%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG062+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 : n022.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 05:05:10 PM UTC 2026
% Result : Theorem 40.44s 24.13s
% Output : CNFRefutation 40.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 30
% Syntax : Number of formulae : 205 ( 98 unt; 0 def)
% Number of atoms : 480 ( 172 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 465 ( 190 ~; 184 |; 70 &)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 149 ( 2 sgn 66 !; 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(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(mMDNeg,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMDNeg) ).
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(m__1930,hypothesis,
( aScalar0(xS)
& xS = sdtasdt0(xF,xD) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(m__1854,hypothesis,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
fof(m__1949,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
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(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(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(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
fof(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__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(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__1766,hypothesis,
( aScalar0(xB)
& xB = sdtlbdtrb0(xt,aDimensionOf0(xt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1766) ).
fof(m__1746,hypothesis,
( aScalar0(xA)
& xA = sdtlbdtrb0(xs,aDimensionOf0(xs)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1746) ).
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(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(mLERef,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
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,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mSumSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(m__2221,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2221) ).
fof(c_0_30,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])])]) ).
cnf(c_0_31,plain,
( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_32,hypothesis,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_33,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
fof(c_0_34,plain,
! [X102,X103] :
( ~ aScalar0(X102)
| ~ aScalar0(X103)
| sdtasdt0(smndt0(X102),smndt0(X103)) = sdtasdt0(X102,X103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMDNeg])]) ).
fof(c_0_35,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_36,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(xR)) = smndt0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_37,plain,
( sdtasdt0(smndt0(X1),smndt0(X2)) = sdtasdt0(X1,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
fof(c_0_39,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_40,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_41,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_42,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_43,plain,
( smndt0(smndt0(X1)) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,hypothesis,
( smndt0(smndt0(xN)) = sdtasdt0(xS,xR)
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33]),c_0_38])]) ).
cnf(c_0_45,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
fof(c_0_46,plain,
! [X88] :
( ~ aScalar0(X88)
| aScalar0(smndt0(X88)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])]) ).
cnf(c_0_47,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,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_31,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_49,hypothesis,
( sdtasdt0(xS,xR) = xN
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).
cnf(c_0_50,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_51,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_52,plain,
( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_53,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_54,hypothesis,
( aScalar0(smndt0(xR))
| ~ aScalar0(smndt0(xG)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42])]) ).
cnf(c_0_55,hypothesis,
sdtasdt0(xS,xR) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_38])]) ).
cnf(c_0_56,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_57,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_58,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_59,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_51]) ).
cnf(c_0_60,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_52,c_0_53]),c_0_38]),c_0_33])]) ).
cnf(c_0_61,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_41])]) ).
cnf(c_0_62,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_63,hypothesis,
sdtasdt0(xS,smndt0(xR)) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_55]),c_0_33]),c_0_38])]) ).
fof(c_0_64,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_65,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_66,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_31,c_0_56]),c_0_57]),c_0_58])]) ).
fof(c_0_67,plain,
! [X122] :
( ~ aScalar0(X122)
| sdtlseqdt0(sz0z00,sdtasdt0(X122,X122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])]) ).
fof(c_0_68,plain,
! [X141] :
( ~ aVector0(X141)
| sdtlseqdt0(sz0z00,sdtasasdt0(X141,X141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])]) ).
fof(c_0_69,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])])]) ).
fof(c_0_70,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])])]) ).
cnf(c_0_71,hypothesis,
( sdtpldt0(sdtasdt0(smndt0(xR),X1),smndt0(xN)) = sdtasdt0(smndt0(xR),sdtpldt0(X1,xS))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_38])]),c_0_61])]) ).
cnf(c_0_72,hypothesis,
( sdtpldt0(sdtasdt0(X1,smndt0(xR)),smndt0(xN)) = sdtasdt0(sdtpldt0(X1,xS),smndt0(xR))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_38])]),c_0_61])]) ).
cnf(c_0_73,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_74,hypothesis,
( sdtasdt0(xR,smndt0(smndt0(xS))) = smndt0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_65]),c_0_33])]) ).
cnf(c_0_75,hypothesis,
( aScalar0(smndt0(xS))
| ~ aScalar0(smndt0(xD)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_66]),c_0_58])]) ).
fof(c_0_76,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_77,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_78,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_79,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_80,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_81,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_82,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_83,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_84,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
cnf(c_0_85,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_86,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_87,hypothesis,
sdtasdt0(sdtpldt0(smndt0(xR),xS),smndt0(xR)) = sdtasdt0(smndt0(xR),sdtpldt0(smndt0(xR),xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_61])]) ).
cnf(c_0_88,hypothesis,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_45]) ).
fof(c_0_89,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_90,hypothesis,
( smndt0(smndt0(xN)) = xN
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_43]),c_0_53]),c_0_38])]) ).
cnf(c_0_91,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_50]),c_0_57])]) ).
cnf(c_0_92,hypothesis,
( aScalar0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_65]),c_0_33])]) ).
cnf(c_0_93,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_94,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79])]) ).
cnf(c_0_95,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82])]) ).
cnf(c_0_96,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_83]),c_0_84])]) ).
cnf(c_0_97,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_85]),c_0_86])]) ).
cnf(c_0_98,hypothesis,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(split_conjunct,[status(thm)],[m__2144]) ).
cnf(c_0_99,plain,
( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X3,smndt0(X2))) = sdtasdt0(sdtpldt0(smndt0(X1),X3),smndt0(X2))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_37]),c_0_50]),c_0_50]) ).
cnf(c_0_100,hypothesis,
sdtasdt0(sdtpldt0(xS,smndt0(xR)),smndt0(xR)) = sdtasdt0(smndt0(xR),sdtpldt0(xS,smndt0(xR))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_38]),c_0_61])]) ).
cnf(c_0_101,plain,
( sdtpldt0(sdtasdt0(X1,smndt0(X2)),sdtasdt0(X3,X2)) = sdtasdt0(sdtpldt0(X1,smndt0(X3)),smndt0(X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_37]),c_0_50]),c_0_50]) ).
cnf(c_0_102,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_89]) ).
cnf(c_0_103,plain,
( sdtpldt0(sz0z00,X1) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_104,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
cnf(c_0_105,plain,
( sdtpldt0(smndt0(X1),X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_106,hypothesis,
smndt0(smndt0(xN)) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
cnf(c_0_107,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_91])]) ).
cnf(c_0_108,hypothesis,
sdtlseqdt0(sz0z00,xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_40]),c_0_94]),c_0_41]),c_0_42])]),c_0_95])]) ).
cnf(c_0_109,hypothesis,
sdtlseqdt0(sz0z00,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_56]),c_0_96]),c_0_57]),c_0_58])]),c_0_97])]) ).
fof(c_0_110,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_111,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(smndt0(xS))) = smndt0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(spm,[status(thm)],[c_0_31,c_0_98]) ).
cnf(c_0_112,hypothesis,
sdtasdt0(smndt0(xR),sdtpldt0(smndt0(xR),xS)) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_99]),c_0_63]),c_0_38]),c_0_33])]) ).
cnf(c_0_113,hypothesis,
sdtasdt0(smndt0(xR),sdtpldt0(xS,smndt0(xR))) = sdtpldt0(smndt0(xN),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_100,c_0_101]),c_0_63]),c_0_38]),c_0_33])]) ).
cnf(c_0_114,hypothesis,
( sdtpldt0(smndt0(xN),sdtasdt0(xR,X1)) = sdtasdt0(xR,sdtpldt0(smndt0(xS),X1))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_65]),c_0_33])]),c_0_91])]) ).
cnf(c_0_115,hypothesis,
( sdtpldt0(smndt0(xN),sdtasdt0(X1,xR)) = sdtasdt0(sdtpldt0(smndt0(xS),X1),xR)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_32]),c_0_33])]),c_0_91])]) ).
cnf(c_0_116,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_102,c_0_103]),c_0_104])]) ).
cnf(c_0_117,hypothesis,
sdtpldt0(xN,smndt0(xN)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]) ).
cnf(c_0_118,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_93,c_0_55]),c_0_33]),c_0_38])]),c_0_108]),c_0_109])]) ).
fof(c_0_119,plain,
! [X104] :
( ~ aScalar0(X104)
| sdtlseqdt0(X104,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])]) ).
cnf(c_0_120,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_110]) ).
cnf(c_0_121,plain,
( sdtasdt0(sz0z00,X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_122,hypothesis,
( sdtpldt0(sdtasdt0(smndt0(xS),X1),smndt0(xN)) = sdtasdt0(smndt0(xS),sdtpldt0(X1,xR))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_32]),c_0_33])]),c_0_91])]) ).
cnf(c_0_123,hypothesis,
( smndt0(sdtasdt0(xS,xS)) = sdtasdt0(xS,smndt0(xS))
| ~ aScalar0(smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_37]),c_0_38])]) ).
cnf(c_0_124,hypothesis,
( aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xS)) ),
inference(spm,[status(thm)],[c_0_47,c_0_98]) ).
cnf(c_0_125,hypothesis,
sdtpldt0(smndt0(xN),sdtasdt0(xR,xR)) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_88]),c_0_113]),c_0_38]),c_0_61])]) ).
cnf(c_0_126,hypothesis,
sdtasdt0(sdtpldt0(smndt0(xS),xR),xR) = sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_33])]) ).
cnf(c_0_127,hypothesis,
( sdtpldt0(sdtasdt0(xR,X1),smndt0(xN)) = sdtasdt0(xR,sdtpldt0(X1,smndt0(xS)))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_65]),c_0_33])]),c_0_91])]) ).
cnf(c_0_128,hypothesis,
( sdtpldt0(sdtasdt0(X1,xR),smndt0(xN)) = sdtasdt0(sdtpldt0(X1,smndt0(xS)),xR)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_32]),c_0_33])]),c_0_91])]) ).
fof(c_0_129,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_130,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_116,c_0_117]),c_0_118]),c_0_107]),c_0_45])]) ).
cnf(c_0_131,plain,
( sdtlseqdt0(X1,X1)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_132,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_120,c_0_60]),c_0_38])]),c_0_61])]) ).
cnf(c_0_133,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_134,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_121]),c_0_104])]) ).
cnf(c_0_135,hypothesis,
sdtasdt0(smndt0(xS),sdtpldt0(smndt0(xS),xR)) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_98]),c_0_91])]) ).
cnf(c_0_136,plain,
( sdtpldt0(X1,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_137,hypothesis,
smndt0(sdtasdt0(xS,xS)) = sdtasdt0(xS,smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_91])]) ).
cnf(c_0_138,hypothesis,
aScalar0(sdtasdt0(xS,xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_50]),c_0_38])]) ).
cnf(c_0_139,hypothesis,
sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) = sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_125]),c_0_126]),c_0_33])]) ).
cnf(c_0_140,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),xR) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_33])]) ).
cnf(c_0_141,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_142,hypothesis,
sdtlseqdt0(smndt0(xN),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_107])]) ).
cnf(c_0_143,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_132,c_0_133]),c_0_134]),c_0_109]),c_0_104])]) ).
cnf(c_0_144,plain,
( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_31]),c_0_47]) ).
cnf(c_0_145,hypothesis,
( sdtasdt0(smndt0(xS),sdtpldt0(X1,smndt0(xS))) = sdtpldt0(sdtasdt0(smndt0(xS),X1),sdtasdt0(xS,xS))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_98]),c_0_91])]) ).
cnf(c_0_146,hypothesis,
sdtasdt0(smndt0(xS),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_88]),c_0_33]),c_0_91])]) ).
cnf(c_0_147,hypothesis,
sdtpldt0(sdtasdt0(xS,xS),sdtasdt0(xS,smndt0(xS))) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138])]) ).
cnf(c_0_148,hypothesis,
sdtpldt0(smndt0(xN),sdtasdt0(xR,xR)) = sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)),
inference(rw,[status(thm)],[c_0_125,c_0_139]) ).
cnf(c_0_149,hypothesis,
sdtasdt0(xR,sdtpldt0(smndt0(xS),xR)) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_139]),c_0_140]),c_0_33])]) ).
cnf(c_0_150,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_141,c_0_142]),c_0_107]),c_0_104])]) ).
cnf(c_0_151,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_131]),c_0_61])]) ).
cnf(c_0_152,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_153,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_144,c_0_48]),c_0_40]),c_0_41]),c_0_42])]) ).
fof(c_0_154,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_155,hypothesis,
sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) = sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_32]),c_0_33])]) ).
cnf(c_0_156,hypothesis,
( sdtpldt0(smndt0(xN),sdtasdt0(xS,X1)) = sdtasdt0(xS,sdtpldt0(smndt0(xR),X1))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_63]),c_0_38])]),c_0_61])]) ).
cnf(c_0_157,hypothesis,
sdtasdt0(xS,sdtpldt0(xS,smndt0(xS))) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_147]),c_0_91]),c_0_38])]) ).
cnf(c_0_158,plain,
( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_159,hypothesis,
sdtpldt0(smndt0(xN),sdtasdt0(xR,xR)) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(rw,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_160,hypothesis,
smndt0(xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151])]) ).
cnf(c_0_161,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_105]),c_0_50]) ).
cnf(c_0_162,hypothesis,
sdtpldt0(smndt0(xR),xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_153]),c_0_61])]) ).
cnf(c_0_163,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
fof(c_0_164,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_165,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_144,c_0_66]),c_0_56]),c_0_57]),c_0_58])]) ).
cnf(c_0_166,hypothesis,
( sdtpldt0(sdtasdt0(xS,X1),smndt0(xN)) = sdtasdt0(xS,sdtpldt0(X1,smndt0(xR)))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_63]),c_0_38])]),c_0_61])]) ).
cnf(c_0_167,hypothesis,
sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)) = sdtasdt0(xS,sdtpldt0(smndt0(xR),xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_38])]) ).
cnf(c_0_168,hypothesis,
sdtasdt0(xS,sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_136]),c_0_38])]) ).
cnf(c_0_169,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_158,c_0_45]) ).
cnf(c_0_170,hypothesis,
sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(rw,[status(thm)],[c_0_139,c_0_149]) ).
cnf(c_0_171,hypothesis,
sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sz0z00,sdtasdt0(xR,xR)),
inference(rw,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_172,plain,
( sdtpldt0(X1,sz0z00) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_173,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_161,c_0_162]),c_0_153]),c_0_33]),c_0_61])]) ).
cnf(c_0_174,negated_conjecture,
( sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),smndt0(xN)) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_152]),c_0_138])]),c_0_107])]) ).
cnf(c_0_175,plain,
( aScalar0(sdtpldt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_176,hypothesis,
sdtpldt0(xS,smndt0(xS)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_165]),c_0_91])]) ).
cnf(c_0_177,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(split_conjunct,[status(thm)],[m__2221]) ).
cnf(c_0_178,hypothesis,
sdtasdt0(xS,sdtpldt0(smndt0(xR),xS)) = sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_167]),c_0_38])]) ).
cnf(c_0_179,hypothesis,
sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) = sdtasdt0(xS,sdtpldt0(smndt0(xR),xS)),
inference(rw,[status(thm)],[c_0_155,c_0_167]) ).
cnf(c_0_180,hypothesis,
sdtasdt0(smndt0(xS),sz0z00) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_168]),c_0_169]),c_0_104]),c_0_38])]) ).
cnf(c_0_181,hypothesis,
sdtasdt0(sdtpldt0(smndt0(xS),xR),xR) = sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),
inference(rw,[status(thm)],[c_0_126,c_0_149]) ).
cnf(c_0_182,plain,
( sdtpldt0(sdtasdt0(X1,X2),sz0z00) = sdtasdt0(X1,sdtpldt0(X2,sz0z00))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_133]),c_0_104])]) ).
cnf(c_0_183,hypothesis,
sdtpldt0(sdtasdt0(xR,xR),sz0z00) = sdtpldt0(sz0z00,sdtasdt0(xR,xR)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_160]),c_0_171]) ).
cnf(c_0_184,hypothesis,
sdtpldt0(sz0z00,xR) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_33])]) ).
cnf(c_0_185,negated_conjecture,
( sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)),smndt0(xN))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(sdtpldt0(sdtasdt0(xS,xS),smndt0(xN)))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_152]),c_0_107])]) ).
cnf(c_0_186,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_175,c_0_59]),c_0_47]),c_0_47]) ).
cnf(c_0_187,hypothesis,
sdtpldt0(smndt0(xS),sz0z00) = sdtpldt0(sz0z00,smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_176]),c_0_91]),c_0_38])]) ).
cnf(c_0_188,hypothesis,
sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtasdt0(xS,sdtpldt0(xS,smndt0(xR)))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_167]),c_0_178]) ).
cnf(c_0_189,hypothesis,
sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)) = sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))),
inference(rw,[status(thm)],[c_0_179,c_0_178]) ).
cnf(c_0_190,hypothesis,
sdtpldt0(sz0z00,sdtasdt0(xS,xS)) = sdtasdt0(xS,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_145,c_0_103]),c_0_98]),c_0_180]),c_0_104]),c_0_91])]) ).
cnf(c_0_191,hypothesis,
sdtasdt0(sdtpldt0(smndt0(xS),xR),xR) = sdtpldt0(sz0z00,sdtasdt0(xR,xR)),
inference(rw,[status(thm)],[c_0_181,c_0_171]) ).
cnf(c_0_192,hypothesis,
sdtpldt0(sz0z00,sdtasdt0(xR,xR)) = 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_182,c_0_183]),c_0_173]),c_0_184]),c_0_33])]) ).
cnf(c_0_193,negated_conjecture,
( sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))),smndt0(xN))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_167]),c_0_167]),c_0_178]),c_0_178]) ).
cnf(c_0_194,hypothesis,
aScalar0(sdtasdt0(xS,sdtpldt0(xS,smndt0(xR)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_178]),c_0_38]),c_0_61])]) ).
cnf(c_0_195,hypothesis,
sdtpldt0(sz0z00,smndt0(xS)) = smndt0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_187]),c_0_91])]) ).
cnf(c_0_196,hypothesis,
sdtpldt0(sdtasdt0(xR,sdtpldt0(xR,smndt0(xS))),sdtasdt0(xS,sdtpldt0(xS,smndt0(xR)))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_139]),c_0_149]) ).
cnf(c_0_197,hypothesis,
sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))) = sdtasdt0(xS,xS),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_160]),c_0_190]) ).
cnf(c_0_198,plain,
( aScalar0(sdtasdt0(sdtpldt0(X1,X2),X3))
| ~ aScalar0(X3)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_62]),c_0_47]),c_0_47]) ).
cnf(c_0_199,hypothesis,
sdtasdt0(sdtpldt0(smndt0(xS),xR),xR) = sdtasdt0(xR,xR),
inference(rw,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_200,negated_conjecture,
( sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(sdtasdt0(xS,sdtpldt0(xS,smndt0(xR))),smndt0(xN))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS)))
| ~ aScalar0(sdtasdt0(xR,xR)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_194])]) ).
cnf(c_0_201,hypothesis,
sdtpldt0(sdtasdt0(xS,xS),sz0z00) = sdtasdt0(xS,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_182,c_0_98]),c_0_187]),c_0_195]),c_0_98]),c_0_91])]) ).
cnf(c_0_202,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197]),c_0_171]),c_0_192]) ).
cnf(c_0_203,hypothesis,
aScalar0(sdtasdt0(xR,xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_199]),c_0_33]),c_0_91])]) ).
cnf(c_0_204,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_160]),c_0_197]),c_0_201]),c_0_202]),c_0_203])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG062+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
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 01:48:21 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 40.44/24.13 % Version : CSE_E---1.7
% 40.44/24.13 % Problem : theBenchmark.p
% 40.44/24.13 % SZS status Theorem for theBenchmark.p
% 40.44/24.13 % SZS output start CNFRefutation
% See solution above
% 40.62/24.31 % Total time : 17.406s
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