%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG060+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 : n014.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 02:06:13 PM UTC 2026
% Result : Theorem 11.72s 2.34s
% Output : CNFRefutation 11.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 28
% Syntax : Number of formulae : 163 ( 73 unt; 0 def)
% Number of atoms : 421 ( 127 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 425 ( 167 ~; 168 |; 69 &)
% ( 0 <=>; 21 =>; 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 : 22 ( 22 usr; 14 con; 0-2 aty)
% Number of variables : 131 ( 2 sgn 62 !; 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(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(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
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(m__1746,hypothesis,
( xA = sdtlbdtrb0(xs,aDimensionOf0(xs))
& aScalar0(xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1746) ).
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(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(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(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(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(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(m__2144,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(xR,smndt0(xS)) = smndt0(xN) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).
fof(mSqrt,axiom,
! [X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1) )
=> ( ( sdtasdt0(X1,X1) = sdtasdt0(X2,X2)
& sdtlseqdt0(sz0z00,X2)
& sdtlseqdt0(sz0z00,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqrt) ).
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(m__1766,hypothesis,
( xB = sdtlbdtrb0(xt,aDimensionOf0(xt))
& aScalar0(xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1766) ).
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(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__,conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(c_0_28,plain,
! [X28,X29] :
( ( ~ aScalar0(X29)
| ~ aScalar0(X28)
| sdtasdt0(smndt0(X28),X29) = smndt0(sdtasdt0(X28,X29)) )
& ( ~ aScalar0(X29)
| ~ aScalar0(X28)
| sdtasdt0(X28,smndt0(X29)) = smndt0(sdtasdt0(X28,X29)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])])]) ).
fof(c_0_29,plain,
! [X7] :
( ( ~ aScalar0(X7)
| smndt0(sz0z00) = sz0z00 )
& ( ~ aScalar0(X7)
| smndt0(smndt0(X7)) = X7 )
& ( ~ aScalar0(X7)
| sdtpldt0(smndt0(X7),X7) = sz0z00 )
& ( ~ aScalar0(X7)
| sdtpldt0(X7,smndt0(X7)) = sz0z00 )
& ( ~ aScalar0(X7)
| sdtasdt0(sz0z00,X7) = sz0z00 )
& ( ~ aScalar0(X7)
| sdtasdt0(X7,sz0z00) = sz0z00 )
& ( ~ aScalar0(X7)
| sdtpldt0(sz0z00,X7) = X7 )
& ( ~ aScalar0(X7)
| sdtpldt0(X7,sz0z00) = X7 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])])]) ).
fof(c_0_30,plain,
! [X26,X27] :
( aScalar0(sdtasdt0(X26,X27))
| ~ aScalar0(X27)
| ~ aScalar0(X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])])]) ).
fof(c_0_31,plain,
! [X39] :
( aScalar0(smndt0(X39))
| ~ aScalar0(X39) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])])]) ).
cnf(c_0_32,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_34,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_35,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_36,plain,
( ~ aScalar0(X1)
| smndt0(sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_38,plain,
( ~ aScalar0(X1)
| smndt0(smndt0(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_41,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_42,plain,
( ~ aScalar0(X1)
| aScalar0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,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_33]),c_0_34]),c_0_35])]) ).
fof(c_0_44,plain,
! [X57] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X57,X57))
| ~ aVector0(X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])])]) ).
fof(c_0_45,hypothesis,
! [X66] :
( xq = sziznziztdt0(xt)
& ( sdtlbdtrb0(xq,X66) = sdtlbdtrb0(xt,X66)
| ~ aNaturalNumber0(X66) )
& 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_46,plain,
! [X36] :
( sdtlseqdt0(sz0z00,sdtasdt0(X36,X36))
| ~ aScalar0(X36) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])])]) ).
cnf(c_0_47,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_48,plain,
( ~ aScalar0(X1)
| sdtasdt0(X1,sz0z00) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_49,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_50,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_51,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_32]),c_0_39]) ).
cnf(c_0_52,hypothesis,
sdtasdt0(xA,smndt0(xA)) = smndt0(xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_40]),c_0_41])]) ).
cnf(c_0_53,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| aScalar0(sdtasdt0(X1,smndt0(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_39]) ).
fof(c_0_54,plain,
! [X49,X50] :
( sdtlseqdt0(X50,X49)
| sdtlseqdt0(X49,X50)
| ~ aScalar0(X50)
| ~ aScalar0(X49) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])])]) ).
cnf(c_0_55,hypothesis,
( ~ aScalar0(smndt0(xD))
| aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_43]),c_0_35])]) ).
fof(c_0_56,plain,
! [X22,X23] :
( ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ sdtlseqdt0(sz0z00,X23)
| ~ sdtlseqdt0(sz0z00,X22)
| sdtlseqdt0(sz0z00,sdtasdt0(X22,X23)) )
& ( ~ aScalar0(X23)
| ~ aScalar0(X22)
| ~ sdtlseqdt0(sz0z00,X23)
| ~ sdtlseqdt0(sz0z00,X22)
| sdtlseqdt0(sz0z00,sdtpldt0(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])])]) ).
cnf(c_0_57,plain,
( ~ aVector0(X1)
| sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_58,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_59,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_60,plain,
( ~ aScalar0(X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_61,plain,
! [X32,X33,X34,X35] :
( sdtlseqdt0(sdtasdt0(X32,X34),sdtasdt0(X33,X35))
| ~ sdtlseqdt0(X34,X35)
| ~ sdtlseqdt0(sz0z00,X34)
| ~ sdtlseqdt0(X32,X33)
| ~ aScalar0(X35)
| ~ aScalar0(X34)
| ~ aScalar0(X33)
| ~ aScalar0(X32) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])])]) ).
cnf(c_0_62,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_47,c_0_48]),c_0_49]),c_0_50])]) ).
cnf(c_0_63,hypothesis,
smndt0(smndt0(xF)) = xF,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_40]),c_0_41])]) ).
cnf(c_0_64,hypothesis,
aScalar0(smndt0(xF)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_52]),c_0_41])]) ).
cnf(c_0_65,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_67,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_68,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
fof(c_0_69,plain,
! [X30,X31] :
( sdtasdt0(smndt0(X30),smndt0(X31)) = sdtasdt0(X30,X31)
| ~ aScalar0(X31)
| ~ aScalar0(X30) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMDNeg])])]) ).
cnf(c_0_70,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_71,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_42]),c_0_34])]) ).
cnf(c_0_72,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
fof(c_0_73,plain,
! [X37,X38] :
( X37 = X38
| sdtasdt0(X37,X37) != sdtasdt0(X38,X38)
| ~ sdtlseqdt0(sz0z00,X38)
| ~ sdtlseqdt0(sz0z00,X37)
| ~ aScalar0(X38)
| ~ aScalar0(X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqrt])])]) ).
cnf(c_0_74,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_75,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_76,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_40]),c_0_41])]) ).
cnf(c_0_77,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_61]) ).
cnf(c_0_78,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_47,c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_79,hypothesis,
sdtasdt0(xF,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64])]) ).
cnf(c_0_80,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(X1,smndt0(xF))
| sdtlseqdt0(smndt0(xF),X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_64]) ).
cnf(c_0_81,plain,
( ~ aScalar0(X1)
| sdtasdt0(sz0z00,X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_82,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_66]),c_0_67]),c_0_68])]) ).
cnf(c_0_83,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
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_47,c_0_70]),c_0_71]),c_0_72])]) ).
cnf(c_0_85,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_86,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
fof(c_0_87,hypothesis,
! [X65] :
( xp = sziznziztdt0(xs)
& ( sdtlbdtrb0(xp,X65) = sdtlbdtrb0(xs,X65)
| ~ aNaturalNumber0(X65) )
& 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_88,plain,
( sdtasdt0(X1,X1) != sdtasdt0(X2,X2)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_89,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_74,c_0_33]),c_0_75]),c_0_76]),c_0_34]),c_0_35])]) ).
cnf(c_0_90,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X2,xD)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X1,smndt0(xF))
| sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_34])]),c_0_64])]) ).
cnf(c_0_91,hypothesis,
sdtasdt0(smndt0(xF),sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_79]),c_0_49]),c_0_50]),c_0_35])]) ).
cnf(c_0_92,hypothesis,
sdtlseqdt0(smndt0(xF),smndt0(xF)),
inference(spm,[status(thm)],[c_0_80,c_0_64]) ).
cnf(c_0_93,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_81]),c_0_50])]) ).
cnf(c_0_94,hypothesis,
( ~ aScalar0(smndt0(xG))
| aScalar0(smndt0(xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_82]),c_0_68])]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_96,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_85]),c_0_86]),c_0_72])]) ).
cnf(c_0_97,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_98,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_99,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_100,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_101,plain,
! [X18,X19,X20,X21] :
( sdtlseqdt0(sdtpldt0(X18,X20),sdtpldt0(X19,X21))
| ~ sdtlseqdt0(X20,X21)
| ~ sdtlseqdt0(X18,X19)
| ~ aScalar0(X21)
| ~ aScalar0(X20)
| ~ aScalar0(X19)
| ~ aScalar0(X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])])]) ).
cnf(c_0_102,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_103,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_51,c_0_43]),c_0_33]),c_0_34]),c_0_35])]) ).
cnf(c_0_104,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(sz0z00,X1)
| sdtasdt0(X1,X1) != sdtasdt0(xS,xS)
| X1 = xS ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_86])]) ).
cnf(c_0_105,hypothesis,
sdtlseqdt0(sz0z00,smndt0(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_90,c_0_91]),c_0_92]),c_0_93]),c_0_75]),c_0_50]),c_0_64])]) ).
cnf(c_0_106,hypothesis,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_107,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_51,c_0_82]),c_0_66]),c_0_67]),c_0_68])]) ).
cnf(c_0_108,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_42]),c_0_67])]) ).
fof(c_0_109,plain,
! [X8,X9,X10] :
( ( ~ aScalar0(X10)
| ~ aScalar0(X9)
| ~ aScalar0(X8)
| sdtasdt0(X8,X9) = sdtasdt0(X9,X8) )
& ( ~ aScalar0(X10)
| ~ aScalar0(X9)
| ~ aScalar0(X8)
| sdtasdt0(sdtasdt0(X8,X9),X10) = sdtasdt0(X8,sdtasdt0(X9,X10)) )
& ( ~ aScalar0(X10)
| ~ aScalar0(X9)
| ~ aScalar0(X8)
| sdtpldt0(X8,X9) = sdtpldt0(X9,X8) )
& ( ~ aScalar0(X10)
| ~ aScalar0(X9)
| ~ aScalar0(X8)
| sdtpldt0(sdtpldt0(X8,X9),X10) = sdtpldt0(X8,sdtpldt0(X9,X10)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])])]) ).
cnf(c_0_110,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(X1,xR)
| sdtlseqdt0(xR,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_72]) ).
cnf(c_0_111,hypothesis,
sdtasdt0(smndt0(smndt0(xS)),xR) = xN,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_95]),c_0_72]),c_0_71])]),c_0_96]) ).
cnf(c_0_112,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_97]),c_0_98])]) ).
cnf(c_0_113,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_99]),c_0_100])]) ).
cnf(c_0_114,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_101]) ).
cnf(c_0_115,plain,
( ~ aScalar0(X1)
| sdtpldt0(sz0z00,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_116,hypothesis,
sdtpldt0(smndt0(xS),xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_71])]) ).
cnf(c_0_117,hypothesis,
smndt0(xS) = xS,
inference(cn,[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_71])]) ).
cnf(c_0_118,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_107]),c_0_108])]) ).
cnf(c_0_119,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_38]),c_0_42]) ).
cnf(c_0_120,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
fof(c_0_121,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_122,plain,
! [X44,X45] :
( X44 = X45
| ~ sdtlseqdt0(X45,X44)
| ~ sdtlseqdt0(X44,X45)
| ~ aScalar0(X45)
| ~ aScalar0(X44) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])])]) ).
cnf(c_0_123,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(xR,X1)
| ~ sdtlseqdt0(xS,X2)
| sdtlseqdt0(xN,sdtasdt0(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_85]),c_0_89]),c_0_86]),c_0_72])]) ).
cnf(c_0_124,hypothesis,
sdtasdt0(xR,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_107]),c_0_108])]) ).
cnf(c_0_125,hypothesis,
sdtlseqdt0(xR,xR),
inference(spm,[status(thm)],[c_0_110,c_0_72]) ).
cnf(c_0_126,hypothesis,
sdtasdt0(xS,xR) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_38]),c_0_86])]) ).
cnf(c_0_127,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_74,c_0_66]),c_0_112]),c_0_113]),c_0_67]),c_0_68])]) ).
cnf(c_0_128,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_114,c_0_115]),c_0_50])]) ).
cnf(c_0_129,hypothesis,
sdtpldt0(xS,xS) = sz0z00,
inference(rw,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_130,hypothesis,
( ~ aScalar0(X1)
| sdtlseqdt0(X1,xS)
| sdtlseqdt0(xS,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_86]) ).
cnf(c_0_131,plain,
( ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_132,plain,
( ~ aScalar0(X1)
| sdtpldt0(smndt0(X1),X1) = sz0z00 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_133,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(X1,smndt0(xR))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_72])]),c_0_42]) ).
cnf(c_0_134,hypothesis,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_37]) ).
fof(c_0_135,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(fof_simplification,[status(thm)],[c_0_121]) ).
cnf(c_0_136,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_137,hypothesis,
( ~ sdtlseqdt0(xS,sz0z00)
| sdtlseqdt0(xN,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]),c_0_50]),c_0_72])]) ).
cnf(c_0_138,hypothesis,
sdtlseqdt0(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_74,c_0_126]),c_0_127]),c_0_89]),c_0_72]),c_0_86])]) ).
cnf(c_0_139,hypothesis,
( ~ aScalar0(X1)
| ~ sdtlseqdt0(X1,xS)
| sdtlseqdt0(X1,sz0z00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_89]),c_0_86])]) ).
cnf(c_0_140,hypothesis,
sdtlseqdt0(xS,xS),
inference(spm,[status(thm)],[c_0_130,c_0_86]) ).
cnf(c_0_141,plain,
( ~ aScalar0(X1)
| ~ aScalar0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_42]) ).
cnf(c_0_142,hypothesis,
sdtpldt0(smndt0(xR),xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_107]),c_0_108])]) ).
cnf(c_0_143,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(smndt0(xR),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_108])]) ).
fof(c_0_144,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(fof_nnf,[status(thm)],[c_0_135]) ).
cnf(c_0_145,hypothesis,
( ~ aScalar0(smndt0(xS))
| aScalar0(smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_70]),c_0_72])]) ).
cnf(c_0_146,hypothesis,
( ~ sdtlseqdt0(xS,sz0z00)
| xN = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138]),c_0_37]),c_0_50])]) ).
cnf(c_0_147,hypothesis,
sdtlseqdt0(xS,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_86])]) ).
cnf(c_0_148,hypothesis,
( ~ sdtlseqdt0(xS,sz0z00)
| xS = sz0z00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_89]),c_0_50]),c_0_86])]) ).
cnf(c_0_149,plain,
( ~ 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_32,c_0_81]),c_0_49]),c_0_50])]) ).
cnf(c_0_150,plain,
( ~ aScalar0(X1)
| sdtpldt0(X1,sz0z00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_151,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_141,c_0_142]),c_0_107]),c_0_72]),c_0_108])]) ).
cnf(c_0_152,hypothesis,
( ~ aScalar0(X1)
| aScalar0(sdtasdt0(xR,smndt0(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_119]),c_0_72])]) ).
cnf(c_0_153,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_154,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_71])]) ).
cnf(c_0_155,hypothesis,
xN = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147])]) ).
cnf(c_0_156,hypothesis,
xS = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_147])]) ).
cnf(c_0_157,hypothesis,
sdtasdt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_49]),c_0_50])]) ).
cnf(c_0_158,hypothesis,
sdtpldt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_49]),c_0_50])]) ).
cnf(c_0_159,hypothesis,
sdtpldt0(sz0z00,xR) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_72])]) ).
cnf(c_0_160,hypothesis,
aScalar0(sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_107]),c_0_108])]) ).
cnf(c_0_161,negated_conjecture,
sdtpldt0(sdtasdt0(xR,xR),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(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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_131]),c_0_154])]),c_0_155]),c_0_49]),c_0_155]),c_0_49]),c_0_156]),c_0_156]),c_0_157]),c_0_158]),c_0_158]),c_0_156]),c_0_49]),c_0_151]),c_0_159]),c_0_156]),c_0_49]),c_0_151]),c_0_159]),c_0_155]),c_0_49]),c_0_156]),c_0_156]),c_0_157]),c_0_158]),c_0_50]),c_0_160])]) ).
cnf(c_0_162,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_150]),c_0_160])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG060+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.47 % Computer : n014.cluster.edu
% 0.19/0.47 % Model : x86_64 x86_64
% 0.19/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47 % Memory : 8046.5625MB
% 0.19/0.47 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Mon Sep 21 04:16:34 UTC 2026
% 0.19/0.48 % CPUTime :
% 0.19/0.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.56 Running first-order theorem proving
% 0.23/0.56 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
% 11.72/2.34 % Version: 3.5.1
% 11.72/2.34 % Preprocessing class: FSLSSMSMSSSNFFN.
% 11.72/2.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.72/2.34 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 11.72/2.34 % Starting new_bool_3 with 300s (1) cores
% 11.72/2.34 % Starting new_bool_1 with 300s (1) cores
% 11.72/2.34 % Starting sh5l with 300s (1) cores
% 11.72/2.34 % sh5l with pid 3115921 completed with status 0
% 11.72/2.34 % Result found by sh5l
% 11.72/2.34 % Preprocessing class: FSLSSMSMSSSNFFN.
% 11.72/2.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.72/2.34 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 11.72/2.34 % Starting new_bool_3 with 300s (1) cores
% 11.72/2.34 % Starting new_bool_1 with 300s (1) cores
% 11.72/2.34 % Starting sh5l with 300s (1) cores
% 11.72/2.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 11.72/2.34 % SinE strategy is gf500_gu_R04_F100_L20000
% 11.72/2.34 % Search class: FGHSF-FFMM21-MFFFFFNN
% 11.72/2.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 11.72/2.34 % Starting SubtermCWHack with 28s (1) cores
% 11.72/2.34 % SubtermCWHack with pid 3115929 completed with status 0
% 11.72/2.34 % Result found by SubtermCWHack
% 11.72/2.34 % Preprocessing class: FSLSSMSMSSSNFFN.
% 11.72/2.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.72/2.34 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 11.72/2.34 % Starting new_bool_3 with 300s (1) cores
% 11.72/2.34 % Starting new_bool_1 with 300s (1) cores
% 11.72/2.34 % Starting sh5l with 300s (1) cores
% 11.72/2.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 11.72/2.34 % SinE strategy is gf500_gu_R04_F100_L20000
% 11.72/2.34 % Search class: FGHSF-FFMM21-MFFFFFNN
% 11.72/2.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 11.72/2.34 % Starting SubtermCWHack with 28s (1) cores
% 11.72/2.34 % Preprocessing time : 0.002 s
% 11.72/2.34
% 11.72/2.34 % Proof found!
% 11.72/2.34 % SZS status Theorem
% 11.72/2.34 % SZS output start CNFRefutation
% See solution above
% 11.72/2.34 % Parsed axioms : 59
% 11.72/2.34 % Removed by relevancy pruning/SinE : 0
% 11.72/2.34 % Initial clauses : 99
% 11.72/2.34 % Removed in clause preprocessing : 5
% 11.72/2.34 % Initial clauses in saturation : 94
% 11.72/2.34 % Processed clauses : 6556
% 11.72/2.34 % ...of these trivial : 513
% 11.72/2.34 % ...subsumed : 3379
% 11.72/2.34 % ...remaining for further processing : 2664
% 11.72/2.34 % Other redundant clauses eliminated : 7
% 11.72/2.34 % Clauses deleted for lack of memory : 0
% 11.72/2.34 % Backward-subsumed : 65
% 11.72/2.34 % Backward-rewritten : 611
% 11.72/2.34 % Generated clauses : 108315
% 11.72/2.34 % ...of the previous two non-redundant : 92498
% 11.72/2.34 % ...aggressively subsumed : 0
% 11.72/2.34 % Contextual simplify-reflections : 113
% 11.72/2.34 % Paramodulations : 108296
% 11.72/2.34 % Factorizations : 0
% 11.72/2.34 % NegExts : 0
% 11.72/2.34 % Equation resolutions : 19
% 11.72/2.34 % Disequality decompositions : 0
% 11.72/2.34 % Total rewrite steps : 152530
% 11.72/2.34 % ...of those cached : 151731
% 11.72/2.34 % Propositional unsat checks : 0
% 11.72/2.34 % Propositional check models : 0
% 11.72/2.34 % Propositional check unsatisfiable : 0
% 11.72/2.34 % Propositional clauses : 0
% 11.72/2.34 % Propositional clauses after purity: 0
% 11.72/2.34 % Propositional unsat core size : 0
% 11.72/2.34 % Propositional preprocessing time : 0.000
% 11.72/2.34 % Propositional encoding time : 0.000
% 11.72/2.34 % Propositional solver time : 0.000
% 11.72/2.34 % Success case prop preproc time : 0.000
% 11.72/2.34 % Success case prop encoding time : 0.000
% 11.72/2.34 % Success case prop solver time : 0.000
% 11.72/2.34 % Current number of processed clauses : 1985
% 11.72/2.34 % Positive orientable unit clauses : 824
% 11.72/2.34 % Positive unorientable unit clauses: 0
% 11.72/2.34 % Negative unit clauses : 3
% 11.72/2.34 % Non-unit-clauses : 1158
% 11.72/2.34 % Current number of unprocessed clauses: 85640
% 11.72/2.34 % ...number of literals in the above : 369724
% 11.72/2.34 % Current number of archived formulas : 0
% 11.72/2.34 % Current number of archived clauses : 676
% 11.72/2.34 % Clause-clause subsumption calls (NU) : 360976
% 11.72/2.34 % Rec. Clause-clause subsumption calls : 206223
% 11.72/2.34 % Non-unit clause-clause subsumptions : 3543
% 11.72/2.34 % Unit Clause-clause subsumption calls : 49874
% 11.72/2.34 % Rewrite failures with RHS unbound : 0
% 11.72/2.34 % BW rewrite match attempts : 3384
% 11.72/2.34 % BW rewrite match successes : 110
% 11.72/2.34 % Condensation attempts : 0
% 11.72/2.34 % Condensation successes : 0
% 11.72/2.34 % Termbank termtop insertions : 2326801
% 11.72/2.34 % Search garbage collected termcells : 927
% 11.72/2.34
% 11.72/2.34 % -------------------------------------------------
% 11.72/2.34 % User time : 1.475 s
% 11.72/2.34 % System time : 0.071 s
% 11.72/2.34 % Total time : 1.546 s
% 11.72/2.34 % Maximum resident set size: 3960 pages
% 11.72/2.34
% 11.72/2.34 % -------------------------------------------------
% 11.72/2.34 % User time : 1.478 s
% 11.72/2.34 % System time : 0.079 s
% 11.72/2.34 % Total time : 1.557 s
% 11.72/2.34 % Maximum resident set size: 4608 pages
% 11.72/2.34 % E exiting
%------------------------------------------------------------------------------