%------------------------------------------------------------------------------
% File : E---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 : n011.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 02:05:41 PM UTC 2026
% Result : Theorem 15.84s 3.35s
% Output : CNFRefutation 15.84s
% 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,
! [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])])])]) ).
fof(c_0_29,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])])])]) ).
fof(c_0_30,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])])]) ).
fof(c_0_31,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_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,
! [X75] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X75,X75))
| ~ aVector0(X75) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])])]) ).
fof(c_0_45,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])])])]) ).
fof(c_0_46,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])])]) ).
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,
! [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_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,
! [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_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,
! [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_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,
! [X33,X34] :
( sdtasdt0(smndt0(X33),smndt0(X34)) = sdtasdt0(X33,X34)
| ~ aScalar0(X34)
| ~ aScalar0(X33) ),
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,
! [X56,X57] :
( X56 = X57
| sdtasdt0(X56,X56) != sdtasdt0(X57,X57)
| ~ sdtlseqdt0(sz0z00,X57)
| ~ sdtlseqdt0(sz0z00,X56)
| ~ aScalar0(X57)
| ~ aScalar0(X56) ),
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,
! [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_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,
! [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_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,
! [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_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,
! [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_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
% 0.00/0.03 % Problem : RNG060+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:16:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 15.84/3.35 % Version: 3.5.1
% 15.84/3.35 % Preprocessing class: FSLSSMSMSSSNFFN.
% 15.84/3.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.84/3.35 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 15.84/3.35 % Starting new_bool_3 with 300s (1) cores
% 15.84/3.35 % Starting new_bool_1 with 300s (1) cores
% 15.84/3.35 % Starting sh5l with 300s (1) cores
% 15.84/3.35 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 952130 completed with status 0
% 15.84/3.35 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 15.84/3.35 % Preprocessing class: FSLSSMSMSSSNFFN.
% 15.84/3.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.84/3.35 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 15.84/3.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.84/3.35 % No SInE strategy applied
% 15.84/3.35 % Search class: FGHSF-FFMM21-MFFFFFNN
% 15.84/3.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 15.84/3.35 % Starting SubtermCWHack with 136s (1) cores
% 15.84/3.35 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 15.84/3.35 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 15.84/3.35 % Starting G-E--_208_C18_F1_SE_CS_SP_PI_PS_S5PRR_S032N with 136s (1) cores
% 15.84/3.35 % Starting new_bool_3 with 136s (1) cores
% 15.84/3.35 % SubtermCWHack with pid 952140 completed with status 0
% 15.84/3.35 % Result found by SubtermCWHack
% 15.84/3.35 % Preprocessing class: FSLSSMSMSSSNFFN.
% 15.84/3.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 15.84/3.35 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 15.84/3.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 15.84/3.35 % No SInE strategy applied
% 15.84/3.35 % Search class: FGHSF-FFMM21-MFFFFFNN
% 15.84/3.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 15.84/3.35 % Starting SubtermCWHack with 136s (1) cores
% 15.84/3.35 % Preprocessing time : 0.002 s
% 15.84/3.35
% 15.84/3.35 % Proof found!
% 15.84/3.35 % SZS status Theorem
% 15.84/3.35 % SZS output start CNFRefutation
% See solution above
% 15.84/3.35 % Parsed axioms : 59
% 15.84/3.35 % Removed by relevancy pruning/SinE : 0
% 15.84/3.35 % Initial clauses : 99
% 15.84/3.35 % Removed in clause preprocessing : 5
% 15.84/3.35 % Initial clauses in saturation : 94
% 15.84/3.35 % Processed clauses : 6556
% 15.84/3.35 % ...of these trivial : 513
% 15.84/3.35 % ...subsumed : 3379
% 15.84/3.35 % ...remaining for further processing : 2664
% 15.84/3.35 % Other redundant clauses eliminated : 7
% 15.84/3.35 % Clauses deleted for lack of memory : 0
% 15.84/3.35 % Backward-subsumed : 65
% 15.84/3.35 % Backward-rewritten : 611
% 15.84/3.35 % Generated clauses : 108315
% 15.84/3.35 % ...of the previous two non-redundant : 92498
% 15.84/3.35 % ...aggressively subsumed : 0
% 15.84/3.35 % Contextual simplify-reflections : 113
% 15.84/3.35 % Paramodulations : 108296
% 15.84/3.35 % Factorizations : 0
% 15.84/3.35 % NegExts : 0
% 15.84/3.35 % Equation resolutions : 19
% 15.84/3.35 % Disequality decompositions : 0
% 15.84/3.35 % Total rewrite steps : 152530
% 15.84/3.35 % ...of those cached : 151731
% 15.84/3.35 % Propositional unsat checks : 0
% 15.84/3.35 % Propositional check models : 0
% 15.84/3.35 % Propositional check unsatisfiable : 0
% 15.84/3.35 % Propositional clauses : 0
% 15.84/3.35 % Propositional clauses after purity: 0
% 15.84/3.35 % Propositional unsat core size : 0
% 15.84/3.35 % Propositional preprocessing time : 0.000
% 15.84/3.35 % Propositional encoding time : 0.000
% 15.84/3.35 % Propositional solver time : 0.000
% 15.84/3.35 % Success case prop preproc time : 0.000
% 15.84/3.35 % Success case prop encoding time : 0.000
% 15.84/3.35 % Success case prop solver time : 0.000
% 15.84/3.35 % Current number of processed clauses : 1985
% 15.84/3.35 % Positive orientable unit clauses : 824
% 15.84/3.35 % Positive unorientable unit clauses: 0
% 15.84/3.35 % Negative unit clauses : 3
% 15.84/3.35 % Non-unit-clauses : 1158
% 15.84/3.35 % Current number of unprocessed clauses: 85640
% 15.84/3.35 % ...number of literals in the above : 369724
% 15.84/3.35 % Current number of archived formulas : 0
% 15.84/3.35 % Current number of archived clauses : 676
% 15.84/3.35 % Clause-clause subsumption calls (NU) : 351039
% 15.84/3.35 % Rec. Clause-clause subsumption calls : 200488
% 15.84/3.35 % Non-unit clause-clause subsumptions : 3543
% 15.84/3.35 % Unit Clause-clause subsumption calls : 49874
% 15.84/3.35 % Rewrite failures with RHS unbound : 0
% 15.84/3.35 % BW rewrite match attempts : 3384
% 15.84/3.35 % BW rewrite match successes : 110
% 15.84/3.35 % Condensation attempts : 0
% 15.84/3.35 % Condensation successes : 0
% 15.84/3.35 % Termbank termtop insertions : 2326801
% 15.84/3.35 % Search garbage collected termcells : 909
% 15.84/3.35
% 15.84/3.35 % -------------------------------------------------
% 15.84/3.35 % User time : 2.725 s
% 15.84/3.35 % System time : 0.108 s
% 15.84/3.35 % Total time : 2.833 s
% 15.84/3.35 % Maximum resident set size: 3704 pages
% 15.84/3.35
% 15.84/3.35 % -------------------------------------------------
% 15.84/3.35 % User time : 12.453 s
% 15.84/3.35 % System time : 0.550 s
% 15.84/3.35 % Total time : 13.003 s
% 15.84/3.35 % Maximum resident set size: 4864 pages
% 15.84/3.35 % E exiting
%------------------------------------------------------------------------------