98]),c_0_99]),c_0_100]),c_0_84]),c_0_85])]) ).
cnf(c_0_111,hypothesis,
sdtasdt0(xG,xC) = xR,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_101]),c_0_60]),c_0_59])]),c_0_102]) ).
cnf(c_0_112,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_103]),c_0_104])]) ).
cnf(c_0_113,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_50]),c_0_105])]) ).
fof(c_0_114,plain,
! [X51,X52] :
( sdtlseqdt0(X52,X51)
| sdtlseqdt0(X51,X52)
| ~ aScalar0(X52)
| ~ aScalar0(X51) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])])]) ).
cnf(c_0_115,plain,
( ~ aScalar0(X1)
| sdtasdt0(X1,sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_116,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_106,c_0_96]) ).
cnf(c_0_117,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_118,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_107]) ).
cnf(c_0_119,plain,
( ~ aScalar0(X1)
| sdtpldt0(sz0z00,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_120,plain,
( ~ aScalar0(X1)
| sdtpldt0(smndt0(X1),X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_121,hypothesis,
smndt0(smndt0(xN)) = xN,
inference(rw,[status(thm)],[c_0_95,c_0_108]) ).
cnf(c_0_122,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_74])]) ).
cnf(c_0_123,hypothesis,
( ~ sdtlseqdt0(sz0z00,xR)
| sdtlseqdt0(sz0z00,xN) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_108]),c_0_110]),c_0_66]),c_0_65])]) ).
cnf(c_0_124,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_97,c_0_111]),c_0_112]),c_0_113]),c_0_60]),c_0_59])]) ).
cnf(c_0_125,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_126,hypothesis,
( ~ aScalar0(X1)
| sdtasdt0(sz0z00,smndt0(X1)) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_115]),c_0_116]),c_0_117])]) ).
cnf(c_0_127,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_118,c_0_119]),c_0_117])]) ).
cnf(c_0_128,hypothesis,
sdtpldt0(xN,smndt0(xN)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122])]) ).
cnf(c_0_129,hypothesis,
sdtlseqdt0(sz0z00,xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]) ).
cnf(c_0_130,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(smndt0(xN),X1)
| sdtlseqdt0(X1,smndt0(xN)) ),
inference(spm,[status(thm)],[c_0_125,c_0_122]) ).
fof(c_0_131,plain,
! [X47,X48,X49,X50] :
( sdtlseqdt0(sdtasdt0(X47,X49),sdtasdt0(X48,X50))
| ~ sdtlseqdt0(X49,X50)
| ~ sdtlseqdt0(sz0z00,X49)
| ~ sdtlseqdt0(X47,X48)
| ~ aScalar0(X50)
| ~ aScalar0(X49)
| ~ aScalar0(X48)
| ~ aScalar0(X47) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])])]) ).
cnf(c_0_132,hypothesis,
sdtasdt0(sz0z00,xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_102]),c_0_74])]) ).
fof(c_0_133,plain,
! [X38,X39] :
( X38 = X39
| ~ sdtlseqdt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aScalar0(X39)
| ~ aScalar0(X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])])]) ).
cnf(c_0_134,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_127,c_0_128]),c_0_129]),c_0_122]),c_0_96])]) ).
cnf(c_0_135,hypothesis,
sdtlseqdt0(smndt0(xN),smndt0(xN)),
inference(spm,[status(thm)],[c_0_130,c_0_122]) ).
cnf(c_0_136,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_131]) ).
cnf(c_0_137,hypothesis,
sdtasdt0(xR,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_132]),c_0_116]),c_0_116]),c_0_117]),c_0_66])]) ).
cnf(c_0_138,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(smndt0(xR),X1)
| sdtlseqdt0(X1,smndt0(xR)) ),
inference(spm,[status(thm)],[c_0_125,c_0_74]) ).
cnf(c_0_139,plain,
( ~ aScalar0(X1)
| sdtasdt0(sz0z00,X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_140,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_141,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
fof(c_0_142,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_143,plain,
! [X40,X41,X42] :
( sdtlseqdt0(X40,X42)
| ~ sdtlseqdt0(X41,X42)
| ~ sdtlseqdt0(X40,X41)
| ~ aScalar0(X42)
| ~ aScalar0(X41)
| ~ aScalar0(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])])]) ).
cnf(c_0_144,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_145,hypothesis,
sdtlseqdt0(smndt0(xN),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_122])]) ).
cnf(c_0_146,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_70]),c_0_65])]),c_0_74])]) ).
cnf(c_0_147,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_57,c_0_137]),c_0_116]),c_0_117]),c_0_66])]) ).
cnf(c_0_148,hypothesis,
sdtlseqdt0(smndt0(xR),smndt0(xR)),
inference(spm,[status(thm)],[c_0_138,c_0_74]) ).
cnf(c_0_149,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_139]),c_0_117])]) ).
cnf(c_0_150,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_120]),c_0_72]) ).
cnf(c_0_151,hypothesis,
sdtpldt0(smndt0(xN),xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_121]),c_0_122])]) ).
fof(c_0_152,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(fof_simplification,[status(thm)],[c_0_142]) ).
cnf(c_0_153,hypothesis,
sdtlseqdt0(sdtasdt0(xP,xP),xN),
inference(split_conjunct,[status(thm)],[m__2004]) ).
cnf(c_0_154,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_155,hypothesis,
( ~ sdtlseqdt0(sz0z00,smndt0(xN))
| smndt0(xN) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_122]),c_0_117])]) ).
cnf(c_0_156,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_146,c_0_147]),c_0_148]),c_0_149]),c_0_110]),c_0_117]),c_0_74])]) ).
cnf(c_0_157,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,sz0z00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_158,hypothesis,
sdtpldt0(xN,sz0z00) = sdtpldt0(sz0z00,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_150,c_0_151]),c_0_95]),c_0_108]),c_0_96]),c_0_122])]) ).
fof(c_0_159,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(fof_nnf,[status(thm)],[c_0_152]) ).
fof(c_0_160,plain,
! [X27,X28,X29,X30] :
( sdtasdt0(sdtpldt0(X27,X28),sdtpldt0(X29,X30)) = sdtpldt0(sdtpldt0(sdtasdt0(X27,X29),sdtasdt0(X27,X30)),sdtpldt0(sdtasdt0(X28,X29),sdtasdt0(X28,X30)))
| ~ aScalar0(X30)
| ~ aScalar0(X29)
| ~ aScalar0(X28)
| ~ aScalar0(X27) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr2])])]) ).
cnf(c_0_161,hypothesis,
( ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(xN,sdtasdt0(xP,xP))
| sdtasdt0(xP,xP) = xN ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_153]),c_0_96])]) ).
cnf(c_0_162,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(sdtasdt0(X2,X2))
| ~ sdtlseqdt0(X1,sz0z00)
| sdtlseqdt0(X1,sdtasdt0(X2,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_86]),c_0_117])]) ).
cnf(c_0_163,hypothesis,
aScalar0(xP),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_164,hypothesis,
smndt0(xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156])]) ).
cnf(c_0_165,hypothesis,
sdtpldt0(sz0z00,xN) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_96])]) ).
cnf(c_0_166,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xR,xS)),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_167,plain,
( ~ aScalar0(X4)
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X4)) = sdtpldt0(sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X4)),sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X2,X4))) ),
inference(split_conjunct,[status(thm)],[c_0_160]) ).
cnf(c_0_168,hypothesis,
( ~ aScalar0(sdtasdt0(xP,xP))
| ~ sdtlseqdt0(xN,sz0z00)
| sdtasdt0(xP,xP) = xN ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_96]),c_0_163])]) ).
cnf(c_0_169,hypothesis,
xN = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_164]),c_0_165]) ).
cnf(c_0_170,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),xN),sdtpldt0(sdtasdt0(xS,xR),sdtasdt0(xS,xS)))),
inference(rw,[status(thm)],[c_0_166,c_0_64]) ).
cnf(c_0_171,hypothesis,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(sdtasdt0(xR,X1),xN),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X2,xS))) = sdtasdt0(sdtpldt0(xR,X2),sdtpldt0(X1,xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_64]),c_0_65]),c_0_66])]) ).
cnf(c_0_172,hypothesis,
( ~ aScalar0(sdtasdt0(xP,xP))
| sdtasdt0(xP,xP) = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_169]),c_0_169]),c_0_149])]) ).
cnf(c_0_173,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP)),sdtpldt0(sdtasdt0(xP,xP),sdtasdt0(xP,xP))),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_66]),c_0_65])]) ).
cnf(c_0_174,hypothesis,
sdtasdt0(xP,xP) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_67]),c_0_163])]) ).
cnf(c_0_175,hypothesis,
sdtpldt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_116]),c_0_117])]) ).
cnf(c_0_176,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_175]),c_0_175]),c_0_175]) ).
fof(c_0_177,plain,
! [X15,X16] :
( aScalar0(sdtpldt0(X15,X16))
| ~ aScalar0(X16)
| ~ aScalar0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])])]) ).
cnf(c_0_178,negated_conjecture,
~ aScalar0(sdtpldt0(xR,xS)),
inference(spm,[status(thm)],[c_0_176,c_0_86]) ).
cnf(c_0_179,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_177]) ).
cnf(c_0_180,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_65]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG068+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/15.39 % Computer : n013.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Mon Sep 21 04:17:08 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.11/15.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/15.43 Running first-order theorem proving
% 0.14/15.43 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
% 14.14/17.55 % Version: 3.5.1
% 14.14/17.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 14.14/17.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.14/17.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 14.14/17.55 % Starting new_bool_3 with 300s (1) cores
% 14.14/17.55 % Starting new_bool_1 with 300s (1) cores
% 14.14/17.55 % Starting sh5l with 300s (1) cores
% 14.14/17.55 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 4119065 completed with status 0
% 14.14/17.55 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 14.14/17.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 14.14/17.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.14/17.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 14.14/17.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.14/17.55 % No SInE strategy applied
% 14.14/17.55 % Search class: FGHSF-FFMM21-MFFFFFNN
% 14.14/17.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 14.14/17.55 % Starting SubtermCWHack with 136s (1) cores
% 14.14/17.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 14.14/17.55 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 14.14/17.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 14.14/17.55 % Starting new_bool_3 with 136s (1) cores
% 14.14/17.55 % G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with pid 4119075 completed with status 0
% 14.14/17.55 % Result found by G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N
% 14.14/17.55 % Preprocessing class: FSLSSMSMSSSNFFN.
% 14.14/17.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.14/17.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 14.14/17.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.14/17.55 % No SInE strategy applied
% 14.14/17.55 % Search class: FGHSF-FFMM21-MFFFFFNN
% 14.14/17.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 14.14/17.55 % Starting SubtermCWHack with 136s (1) cores
% 14.14/17.55 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 14.14/17.55 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 14.14/17.55 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 14.14/17.55 % Preprocessing time : 0.003 s
% 14.14/17.55 % Presaturation interreduction done
% 14.14/17.55
% 14.14/17.55 % Proof found!
% 14.14/17.55 % SZS status Theorem
% 14.14/17.55 % SZS output start CNFRefutation
% See solution above
% 14.14/17.55 % Parsed axioms : 61
% 14.14/17.55 % Removed by relevancy pruning/SinE : 0
% 14.14/17.55 % Initial clauses : 99
% 14.14/17.55 % Removed in clause preprocessing : 5
% 14.14/17.55 % Initial clauses in saturation : 94
% 14.14/17.55 % Processed clauses : 5107
% 14.14/17.55 % ...of these trivial : 315
% 14.14/17.55 % ...subsumed : 2762
% 14.14/17.55 % ...remaining for further processing : 2030
% 14.14/17.55 % Other redundant clauses eliminated : 6
% 14.14/17.55 % Clauses deleted for lack of memory : 0
% 14.14/17.55 % Backward-subsumed : 110
% 14.14/17.55 % Backward-rewritten : 434
% 14.14/17.55 % Generated clauses : 79420
% 14.14/17.55 % ...of the previous two non-redundant : 73702
% 14.14/17.55 % ...aggressively subsumed : 0
% 14.14/17.55 % Contextual simplify-reflections : 135
% 14.14/17.55 % Paramodulations : 79400
% 14.14/17.55 % Factorizations : 0
% 14.14/17.55 % NegExts : 0
% 14.14/17.55 % Equation resolutions : 20
% 14.14/17.55 % Disequality decompositions : 0
% 14.14/17.55 % Total rewrite steps : 134023
% 14.14/17.55 % ...of those cached : 133589
% 14.14/17.55 % Propositional unsat checks : 0
% 14.14/17.55 % Propositional check models : 0
% 14.14/17.55 % Propositional check unsatisfiable : 0
% 14.14/17.55 % Propositional clauses : 0
% 14.14/17.55 % Propositional clauses after purity: 0
% 14.14/17.55 % Propositional unsat core size : 0
% 14.14/17.55 % Propositional preprocessing time : 0.000
% 14.14/17.55 % Propositional encoding time : 0.000
% 14.14/17.55 % Propositional solver time : 0.000
% 14.14/17.55 % Success case prop preproc time : 0.000
% 14.14/17.55 % Success case prop encoding time : 0.000
% 14.14/17.55 % Success case prop solver time : 0.000
% 14.14/17.55 % Current number of processed clauses : 1389
% 14.14/17.55 % Positive orientable unit clauses : 405
% 14.14/17.55 % Positive unorientable unit clauses: 0
% 14.14/17.55 % Negative unit clauses : 63
% 14.14/17.55 % Non-unit-clauses : 921
% 14.14/17.55 % Current number of unprocessed clauses: 68597
% 14.14/17.55 % ...number of literals in the above : 301589
% 14.14/17.55 % Current number of archived formulas : 0
% 14.14/17.55 % Current number of archived clauses : 638
% 14.14/17.55 % Clause-clause subsumption calls (NU) : 231952
% 14.14/17.55 % Rec. Clause-clause subsumption calls : 101333
% 14.14/17.55 % Non-unit clause-clause subsumptions : 2453
% 14.14/17.55 % Unit Clause-clause subsumption calls : 15509
% 14.14/17.55 % Rewrite failures with RHS unbound : 0
% 14.14/17.55 % BW rewrite match attempts : 170
% 14.14/17.55 % BW rewrite match successes : 57
% 14.14/17.55 % Condensation attempts : 0
% 14.14/17.55 % Condensation successes : 0
% 14.14/17.55 % Termbank termtop insertions : 2085509
% 14.14/17.55 % Search garbage collected termcells : 888
% 14.14/17.55
% 14.14/17.55 % -------------------------------------------------
% 14.14/17.55 % User time : 1.770 s
% 14.14/17.55 % System time : 0.089 s
% 14.14/17.55 % Total time : 1.859 s
% 14.14/17.55 % Maximum resident set size: 3708 pages
% 14.14/17.55
% 14.14/17.55 % -------------------------------------------------
% 14.14/17.55 % User time : 9.489 s
% 14.14/17.55 % System time : 0.480 s
% 14.14/17.55 % Total time : 9.969 s
% 14.14/17.55 % Maximum resident set size: 4864 pages
% 14.14/17.55 % E exiting
%------------------------------------------------------------------------------