%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG056+1 : 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 : n023.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 05:05:09 PM UTC 2026
% Result : Theorem 240.14s 96.91s
% Output : CNFRefutation 240.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 29
% Syntax : Number of formulae : 208 ( 108 unt; 0 def)
% Number of atoms : 489 ( 139 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 481 ( 200 ~; 200 |; 61 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 15 con; 0-2 aty)
% Number of variables : 155 ( 2 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(m__1873,hypothesis,
( aScalar0(xH)
& xH = sdtasdt0(xA,xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1873) ).
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(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__1854,hypothesis,
( aScalar0(xG)
& xG = sdtasdt0(xB,xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1854) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(mNegSc,axiom,
! [X1] :
( aScalar0(X1)
=> aScalar0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
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__1949,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1949) ).
fof(mSqPos,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(sz0z00,sdtasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqPos) ).
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(mSZeroSc,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
fof(mLETrn,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETrn) ).
fof(m__1892,hypothesis,
( aScalar0(xR)
& xR = sdtasdt0(xC,xG) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(m__1783,hypothesis,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1783) ).
fof(mScSqPos,axiom,
! [X1] :
( aVector0(X1)
=> sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSqPos) ).
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__1837,hypothesis,
( aScalar0(xF)
& xF = sdtasdt0(xA,xA) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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__1709,hypothesis,
( aVector0(xp)
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1709) ).
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__1726,hypothesis,
( aVector0(xq)
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1726) ).
fof(mLERef,axiom,
! [X1] :
( aScalar0(X1)
=> sdtlseqdt0(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
fof(mLETot,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> ( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETot) ).
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(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__,conjecture,
xN = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_29,plain,
! [X88,X89,X90] :
( ( sdtpldt0(sdtpldt0(X88,X89),X90) = sdtpldt0(X88,sdtpldt0(X89,X90))
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) )
& ( sdtpldt0(X88,X89) = sdtpldt0(X89,X88)
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) )
& ( sdtasdt0(sdtasdt0(X88,X89),X90) = sdtasdt0(X88,sdtasdt0(X89,X90))
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) )
& ( sdtasdt0(X88,X89) = sdtasdt0(X89,X88)
| ~ aScalar0(X88)
| ~ aScalar0(X89)
| ~ aScalar0(X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])]) ).
cnf(c_0_30,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_31,hypothesis,
xH = sdtasdt0(xA,xB),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_32,hypothesis,
aScalar0(xB),
inference(split_conjunct,[status(thm)],[m__1766]) ).
cnf(c_0_33,hypothesis,
aScalar0(xA),
inference(split_conjunct,[status(thm)],[m__1746]) ).
fof(c_0_34,plain,
! [X98,X99] :
( ( sdtasdt0(X98,smndt0(X99)) = smndt0(sdtasdt0(X98,X99))
| ~ aScalar0(X98)
| ~ aScalar0(X99) )
& ( sdtasdt0(smndt0(X98),X99) = smndt0(sdtasdt0(X98,X99))
| ~ aScalar0(X98)
| ~ aScalar0(X99) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMNeg])])]) ).
cnf(c_0_35,hypothesis,
( sdtasdt0(xA,sdtasdt0(xB,X1)) = sdtasdt0(xH,X1)
| ~ aScalar0(X1) ),
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])]) ).
cnf(c_0_36,hypothesis,
xG = sdtasdt0(xB,xB),
inference(split_conjunct,[status(thm)],[m__1854]) ).
cnf(c_0_37,plain,
( sdtasdt0(X1,smndt0(X2)) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,hypothesis,
sdtasdt0(xA,xG) = sdtasdt0(xH,xB),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_32])]) ).
cnf(c_0_39,hypothesis,
aScalar0(xG),
inference(split_conjunct,[status(thm)],[m__1854]) ).
fof(c_0_40,plain,
! [X84,X85] :
( ~ aScalar0(X84)
| ~ aScalar0(X85)
| aScalar0(sdtasdt0(X84,X85)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])]) ).
cnf(c_0_41,plain,
( sdtasdt0(smndt0(X1),X2) = smndt0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,hypothesis,
smndt0(sdtasdt0(xH,xB)) = sdtasdt0(xA,smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_33])]) ).
cnf(c_0_43,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_44,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,hypothesis,
sdtasdt0(xA,smndt0(xB)) = smndt0(xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_31]),c_0_32]),c_0_33])]) ).
fof(c_0_46,plain,
! [X86] :
( ~ aScalar0(X86)
| aScalar0(smndt0(X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mNegSc])]) ).
fof(c_0_47,plain,
! [X87] :
( ( sdtpldt0(X87,sz0z00) = X87
| ~ aScalar0(X87) )
& ( sdtpldt0(sz0z00,X87) = X87
| ~ aScalar0(X87) )
& ( sdtasdt0(X87,sz0z00) = sz0z00
| ~ aScalar0(X87) )
& ( sdtasdt0(sz0z00,X87) = sz0z00
| ~ aScalar0(X87) )
& ( sdtpldt0(X87,smndt0(X87)) = sz0z00
| ~ aScalar0(X87) )
& ( sdtpldt0(smndt0(X87),X87) = sz0z00
| ~ aScalar0(X87) )
& ( smndt0(smndt0(X87)) = X87
| ~ aScalar0(X87) )
& ( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X87) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScZero])])]) ).
cnf(c_0_48,hypothesis,
sdtasdt0(smndt0(xH),xB) = sdtasdt0(xA,smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_32]),c_0_43])]) ).
cnf(c_0_49,hypothesis,
sdtasdt0(xA,smndt0(xG)) = sdtasdt0(xH,smndt0(xB)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_42]),c_0_32]),c_0_43])]) ).
cnf(c_0_50,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_51,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_52,hypothesis,
( aScalar0(smndt0(xH))
| ~ aScalar0(smndt0(xB)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_33])]) ).
cnf(c_0_53,plain,
( aScalar0(smndt0(X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_54,plain,
( smndt0(smndt0(X1)) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_55,plain,
! [X120] :
( ~ aScalar0(X120)
| sdtlseqdt0(sz0z00,sdtasdt0(X120,X120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSqPos])]) ).
cnf(c_0_56,hypothesis,
sdtasdt0(smndt0(xH),xB) = sdtasdt0(xH,smndt0(xB)),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,hypothesis,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,hypothesis,
aScalar0(smndt0(xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_32])]) ).
cnf(c_0_59,hypothesis,
smndt0(sdtasdt0(xH,xB)) = sdtasdt0(xH,smndt0(xB)),
inference(rw,[status(thm)],[c_0_42,c_0_49]) ).
cnf(c_0_60,hypothesis,
aScalar0(sdtasdt0(xH,xB)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_38]),c_0_39]),c_0_33])]) ).
cnf(c_0_61,plain,
( smndt0(sdtasdt0(X1,smndt0(X2))) = sdtasdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_37]),c_0_44]) ).
fof(c_0_62,plain,
! [X112,X113,X114,X115] :
( ~ aScalar0(X112)
| ~ aScalar0(X113)
| ~ aScalar0(X114)
| ~ aScalar0(X115)
| ~ sdtlseqdt0(X112,X113)
| ~ sdtlseqdt0(sz0z00,X114)
| ~ sdtlseqdt0(X114,X115)
| sdtlseqdt0(sdtasdt0(X112,X114),sdtasdt0(X113,X115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMonM])]) ).
cnf(c_0_63,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X1))
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_64,plain,
( sdtasdt0(sz0z00,X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_65,plain,
aScalar0(sz0z00),
inference(split_conjunct,[status(thm)],[mSZeroSc]) ).
fof(c_0_66,plain,
! [X105,X106,X107] :
( ~ aScalar0(X105)
| ~ aScalar0(X106)
| ~ aScalar0(X107)
| ~ sdtlseqdt0(X105,X106)
| ~ sdtlseqdt0(X106,X107)
| sdtlseqdt0(X105,X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETrn])]) ).
cnf(c_0_67,hypothesis,
xR = sdtasdt0(xC,xG),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_68,hypothesis,
aScalar0(xC),
inference(split_conjunct,[status(thm)],[m__1783]) ).
fof(c_0_69,plain,
! [X139] :
( ~ aVector0(X139)
| sdtlseqdt0(sz0z00,sdtasasdt0(X139,X139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mScSqPos])]) ).
cnf(c_0_70,hypothesis,
sdtasdt0(xB,smndt0(xH)) = sdtasdt0(xH,smndt0(xB)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_32])]) ).
cnf(c_0_71,hypothesis,
smndt0(sdtasdt0(xH,smndt0(xB))) = sdtasdt0(xH,xB),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_59]),c_0_60])]) ).
cnf(c_0_72,hypothesis,
smndt0(smndt0(xH)) = xH,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_45]),c_0_31]),c_0_32]),c_0_33])]) ).
fof(c_0_73,plain,
! [X108,X109,X110,X111] :
( ~ aScalar0(X108)
| ~ aScalar0(X109)
| ~ aScalar0(X110)
| ~ aScalar0(X111)
| ~ sdtlseqdt0(X108,X109)
| ~ sdtlseqdt0(X110,X111)
| sdtlseqdt0(sdtpldt0(X108,X110),sdtpldt0(X109,X111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEMon])]) ).
cnf(c_0_74,plain,
( sdtpldt0(X1,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_75,hypothesis,
xF = sdtasdt0(xA,xA),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_76,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_62]) ).
cnf(c_0_77,plain,
( sdtasdt0(X1,sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_78,plain,
sdtlseqdt0(sz0z00,sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65])]) ).
cnf(c_0_79,plain,
( sdtlseqdt0(X1,X3)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_80,hypothesis,
sdtlseqdt0(sz0z00,xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_36]),c_0_32])]) ).
cnf(c_0_81,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_37,c_0_67]),c_0_39]),c_0_68])]) ).
cnf(c_0_82,plain,
( aScalar0(sdtasdt0(X1,smndt0(X2)))
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_37]),c_0_44]) ).
fof(c_0_83,plain,
! [X118,X119] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X118,X119))
| ~ sdtlseqdt0(sz0z00,X118)
| ~ sdtlseqdt0(sz0z00,X119)
| ~ aScalar0(X118)
| ~ aScalar0(X119) )
& ( sdtlseqdt0(sz0z00,sdtasdt0(X118,X119))
| ~ sdtlseqdt0(sz0z00,X118)
| ~ sdtlseqdt0(sz0z00,X119)
| ~ aScalar0(X118)
| ~ aScalar0(X119) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPosMon])])]) ).
cnf(c_0_84,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(X1,X1))
| ~ aVector0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_85,hypothesis,
xC = sdtasasdt0(xp,xp),
inference(split_conjunct,[status(thm)],[m__1783]) ).
cnf(c_0_86,hypothesis,
aVector0(xp),
inference(split_conjunct,[status(thm)],[m__1709]) ).
cnf(c_0_87,hypothesis,
xN = sdtasdt0(xR,xS),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_88,hypothesis,
aScalar0(xS),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_89,hypothesis,
aScalar0(xR),
inference(split_conjunct,[status(thm)],[m__1892]) ).
cnf(c_0_90,hypothesis,
xD = sdtasasdt0(xq,xq),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_91,hypothesis,
aVector0(xq),
inference(split_conjunct,[status(thm)],[m__1726]) ).
cnf(c_0_92,hypothesis,
sdtasdt0(xB,xH) = sdtasdt0(xH,xB),
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_37,c_0_70]),c_0_71]),c_0_72]),c_0_58]),c_0_32])]) ).
cnf(c_0_93,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_73]) ).
cnf(c_0_94,plain,
( sdtpldt0(sz0z00,X1) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_95,plain,
( sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,smndt0(X2))) = sz0z00
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_37]),c_0_44]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(xA,smndt0(xA)) = smndt0(xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_75]),c_0_33])]) ).
cnf(c_0_97,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X3,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_65])]) ).
cnf(c_0_98,hypothesis,
( sdtlseqdt0(X1,xG)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_39]),c_0_65])]) ).
fof(c_0_99,plain,
! [X102] :
( ~ aScalar0(X102)
| sdtlseqdt0(X102,X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERef])]) ).
cnf(c_0_100,plain,
( sdtpldt0(smndt0(X1),X1) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_101,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_61,c_0_81]),c_0_67]),c_0_39]),c_0_68])]) ).
cnf(c_0_102,hypothesis,
aScalar0(smndt0(xR)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_81]),c_0_39]),c_0_68])]) ).
cnf(c_0_103,plain,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,X2))
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_104,hypothesis,
sdtlseqdt0(sz0z00,xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
cnf(c_0_105,hypothesis,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_87]),c_0_88]),c_0_89])]) ).
cnf(c_0_106,hypothesis,
xS = sdtasdt0(xF,xD),
inference(split_conjunct,[status(thm)],[m__1930]) ).
cnf(c_0_107,hypothesis,
sdtlseqdt0(sz0z00,xD),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_90]),c_0_91])]) ).
cnf(c_0_108,hypothesis,
sdtlseqdt0(sz0z00,xF),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_75]),c_0_33])]) ).
cnf(c_0_109,hypothesis,
aScalar0(xD),
inference(split_conjunct,[status(thm)],[m__1800]) ).
cnf(c_0_110,hypothesis,
aScalar0(xF),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_111,hypothesis,
( sdtasdt0(xA,sdtasdt0(xA,X1)) = sdtasdt0(xF,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_75]),c_0_33])]) ).
cnf(c_0_112,hypothesis,
sdtasdt0(xA,sdtasdt0(xH,xB)) = sdtasdt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_92]),c_0_43])]) ).
cnf(c_0_113,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_93,c_0_94]),c_0_65])]) ).
cnf(c_0_114,hypothesis,
sdtpldt0(xF,smndt0(xF)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_75]),c_0_33])]) ).
cnf(c_0_115,hypothesis,
aScalar0(smndt0(xF)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_96]),c_0_33])]) ).
cnf(c_0_116,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,xG))
| ~ sdtlseqdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_39]),c_0_78]),c_0_65])]) ).
cnf(c_0_117,plain,
( sdtlseqdt0(X1,X1)
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_118,hypothesis,
sdtpldt0(xR,smndt0(xR)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102])]) ).
cnf(c_0_119,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_103,c_0_67]),c_0_80]),c_0_104]),c_0_39]),c_0_68])]) ).
cnf(c_0_120,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_61,c_0_105]),c_0_87]),c_0_88]),c_0_89])]) ).
cnf(c_0_121,hypothesis,
aScalar0(smndt0(xN)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_105]),c_0_88]),c_0_89])]) ).
cnf(c_0_122,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_103,c_0_106]),c_0_107]),c_0_108]),c_0_109]),c_0_110])]) ).
cnf(c_0_123,hypothesis,
sdtasdt0(xF,xG) = sdtasdt0(xH,xH),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_38]),c_0_112]),c_0_39])]) ).
fof(c_0_124,plain,
! [X116,X117] :
( ~ aScalar0(X116)
| ~ aScalar0(X117)
| sdtlseqdt0(X116,X117)
| sdtlseqdt0(X117,X116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETot])]) ).
cnf(c_0_125,hypothesis,
( sdtlseqdt0(X1,xC)
| ~ sdtlseqdt0(X1,sz0z00)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_104]),c_0_68]),c_0_65])]) ).
cnf(c_0_126,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ sdtlseqdt0(X1,smndt0(xF))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_108]),c_0_115]),c_0_110])]) ).
fof(c_0_127,plain,
! [X103,X104] :
( ~ aScalar0(X103)
| ~ aScalar0(X104)
| ~ sdtlseqdt0(X103,X104)
| ~ sdtlseqdt0(X104,X103)
| X103 = X104 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEASm])]) ).
cnf(c_0_128,hypothesis,
( sdtlseqdt0(sz0z00,sdtasdt0(X1,xG))
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_129,hypothesis,
sdtasdt0(smndt0(xC),xG) = smndt0(xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_67]),c_0_39]),c_0_68])]) ).
cnf(c_0_130,hypothesis,
( sdtlseqdt0(X1,sz0z00)
| ~ 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_113,c_0_118]),c_0_119]),c_0_102]),c_0_89])]) ).
cnf(c_0_131,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_132,hypothesis,
sdtasdt0(xB,smndt0(xB)) = smndt0(xG),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_36]),c_0_32])]) ).
cnf(c_0_133,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_37,c_0_106]),c_0_109]),c_0_110])]) ).
cnf(c_0_134,hypothesis,
sdtpldt0(xN,smndt0(xN)) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_120]),c_0_121])]) ).
cnf(c_0_135,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_103,c_0_87]),c_0_88]),c_0_89])]),c_0_122]),c_0_119])]) ).
cnf(c_0_136,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_41,c_0_106]),c_0_109]),c_0_110])]) ).
cnf(c_0_137,hypothesis,
smndt0(sdtasdt0(xH,xH)) = sdtasdt0(xF,smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_123]),c_0_39]),c_0_110])]) ).
cnf(c_0_138,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_139,hypothesis,
( sdtlseqdt0(X1,xC)
| ~ sdtlseqdt0(X2,sz0z00)
| ~ sdtlseqdt0(X1,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_125]),c_0_68])]) ).
cnf(c_0_140,hypothesis,
sdtlseqdt0(smndt0(xF),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_117]),c_0_115])]) ).
cnf(c_0_141,plain,
( X1 = X2
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_142,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xR))
| ~ aScalar0(smndt0(xC)) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_143,hypothesis,
sdtlseqdt0(smndt0(xR),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_117]),c_0_102])]) ).
cnf(c_0_144,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_100]),c_0_53]) ).
cnf(c_0_145,hypothesis,
sdtpldt0(smndt0(xR),xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_101]),c_0_102])]) ).
cnf(c_0_146,hypothesis,
smndt0(smndt0(xG)) = xG,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_132]),c_0_36]),c_0_32])]) ).
cnf(c_0_147,hypothesis,
aScalar0(smndt0(xG)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_132]),c_0_32])]) ).
cnf(c_0_148,hypothesis,
aScalar0(smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_133]),c_0_109]),c_0_110])]) ).
cnf(c_0_149,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_113,c_0_134]),c_0_135]),c_0_121]),c_0_51])]) ).
cnf(c_0_150,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),smndt0(xS))
| ~ sdtlseqdt0(X1,smndt0(xF))
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xD)
| ~ 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_76,c_0_136]),c_0_109])]),c_0_115])]) ).
cnf(c_0_151,hypothesis,
sdtpldt0(smndt0(xN),xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_120]),c_0_121])]) ).
cnf(c_0_152,hypothesis,
sdtasdt0(smndt0(xF),xG) = sdtasdt0(xF,smndt0(xG)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_123]),c_0_39]),c_0_110])]),c_0_137]) ).
cnf(c_0_153,hypothesis,
sdtasdt0(xF,smndt0(xG)) = sdtasdt0(xH,smndt0(xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_137]),c_0_43])]) ).
cnf(c_0_154,hypothesis,
( sdtlseqdt0(X1,xG)
| sdtlseqdt0(xG,X1)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_138,c_0_39]) ).
cnf(c_0_155,hypothesis,
( sdtlseqdt0(X1,xC)
| ~ sdtlseqdt0(X1,smndt0(xF))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_115])]) ).
cnf(c_0_156,hypothesis,
( smndt0(xR) = sz0z00
| ~ aScalar0(smndt0(xC)) ),
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_143]),c_0_65]),c_0_102])]) ).
cnf(c_0_157,plain,
( sdtpldt0(X1,sz0z00) = X1
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_158,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_144,c_0_145]),c_0_101]),c_0_89]),c_0_102])]) ).
cnf(c_0_159,hypothesis,
( aScalar0(sdtasdt0(xH,X1))
| ~ aScalar0(sdtasdt0(xB,X1))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_35]),c_0_33])]) ).
cnf(c_0_160,hypothesis,
( aScalar0(sdtasdt0(X1,xH))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_72]),c_0_58])]) ).
cnf(c_0_161,hypothesis,
sdtpldt0(smndt0(xG),xG) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_146]),c_0_147])]) ).
cnf(c_0_162,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xN))
| ~ sdtlseqdt0(sz0z00,smndt0(xS)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_105]),c_0_119]),c_0_89])]),c_0_148])]) ).
cnf(c_0_163,hypothesis,
sdtlseqdt0(smndt0(xN),sz0z00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_117]),c_0_121])]) ).
cnf(c_0_164,hypothesis,
( sdtlseqdt0(sz0z00,smndt0(xS))
| ~ sdtlseqdt0(X1,smndt0(xF))
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_77]),c_0_78]),c_0_107]),c_0_65])]) ).
cnf(c_0_165,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_144,c_0_151]),c_0_120]),c_0_51]),c_0_121])]) ).
cnf(c_0_166,hypothesis,
( sdtlseqdt0(sdtasdt0(X1,X2),xR)
| ~ sdtlseqdt0(sz0z00,X2)
| ~ sdtlseqdt0(X2,xG)
| ~ sdtlseqdt0(X1,xC)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_67]),c_0_39]),c_0_68])]) ).
cnf(c_0_167,hypothesis,
sdtasdt0(smndt0(xF),xG) = sdtasdt0(xH,smndt0(xH)),
inference(rw,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_168,hypothesis,
sdtlseqdt0(xG,xG),
inference(spm,[status(thm)],[c_0_154,c_0_39]) ).
cnf(c_0_169,hypothesis,
sdtlseqdt0(smndt0(xF),xC),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_117]),c_0_115])]) ).
cnf(c_0_170,hypothesis,
smndt0(xR) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_53]),c_0_68])]) ).
cnf(c_0_171,hypothesis,
sdtpldt0(sz0z00,xR) = xR,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_89])]) ).
cnf(c_0_172,hypothesis,
aScalar0(sdtasdt0(xH,xH)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_43]),c_0_32])]) ).
fof(c_0_173,plain,
! [X91,X92,X93] :
( ( sdtasdt0(X91,sdtpldt0(X92,X93)) = sdtpldt0(sdtasdt0(X91,X92),sdtasdt0(X91,X93))
| ~ aScalar0(X91)
| ~ aScalar0(X92)
| ~ aScalar0(X93) )
& ( sdtasdt0(sdtpldt0(X91,X92),X93) = sdtpldt0(sdtasdt0(X91,X93),sdtasdt0(X92,X93))
| ~ aScalar0(X91)
| ~ aScalar0(X92)
| ~ aScalar0(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistr])])]) ).
cnf(c_0_174,hypothesis,
sdtpldt0(xG,sz0z00) = sdtpldt0(sz0z00,xG),
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_161]),c_0_146]),c_0_39]),c_0_147])]) ).
cnf(c_0_175,hypothesis,
( smndt0(xN) = sz0z00
| ~ sdtlseqdt0(sz0z00,smndt0(xS)) ),
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_162]),c_0_163]),c_0_65]),c_0_121])]) ).
cnf(c_0_176,hypothesis,
sdtlseqdt0(sz0z00,smndt0(xS)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_117]),c_0_115])]) ).
cnf(c_0_177,hypothesis,
sdtpldt0(sz0z00,xN) = xN,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_165]),c_0_51])]) ).
cnf(c_0_178,hypothesis,
sdtlseqdt0(sdtasdt0(xH,smndt0(xH)),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_166,c_0_167]),c_0_80]),c_0_168]),c_0_169]),c_0_39]),c_0_115])]) ).
cnf(c_0_179,hypothesis,
xR = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_170]),c_0_171]) ).
cnf(c_0_180,hypothesis,
aScalar0(sdtasdt0(xF,smndt0(xG))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_137]),c_0_172])]) ).
cnf(c_0_181,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_173]) ).
cnf(c_0_182,hypothesis,
sdtpldt0(sz0z00,xG) = xG,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_174]),c_0_39])]) ).
cnf(c_0_183,plain,
( smndt0(sz0z00) = sz0z00
| ~ aScalar0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_184,negated_conjecture,
xN != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_185,hypothesis,
smndt0(xN) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_176])]) ).
cnf(c_0_186,hypothesis,
sdtpldt0(xN,sz0z00) = xN,
inference(rw,[status(thm)],[c_0_165,c_0_177]) ).
cnf(c_0_187,plain,
( sdtpldt0(sdtasdt0(X1,smndt0(X2)),sdtasdt0(X1,X2)) = sz0z00
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_37]),c_0_44]) ).
cnf(c_0_188,hypothesis,
sdtlseqdt0(sz0z00,sdtasdt0(xH,smndt0(xH))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_167]),c_0_115])]) ).
cnf(c_0_189,hypothesis,
sdtlseqdt0(sdtasdt0(xH,smndt0(xH)),sz0z00),
inference(rw,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_190,hypothesis,
aScalar0(sdtasdt0(xH,smndt0(xH))),
inference(rw,[status(thm)],[c_0_180,c_0_153]) ).
cnf(c_0_191,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_181,c_0_77]),c_0_65])]) ).
cnf(c_0_192,hypothesis,
sdtpldt0(xG,sz0z00) = xG,
inference(rw,[status(thm)],[c_0_174,c_0_182]) ).
cnf(c_0_193,hypothesis,
smndt0(sz0z00) = sz0z00,
inference(spm,[status(thm)],[c_0_183,c_0_51]) ).
cnf(c_0_194,negated_conjecture,
xN != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)),
inference(split_conjunct,[status(thm)],[c_0_184]) ).
cnf(c_0_195,hypothesis,
xN = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_185]),c_0_186]) ).
cnf(c_0_196,hypothesis,
sdtpldt0(sdtasdt0(xH,xH),sdtasdt0(xH,smndt0(xH))) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_153]),c_0_146]),c_0_123]),c_0_147]),c_0_110])]) ).
cnf(c_0_197,hypothesis,
sdtasdt0(xH,smndt0(xH)) = sz0z00,
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_188]),c_0_189]),c_0_65]),c_0_190])]) ).
cnf(c_0_198,hypothesis,
sdtpldt0(sdtasdt0(xH,xH),sz0z00) = sdtasdt0(xH,xH),
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_191,c_0_123]),c_0_192]),c_0_123]),c_0_39]),c_0_110])]) ).
cnf(c_0_199,plain,
( sdtasdt0(sz0z00,smndt0(X1)) = sz0z00
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_64]),c_0_193]),c_0_65])]) ).
cnf(c_0_200,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_61,c_0_133]),c_0_106]),c_0_109]),c_0_110])]) ).
cnf(c_0_201,negated_conjecture,
sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xC,xD)) != sz0z00,
inference(rw,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_202,hypothesis,
sdtasdt0(xH,xH) = sz0z00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197]),c_0_198]) ).
cnf(c_0_203,plain,
( sdtasdt0(sz0z00,sdtasdt0(X1,X2)) = sdtasdt0(sz0z00,X2)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_64]),c_0_65])]) ).
cnf(c_0_204,hypothesis,
sdtasdt0(sz0z00,xS) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_148])]) ).
cnf(c_0_205,negated_conjecture,
sdtasdt0(sz0z00,sdtasdt0(xC,xD)) != sz0z00,
inference(rw,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_206,hypothesis,
sdtasdt0(sz0z00,xD) = sz0z00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_106]),c_0_204]),c_0_109]),c_0_110])]) ).
cnf(c_0_207,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_203]),c_0_206]),c_0_109]),c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG056+1 : 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
% 0.16/0.33 % Computer : n023.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:49:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 240.14/96.91 % Version : CSE_E---1.7
% 240.14/96.91 % Problem : theBenchmark.p
% 240.14/96.91 % SZS status Theorem for theBenchmark.p
% 240.14/96.91 % SZS output start CNFRefutation
% See solution above
% 240.74/97.50 % Total time : 75.139s
%------------------------------------------------------------------------------