%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG064+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:05:11 PM UTC 2026
% Result : Theorem 14.58s 9.88s
% Output : CNFRefutation 14.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 28
% Syntax : Number of formulae : 142 ( 57 unt; 0 def)
% Number of atoms : 384 ( 101 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 400 ( 158 ~; 153 |; 69 &)
% ( 0 <=>; 20 =>; 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 : 126 ( 2 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mMNeg,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
& sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1930,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(m__1800,hypothesis,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1800) ).
fof(m__1837,hypothesis,
( aScalar0(xF)
& xF = sdtasdt0(xA,xA) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(mScZero,axiom,
! [X1] :
( aScalar0(X1)
=> ( sdtpldt0(X1,sz0z00) = X1
& sdtpldt0(sz0z00,X1) = X1
& sdtasdt0(X1,sz0z00) = sz0z00
& sdtasdt0(sz0z00,X1) = sz0z00
& sdtpldt0(X1,smndt0(X1)) = sz0z00
& sdtpldt0(smndt0(X1),X1) = sz0z00
& smndt0(smndt0(X1)) = X1
& smndt0(sz0z00) = sz0z00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
fof(m__1726,hypothesis,
( aVector0(xq)
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xq,X1) = sdtlbdtrb0(xt,X1) )
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
fof(m__1709,hypothesis,
( aVector0(xp)
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(xp,X1) = sdtlbdtrb0(xs,X1) )
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).
fof(m__2144,hypothesis,
( sdtasdt0(xR,smndt0(xS)) = smndt0(xN)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).
fof(m__1892,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(mPosMon,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X2) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(X1,X2))
& sdtlseqdt0(sz0z00,sdtasdt0(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPosMon) ).
fof(m__1746,hypothesis,
( aScalar0(xA)
& xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).
fof(m__1854,hypothesis,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
fof(m__1766,hypothesis,
( aScalar0(xB)
& xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
fof(mLEMon,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3)
& aScalar0(X4) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X3,X4) )
=> sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMon) ).
fof(m__1949,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
fof(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mLEMonM,axiom,
! [X1,X2,X3,X4] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3)
& aScalar0(X4) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(sz0z00,X3)
& sdtlseqdt0(X3,X4) )
=> sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEMonM) ).
fof(mDistr,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).
fof(mLERef,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
fof(mArith,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(mLEASm,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
fof(m__,conjecture,
sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_28,plain,
! [X100,X101] :
( ( sdtasdt0(X100,smndt0(X101)) = smndt0(sdtasdt0(X100,X101))
| ~ aScalar0(X100)
| ~ aScalar0(X101) )
& ( sdtasdt0(smndt0(X100),X101) = smndt0(sdtasdt0(X100,X101))
| ~ aScalar0(X100)
| ~ aScalar0(X101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])]) ).
fof(c_0_29,plain,
! [X86,X87] :
( ~ aScalar0(X86)
| ~ aScalar0(X87)
| aScalar0(sdtasdt0(X86,X87)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])]) ).
cnf(c_0_30,plain,
( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_31,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_32,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_33,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_34,plain,
! [X89] :
( ( sdtpldt0(X89,sz0z00) = X89
| ~ aScalar0(X89) )
& ( sdtpldt0(sz0z00,X89) = X89
| ~ aScalar0(X89) )
& ( sdtasdt0(X89,sz0z00) = sz0z00
| ~ aScalar0(X89) )
& ( sdtasdt0(sz0z00,X89) = sz0z00
| ~ aScalar0(X89) )
& ( sdtpldt0(X89,smndt0(X89)) = sz0z00
| ~ aScalar0(X89) )
& ( sdtpldt0(smndt0(X89),X89) = sz0z00
| ~ aScalar0(X89) )
& ( smndt0(smndt0(X89)) = X89
| ~ aScalar0(X89) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X89) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])]) ).
cnf(c_0_35,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,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_30,c_0_31]),c_0_32]),c_0_33])]) ).
fof(c_0_37,plain,
! [X88] :
( ~ aScalar0(X88)
| aScalar0(smndt0(X88)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])]) ).
fof(c_0_38,plain,
! [X141] :
( ~ aVector0(X141)
| sdtlseqdt0(sz0z00,sdtasasdt0(X141,X141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])]) ).
fof(c_0_39,hypothesis,
! [X145] :
( aVector0(xq)
& szszuzczcdt0(aDimensionOf0(xq)) = aDimensionOf0(xt)
& ( ~ aNaturalNumber0(X145)
| sdtlbdtrb0(xq,X145) = sdtlbdtrb0(xt,X145) )
& xq = sziznziztdt0(xt) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1726])])]) ).
fof(c_0_40,plain,
! [X122] :
( ~ aScalar0(X122)
| sdtlseqdt0(sz0z00,sdtasdt0(X122,X122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])]) ).
fof(c_0_41,hypothesis,
! [X144] :
( aVector0(xp)
& szszuzczcdt0(aDimensionOf0(xp)) = aDimensionOf0(xs)
& ( ~ aNaturalNumber0(X144)
| sdtlbdtrb0(xp,X144) = sdtlbdtrb0(xs,X144) )
& xp = sziznziztdt0(xs) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1709])])]) ).
cnf(c_0_42,plain,
( smndt0(smndt0(X1)) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_44,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_45,hypothesis,
( aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xD)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33])]) ).
cnf(c_0_46,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_47,plain,
! [X120,X121] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X120,X121))
| ~ sdtlseqdt0(sz0z00,X120)
| ~ sdtlseqdt0(sz0z00,X121)
| ~ aScalar0(X120)
| ~ aScalar0(X121) )
& ( sdtlseqdt0(sz0z00,sdtasdt0(X120,X121))
| ~ sdtlseqdt0(sz0z00,X120)
| ~ sdtlseqdt0(sz0z00,X121)
| ~ aScalar0(X120)
| ~ aScalar0(X121) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])]) ).
cnf(c_0_48,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_49,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_50,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_51,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_53,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_54,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_55,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_56,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_57,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
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,
! [X110,X111,X112,X113] :
( ~ aScalar0(X110)
| ~ aScalar0(X111)
| ~ aScalar0(X112)
| ~ aScalar0(X113)
| ~ sdtlseqdt0(X110,X111)
| ~ sdtlseqdt0(X112,X113)
| sdtlseqdt0(sdtpldt0(X110,X112),sdtpldt0(X111,X113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])]) ).
cnf(c_0_62,plain,
( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_30]),c_0_35]) ).
cnf(c_0_63,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_64,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_65,hypothesis,
( aScalar0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_43]),c_0_44])]) ).
cnf(c_0_66,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_32])]) ).
cnf(c_0_67,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_68,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_69,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_70,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_54]),c_0_55])]) ).
cnf(c_0_71,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_56]),c_0_57])]) ).
cnf(c_0_72,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_30,c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_73,plain,
( sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X4))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,plain,
( sdtpldt0(sz0z00,X1) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_75,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_76,plain,
( sdtpldt0(smndt0(X1),X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_77,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_62,c_0_43]),c_0_63]),c_0_64]),c_0_44])]) ).
cnf(c_0_78,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_79,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_67,c_0_31]),c_0_68]),c_0_69]),c_0_32]),c_0_33])]) ).
cnf(c_0_80,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_67,c_0_58]),c_0_70]),c_0_71]),c_0_59]),c_0_60])]) ).
fof(c_0_81,plain,
! [X114,X115,X116,X117] :
( ~ aScalar0(X114)
| ~ aScalar0(X115)
| ~ aScalar0(X116)
| ~ aScalar0(X117)
| ~ sdtlseqdt0(X114,X115)
| ~ sdtlseqdt0(sz0z00,X116)
| ~ sdtlseqdt0(X116,X117)
| sdtlseqdt0(sdtasdt0(X114,X116),sdtasdt0(X115,X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])]) ).
cnf(c_0_82,plain,
( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_83,hypothesis,
( aScalar0(smndt0(xR))
| ~ aScalar0(smndt0(xG)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_72]),c_0_60])]) ).
fof(c_0_84,plain,
! [X93,X94,X95] :
( ( sdtasdt0(X93,sdtpldt0(X94,X95)) = sdtpldt0(sdtasdt0(X93,X94),sdtasdt0(X93,X95))
| ~ aScalar0(X93)
| ~ aScalar0(X94)
| ~ aScalar0(X95) )
& ( sdtasdt0(sdtpldt0(X93,X94),X95) = sdtpldt0(sdtasdt0(X93,X95),sdtasdt0(X94,X95))
| ~ aScalar0(X93)
| ~ aScalar0(X94)
| ~ aScalar0(X95) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])]) ).
cnf(c_0_85,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X3))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aScalar0(X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_86,hypothesis,
sdtpldt0(xN,smndt0(xN)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]) ).
cnf(c_0_87,hypothesis,
sdtlseqdt0(sz0z00,xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_63]),c_0_64]),c_0_44])]),c_0_79]),c_0_80])]) ).
cnf(c_0_88,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
fof(c_0_89,plain,
! [X104] :
( ~ aScalar0(X104)
| sdtlseqdt0(X104,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])]) ).
cnf(c_0_90,plain,
( sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X2,X4))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ aScalar0(X4)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(sz0z00,X3)
| ~ sdtlseqdt0(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_91,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_82,c_0_63]),c_0_64]),c_0_44])]) ).
cnf(c_0_92,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_46]),c_0_59])]) ).
cnf(c_0_93,plain,
( sdtasdt0(sz0z00,X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_94,plain,
! [X90,X91,X92] :
( ( sdtpldt0(sdtpldt0(X90,X91),X92) = sdtpldt0(X90,sdtpldt0(X91,X92))
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtpldt0(X90,X91) = sdtpldt0(X91,X90)
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtasdt0(sdtasdt0(X90,X91),X92) = sdtasdt0(X90,sdtasdt0(X91,X92))
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtasdt0(X90,X91) = sdtasdt0(X91,X90)
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(split_conjunct,[status(thm)],[m__2144]) ).
fof(c_0_96,plain,
! [X84,X85] :
( ~ aScalar0(X84)
| ~ aScalar0(X85)
| aScalar0(sdtpldt0(X84,X85)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSumSc])]) ).
cnf(c_0_97,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_98,plain,
! [X105,X106] :
( ~ aScalar0(X105)
| ~ aScalar0(X106)
| ~ sdtlseqdt0(X105,X106)
| ~ sdtlseqdt0(X106,X105)
| X105 = X106 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])]) ).
cnf(c_0_99,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X1,smndt0(xN))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_78]),c_0_88])]) ).
cnf(c_0_100,plain,
( sdtlseqdt0(X1,X1)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_101,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xN))
| ~ sdtlseqdt0(X1,smndt0(xR))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xS)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_64])]),c_0_92])]) ).
cnf(c_0_102,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_103,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_93]),c_0_75])]) ).
cnf(c_0_104,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_105,plain,
( sdtpldt0(X1,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_106,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_107,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_108,hypothesis,
( aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(spm,[status(thm)],[c_0_35,c_0_95]) ).
cnf(c_0_109,plain,
( aScalar0(sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_110,hypothesis,
( sdtpldt0(sdtasdt0(xR,X1),xN) = sdtasdt0(xR,sdtpldt0(X1,xS))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_63]),c_0_64]),c_0_44])]) ).
cnf(c_0_111,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_112,hypothesis,
sdtlseqdt0(smndt0(xN),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_78])]) ).
cnf(c_0_113,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xN))
| ~ sdtlseqdt0(X1,smndt0(xR))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_79]),c_0_75])]) ).
cnf(c_0_114,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_76]),c_0_46]) ).
cnf(c_0_115,hypothesis,
sdtpldt0(smndt0(xN),xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_77]),c_0_78])]) ).
cnf(c_0_116,negated_conjecture,
~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS))),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_117,hypothesis,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_88]) ).
cnf(c_0_118,hypothesis,
aScalar0(sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_46]),c_0_64])]) ).
cnf(c_0_119,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(spm,[status(thm)],[c_0_51,c_0_95]) ).
cnf(c_0_120,plain,
( aScalar0(sdtasdt0(X1,sdtpldt0(X2,X3)))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_97]),c_0_35]),c_0_35]) ).
cnf(c_0_121,hypothesis,
sdtasdt0(xR,sdtpldt0(xS,xS)) = sdtpldt0(xN,xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_63]),c_0_64])]) ).
cnf(c_0_122,hypothesis,
( smndt0(xN) = sz0z00
| ~ sdtlseqdt0(sz0z00,smndt0(xN)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_78]),c_0_75])]) ).
cnf(c_0_123,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_100]),c_0_92])]) ).
cnf(c_0_124,plain,
( sdtpldt0(X1,sz0z00) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_125,hypothesis,
sdtpldt0(xN,sz0z00) = sdtpldt0(sz0z00,xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_77]),c_0_88]),c_0_78])]) ).
cnf(c_0_126,plain,
( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_127,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_128,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtpldt0(sdtasdt0(xS,xS),sdtasdt0(xR,xR)))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118])]) ).
cnf(c_0_129,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_66])]) ).
cnf(c_0_130,hypothesis,
aScalar0(sdtpldt0(xN,xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_64]),c_0_44])]) ).
cnf(c_0_131,hypothesis,
smndt0(xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123])]) ).
cnf(c_0_132,hypothesis,
sdtpldt0(sz0z00,xN) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_88])]) ).
cnf(c_0_133,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_126,c_0_88]) ).
cnf(c_0_134,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,sdtasdt0(X2,sdtasdt0(X1,X2))))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_127]),c_0_35]) ).
cnf(c_0_135,hypothesis,
( sdtasdt0(xC,sdtasdt0(xG,X1)) = sdtasdt0(xR,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_58]),c_0_59]),c_0_60])]) ).
cnf(c_0_136,negated_conjecture,
( ~ sdtlseqdt0(sdtpldt0(xN,xN),sdtasdt0(xR,xR))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_85]),c_0_129]),c_0_130]),c_0_118])]) ).
cnf(c_0_137,hypothesis,
xN = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_131]),c_0_125]),c_0_132]) ).
cnf(c_0_138,hypothesis,
sdtpldt0(sz0z00,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_133]),c_0_75])]) ).
cnf(c_0_139,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_58]),c_0_59]),c_0_60]),c_0_58]),c_0_44])]) ).
cnf(c_0_140,negated_conjecture,
~ aScalar0(sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137]),c_0_137]),c_0_138]),c_0_139])]) ).
cnf(c_0_141,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_35]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG064+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:48:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 14.58/9.88 % Version : CSE_E---1.7
% 14.58/9.88 % Problem : theBenchmark.p
% 14.58/9.88 % SZS status Theorem for theBenchmark.p
% 14.58/9.88 % SZS output start CNFRefutation
% See solution above
% 14.67/9.93 % Total time : 7.381s
%------------------------------------------------------------------------------