%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM527+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 : n027.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 04:57:41 PM UTC 2026
% Result : Theorem 6.86s 4.78s
% Output : CNFRefutation 6.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 30
% Syntax : Number of formulae : 205 ( 83 unt; 0 def)
% Number of atoms : 631 ( 182 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 726 ( 300 ~; 320 |; 66 &)
% ( 3 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 217 ( 0 sgn 100 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3082) ).
fof(m__2987,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(m__3046,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
fof(mPDP,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( isPrime0(X3)
& doDivides0(X3,sdtasdt0(X1,X2)) )
=> ( doDivides0(X3,X1)
| doDivides0(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPDP) ).
fof(mDivMin,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,sdtpldt0(X2,X3)) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
fof(m__3025,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X2,X3) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,X3) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(m__,conjecture,
( sdtlseqdt0(xn,xm)
=> sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(c_0_30,plain,
! [X148,X149,X151] :
( ( aNaturalNumber0(esk2_2(X148,X149))
| ~ doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) )
& ( X149 = sdtasdt0(X148,esk2_2(X148,X149))
| ~ doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) )
& ( ~ aNaturalNumber0(X151)
| X149 != sdtasdt0(X148,X151)
| doDivides0(X148,X149)
| ~ aNaturalNumber0(X148)
| ~ aNaturalNumber0(X149) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_31,plain,
! [X94,X95] :
( ~ aNaturalNumber0(X94)
| ~ aNaturalNumber0(X95)
| aNaturalNumber0(sdtasdt0(X94,X95)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_32,plain,
! [X152,X153,X154] :
( ( aNaturalNumber0(X154)
| X154 != sdtsldt0(X153,X152)
| X152 = sz00
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) )
& ( X153 = sdtasdt0(X152,X154)
| X154 != sdtsldt0(X153,X152)
| X152 = sz00
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) )
& ( ~ aNaturalNumber0(X154)
| X153 != sdtasdt0(X152,X154)
| X154 = sdtsldt0(X153,X152)
| X152 = sz00
| ~ doDivides0(X152,X153)
| ~ aNaturalNumber0(X152)
| ~ aNaturalNumber0(X153) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_33,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_34]) ).
cnf(c_0_37,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_38,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_39,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_40,hypothesis,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_41,hypothesis,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_43,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_44,plain,
! [X174,X175,X176] :
( ~ aNaturalNumber0(X174)
| ~ aNaturalNumber0(X175)
| ~ aNaturalNumber0(X176)
| ~ isPrime0(X176)
| ~ doDivides0(X176,sdtasdt0(X174,X175))
| doDivides0(X176,X174)
| doDivides0(X176,X175) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPDP])]) ).
cnf(c_0_45,hypothesis,
( doDivides0(xp,sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_46,hypothesis,
aNaturalNumber0(xq),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_38]),c_0_42])]),c_0_43]) ).
fof(c_0_47,plain,
! [X161,X162,X163] :
( ~ aNaturalNumber0(X161)
| ~ aNaturalNumber0(X162)
| ~ aNaturalNumber0(X163)
| ~ doDivides0(X161,X162)
| ~ doDivides0(X161,sdtpldt0(X162,X163))
| doDivides0(X161,X163) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
cnf(c_0_48,plain,
( doDivides0(X3,X1)
| doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ isPrime0(X3)
| ~ doDivides0(X3,sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,hypothesis,
doDivides0(xp,sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_34]),c_0_46])]) ).
cnf(c_0_50,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__3025]) ).
cnf(c_0_51,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__2987]) ).
fof(c_0_52,plain,
! [X164,X165] :
( ~ aNaturalNumber0(X164)
| ~ aNaturalNumber0(X165)
| ~ doDivides0(X164,X165)
| X165 = sz00
| sdtlseqdt0(X164,X165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
fof(c_0_53,plain,
! [X122,X123,X125] :
( ( aNaturalNumber0(esk1_2(X122,X123))
| ~ sdtlseqdt0(X122,X123)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123) )
& ( sdtpldt0(X122,esk1_2(X122,X123)) = X123
| ~ sdtlseqdt0(X122,X123)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123) )
& ( ~ aNaturalNumber0(X125)
| sdtpldt0(X122,X125) != X123
| sdtlseqdt0(X122,X123)
| ~ aNaturalNumber0(X122)
| ~ aNaturalNumber0(X123) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
fof(c_0_54,plain,
! [X92,X93] :
( ~ aNaturalNumber0(X92)
| ~ aNaturalNumber0(X93)
| aNaturalNumber0(sdtpldt0(X92,X93)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_55,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,hypothesis,
doDivides0(xp,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_38]),c_0_51])]) ).
fof(c_0_57,plain,
! [X101] :
( ( sdtpldt0(X101,sz00) = X101
| ~ aNaturalNumber0(X101) )
& ( X101 = sdtpldt0(sz00,X101)
| ~ aNaturalNumber0(X101) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_58,plain,
! [X132,X133,X134] :
( ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133)
| ~ aNaturalNumber0(X134)
| ~ sdtlseqdt0(X132,X133)
| ~ sdtlseqdt0(X133,X134)
| sdtlseqdt0(X132,X134) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_59,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_61,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_62,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_63,plain,
! [X155,X156,X157] :
( ~ aNaturalNumber0(X155)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157)
| ~ doDivides0(X155,X156)
| ~ doDivides0(X156,X157)
| doDivides0(X155,X157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
cnf(c_0_64,hypothesis,
( doDivides0(xp,X1)
| ~ doDivides0(xp,sdtpldt0(xm,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_51]),c_0_38])]) ).
cnf(c_0_65,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_67,plain,
! [X107] :
( ( sdtasdt0(X107,sz10) = X107
| ~ aNaturalNumber0(X107) )
& ( X107 = sdtasdt0(sz10,X107)
| ~ aNaturalNumber0(X107) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_68,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,hypothesis,
sdtlseqdt0(xp,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_40]),c_0_42]),c_0_38])]),c_0_60]) ).
cnf(c_0_70,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_61]),c_0_62]) ).
cnf(c_0_71,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_72,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_56]),c_0_66]),c_0_51])]) ).
cnf(c_0_74,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_75,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_76,hypothesis,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_42]),c_0_38])]) ).
cnf(c_0_77,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_66])]) ).
fof(c_0_78,plain,
! [X158,X159,X160] :
( ~ aNaturalNumber0(X158)
| ~ aNaturalNumber0(X159)
| ~ aNaturalNumber0(X160)
| ~ doDivides0(X158,X159)
| ~ doDivides0(X158,X160)
| doDivides0(X158,sdtpldt0(X159,X160)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_79,hypothesis,
( doDivides0(X1,sz00)
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_66]),c_0_38])]) ).
cnf(c_0_80,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_74]),c_0_75])]) ).
cnf(c_0_81,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_82,hypothesis,
sdtlseqdt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_66]),c_0_38])]) ).
cnf(c_0_83,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_84,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_85,hypothesis,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_75]),c_0_38])]) ).
fof(c_0_86,plain,
! [X96,X97] :
( ~ aNaturalNumber0(X96)
| ~ aNaturalNumber0(X97)
| sdtpldt0(X96,X97) = sdtpldt0(X97,X96) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_87,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_42]),c_0_66])]) ).
cnf(c_0_88,hypothesis,
aNaturalNumber0(esk1_2(sz00,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_82]),c_0_42]),c_0_66])]) ).
cnf(c_0_89,hypothesis,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_37]),c_0_38])]) ).
cnf(c_0_90,hypothesis,
( doDivides0(sz10,sdtpldt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_66]),c_0_75])]),c_0_80]) ).
cnf(c_0_91,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_92,hypothesis,
esk1_2(sz00,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_87]),c_0_88])]) ).
fof(c_0_93,plain,
! [X104,X105,X106] :
( ~ aNaturalNumber0(X104)
| ~ aNaturalNumber0(X105)
| ~ aNaturalNumber0(X106)
| sdtasdt0(sdtasdt0(X104,X105),X106) = sdtasdt0(X104,sdtasdt0(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_94,hypothesis,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xq) ),
inference(spm,[status(thm)],[c_0_89,c_0_34]) ).
cnf(c_0_95,hypothesis,
( doDivides0(sz10,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_66])]) ).
cnf(c_0_96,hypothesis,
sdtpldt0(sz00,xn) = xn,
inference(rw,[status(thm)],[c_0_87,c_0_92]) ).
fof(c_0_97,plain,
! [X144,X145] :
( ~ aNaturalNumber0(X144)
| ~ aNaturalNumber0(X145)
| X144 = sz00
| sdtlseqdt0(X145,sdtasdt0(X145,X144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_98,plain,
! [X102,X103] :
( ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| sdtasdt0(X102,X103) = sdtasdt0(X103,X102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_99,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_100,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_101,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_102,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_103,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_46])]) ).
cnf(c_0_104,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_105,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_42])]) ).
cnf(c_0_106,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_107,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_108,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_109,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_99]) ).
fof(c_0_110,negated_conjecture,
~ ( sdtlseqdt0(xn,xm)
=> sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_111,plain,
! [X115,X116,X117] :
( ( sdtasdt0(X115,X116) != sdtasdt0(X115,X117)
| X116 = X117
| ~ aNaturalNumber0(X116)
| ~ aNaturalNumber0(X117)
| X115 = sz00
| ~ aNaturalNumber0(X115) )
& ( sdtasdt0(X116,X115) != sdtasdt0(X117,X115)
| X116 = X117
| ~ aNaturalNumber0(X116)
| ~ aNaturalNumber0(X117)
| X115 = sz00
| ~ aNaturalNumber0(X115) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_112,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_75])]),c_0_34]) ).
cnf(c_0_113,hypothesis,
( sdtasdt0(xp,sdtasdt0(sdtasdt0(xm,xm),X1)) = sdtasdt0(sdtasdt0(xn,xn),X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_38])]),c_0_103])]) ).
cnf(c_0_114,hypothesis,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_102]),c_0_38])]) ).
cnf(c_0_115,hypothesis,
sdtasdt0(sz10,esk2_2(sz10,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_75]),c_0_42])]) ).
cnf(c_0_116,hypothesis,
aNaturalNumber0(esk2_2(sz10,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_105]),c_0_42]),c_0_75])]) ).
cnf(c_0_117,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_118,hypothesis,
sdtasdt0(xp,xq) = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_40]),c_0_41]),c_0_38]),c_0_42])]),c_0_43]) ).
fof(c_0_119,plain,
! [X140,X141,X142] :
( ( sdtasdt0(X140,X141) != sdtasdt0(X140,X142)
| X140 = sz00
| X141 = X142
| ~ sdtlseqdt0(X141,X142)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142) )
& ( sdtlseqdt0(sdtasdt0(X140,X141),sdtasdt0(X140,X142))
| X140 = sz00
| X141 = X142
| ~ sdtlseqdt0(X141,X142)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142) )
& ( sdtasdt0(X141,X140) != sdtasdt0(X142,X140)
| X140 = sz00
| X141 = X142
| ~ sdtlseqdt0(X141,X142)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142) )
& ( sdtlseqdt0(sdtasdt0(X141,X140),sdtasdt0(X142,X140))
| X140 = sz00
| X141 = X142
| ~ sdtlseqdt0(X141,X142)
| ~ aNaturalNumber0(X140)
| ~ aNaturalNumber0(X141)
| ~ aNaturalNumber0(X142) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
fof(c_0_120,negated_conjecture,
( sdtlseqdt0(xn,xm)
& ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(fof_nnf,[status(thm)],[c_0_110]) ).
cnf(c_0_121,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_122,hypothesis,
sdtasdt0(sdtasdt0(xn,xn),sz10) = sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_102]),c_0_103]),c_0_38]),c_0_75])]) ).
cnf(c_0_123,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_34]),c_0_51])]) ).
cnf(c_0_124,hypothesis,
esk2_2(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_115]),c_0_116])]) ).
cnf(c_0_125,hypothesis,
sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_102]),c_0_103]),c_0_38])]),c_0_43]) ).
cnf(c_0_126,hypothesis,
( sdtasdt0(xp,sdtasdt0(xq,X1)) = sdtasdt0(xn,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_118]),c_0_46]),c_0_38])]) ).
cnf(c_0_127,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_128,negated_conjecture,
sdtlseqdt0(xn,xm),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_129,plain,
( X1 = sdtasdt0(X2,X3)
| X4 = sz00
| sdtasdt0(X1,X4) != sdtasdt0(X2,sdtasdt0(X3,X4))
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_101]),c_0_34]) ).
cnf(c_0_130,hypothesis,
sdtasdt0(sz10,sdtasdt0(xn,xn)) = sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_122]),c_0_75]),c_0_123])]) ).
cnf(c_0_131,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[c_0_115,c_0_124]) ).
cnf(c_0_132,plain,
( doDivides0(sdtasdt0(X1,X2),sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_101]),c_0_34]) ).
cnf(c_0_133,hypothesis,
( sdtlseqdt0(X1,sdtasdt0(xn,xn))
| ~ sdtlseqdt0(X1,sdtasdt0(xm,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_125]),c_0_123]),c_0_103])]) ).
cnf(c_0_134,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_126]),c_0_46])]) ).
cnf(c_0_135,negated_conjecture,
( xm = xn
| X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_51]),c_0_42])]) ).
cnf(c_0_136,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[m__2987]) ).
cnf(c_0_137,hypothesis,
( X1 = xn
| sdtasdt0(X1,xn) != sdtasdt0(xn,xn)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_42]),c_0_75])]),c_0_60]) ).
cnf(c_0_138,hypothesis,
doDivides0(xn,sdtasdt0(xn,xn)),
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_130]),c_0_131]),c_0_42]),c_0_75])]) ).
cnf(c_0_139,hypothesis,
( sdtlseqdt0(X1,sdtasdt0(xn,xn))
| ~ sdtlseqdt0(X1,sdtasdt0(xn,xq))
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_140,hypothesis,
( xm = xn
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xq)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_134]),c_0_51])]),c_0_136]) ).
cnf(c_0_141,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_108]) ).
cnf(c_0_142,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_143,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_101]),c_0_34]) ).
cnf(c_0_144,hypothesis,
sdtasdt0(xp,sdtasdt0(xn,xq)) = sdtasdt0(xn,xn),
inference(rw,[status(thm)],[c_0_102,c_0_134]) ).
cnf(c_0_145,hypothesis,
( X1 = xn
| sdtasdt0(xn,X1) != sdtasdt0(xn,xn)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_108]),c_0_42])]) ).
cnf(c_0_146,hypothesis,
sdtasdt0(xn,sdtsldt0(sdtasdt0(xn,xn),xn)) = sdtasdt0(xn,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_138]),c_0_42]),c_0_123])]),c_0_60]) ).
cnf(c_0_147,hypothesis,
aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xn),xn)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_138]),c_0_42]),c_0_123])]),c_0_60]) ).
cnf(c_0_148,hypothesis,
( xm = xn
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_149,hypothesis,
doDivides0(xq,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_118]),c_0_46]),c_0_38])]) ).
cnf(c_0_150,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_142]),c_0_34]),c_0_36]) ).
cnf(c_0_151,hypothesis,
sdtasdt0(xn,sdtasdt0(xq,xp)) = sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_38]),c_0_46]),c_0_42])]) ).
cnf(c_0_152,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147])]) ).
fof(c_0_153,plain,
! [X130,X131] :
( ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131)
| ~ sdtlseqdt0(X130,X131)
| ~ sdtlseqdt0(X131,X130)
| X130 = X131 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_154,hypothesis,
( xm = xn
| sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xn,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_34]),c_0_42]),c_0_51])]) ).
cnf(c_0_155,hypothesis,
( doDivides0(xq,X1)
| ~ doDivides0(xq,sdtpldt0(xn,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_149]),c_0_42]),c_0_46])]) ).
cnf(c_0_156,hypothesis,
( doDivides0(xq,sdtpldt0(X1,xn))
| ~ doDivides0(xq,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_149]),c_0_42]),c_0_46])]) ).
cnf(c_0_157,plain,
( doDivides0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_100]),c_0_75])]) ).
cnf(c_0_158,hypothesis,
( sz10 = X1
| sdtasdt0(X1,xn) != xn
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_131]),c_0_42]),c_0_75])]),c_0_60]) ).
cnf(c_0_159,hypothesis,
doDivides0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_131]),c_0_42]),c_0_75])]) ).
cnf(c_0_160,hypothesis,
( sdtasdt0(xq,xp) = xn
| ~ aNaturalNumber0(sdtasdt0(xq,xp)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_152]),c_0_42])]),c_0_60]) ).
cnf(c_0_161,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_153]) ).
cnf(c_0_162,hypothesis,
( xm = xn
| sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xn,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_108]),c_0_42]),c_0_51])]) ).
cnf(c_0_163,hypothesis,
( doDivides0(xq,X1)
| ~ doDivides0(xq,sdtpldt0(X1,xn))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_91]),c_0_42])]) ).
cnf(c_0_164,hypothesis,
doDivides0(xq,sdtpldt0(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_46])]) ).
cnf(c_0_165,hypothesis,
( sz10 = X1
| sdtasdt0(xn,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_108]),c_0_42])]) ).
cnf(c_0_166,hypothesis,
sdtasdt0(xn,esk2_2(xn,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_159]),c_0_42])]) ).
cnf(c_0_167,hypothesis,
aNaturalNumber0(esk2_2(xn,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_159]),c_0_42])]) ).
cnf(c_0_168,hypothesis,
sdtasdt0(xq,esk2_2(xq,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_149]),c_0_46]),c_0_42])]) ).
cnf(c_0_169,hypothesis,
aNaturalNumber0(esk2_2(xq,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_149]),c_0_42]),c_0_46])]) ).
cnf(c_0_170,hypothesis,
sdtasdt0(xq,xp) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_34]),c_0_38]),c_0_46])]) ).
cnf(c_0_171,hypothesis,
( sdtasdt0(xn,xm) = sdtasdt0(xn,xn)
| xm = xn
| ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_123])]) ).
cnf(c_0_172,hypothesis,
doDivides0(xq,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_46])]) ).
cnf(c_0_173,hypothesis,
esk2_2(xn,xn) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_167])]) ).
cnf(c_0_174,hypothesis,
sdtasdt0(xn,esk2_2(xq,xn)) = sdtasdt0(xp,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_168]),c_0_169])]) ).
cnf(c_0_175,hypothesis,
sdtasdt0(xp,xn) = sdtasdt0(xn,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_170]),c_0_38])]) ).
cnf(c_0_176,hypothesis,
sdtasdt0(xm,sdtasdt0(xm,xp)) = sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_143]),c_0_38]),c_0_51])]) ).
cnf(c_0_177,negated_conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(xn,xn)
| xm = xn
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_135]),c_0_42])]),c_0_60]) ).
cnf(c_0_178,hypothesis,
sdtasdt0(xq,esk2_2(xq,xq)) = xq,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_172]),c_0_46])]) ).
cnf(c_0_179,hypothesis,
aNaturalNumber0(esk2_2(xq,xq)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_172]),c_0_46])]) ).
cnf(c_0_180,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(rw,[status(thm)],[c_0_166,c_0_173]) ).
cnf(c_0_181,hypothesis,
sdtasdt0(xn,esk2_2(xq,xn)) = sdtasdt0(xn,xp),
inference(rw,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_182,hypothesis,
( sdtsldt0(sdtasdt0(xn,xn),xm) = sdtasdt0(xm,xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xp)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_176]),c_0_51])]),c_0_136]) ).
cnf(c_0_183,negated_conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(xn,xn)
| xm = xn ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_34]),c_0_51]),c_0_42])]) ).
cnf(c_0_184,hypothesis,
sdtasdt0(xn,esk2_2(xq,xq)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_178]),c_0_118]),c_0_179])]) ).
cnf(c_0_185,hypothesis,
sdtsldt0(xn,xn) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_180]),c_0_42]),c_0_75])]),c_0_60]) ).
fof(c_0_186,plain,
! [X118,X119] :
( ( X118 = sz00
| sdtpldt0(X118,X119) != sz00
| ~ aNaturalNumber0(X118)
| ~ aNaturalNumber0(X119) )
& ( X119 = sz00
| sdtpldt0(X118,X119) != sz00
| ~ aNaturalNumber0(X118)
| ~ aNaturalNumber0(X119) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_187,hypothesis,
sdtlseqdt0(xm,sdtasdt0(xn,xn)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_107]),c_0_51])]),c_0_136]) ).
cnf(c_0_188,hypothesis,
esk2_2(xq,xn) = sdtsldt0(sdtasdt0(xn,xp),xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_181]),c_0_42]),c_0_169])]),c_0_60]) ).
cnf(c_0_189,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xm) = sdtasdt0(xm,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_34]),c_0_38]),c_0_51])]) ).
cnf(c_0_190,negated_conjecture,
xm = xn,
inference(sr,[status(thm)],[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_183]),c_0_152]),c_0_42]),c_0_51])]),c_0_60]) ).
cnf(c_0_191,hypothesis,
esk2_2(xq,xq) = sz10,
inference(sr,[status(thm)],[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_184]),c_0_185]),c_0_42]),c_0_179])]),c_0_60]) ).
cnf(c_0_192,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_186]) ).
cnf(c_0_193,hypothesis,
sdtpldt0(xm,esk1_2(xm,sdtasdt0(xn,xn))) = sdtasdt0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_187]),c_0_123]),c_0_51])]) ).
cnf(c_0_194,hypothesis,
aNaturalNumber0(esk1_2(xm,sdtasdt0(xn,xn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_187]),c_0_123]),c_0_51])]) ).
cnf(c_0_195,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_196,hypothesis,
sdtasdt0(xq,sdtsldt0(sdtasdt0(xn,xp),xn)) = xn,
inference(rw,[status(thm)],[c_0_168,c_0_188]) ).
cnf(c_0_197,hypothesis,
sdtasdt0(xn,xp) = xn,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_190]),c_0_152]),c_0_190]) ).
cnf(c_0_198,hypothesis,
sdtasdt0(xq,sz10) = xq,
inference(rw,[status(thm)],[c_0_178,c_0_191]) ).
cnf(c_0_199,plain,
( sdtasdt0(X1,X2) = sz00
| sdtlseqdt0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_36]),c_0_34]) ).
cnf(c_0_200,hypothesis,
sdtasdt0(xn,xn) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_194]),c_0_51])]),c_0_136]) ).
cnf(c_0_201,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xn,xq)),
inference(rw,[status(thm)],[c_0_195,c_0_134]) ).
cnf(c_0_202,hypothesis,
xq = xn,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197]),c_0_185]),c_0_198]) ).
cnf(c_0_203,hypothesis,
sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xn,xn)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_122]),c_0_123]),c_0_75])]),c_0_200]) ).
cnf(c_0_204,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_202]),c_0_203])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM527+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
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 5 00:41:49 EDT 2026
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % start to proof: theBenchmark
% 6.86/4.78 % Version : CSE_E---1.7
% 6.86/4.78 % Problem : theBenchmark.p
% 6.86/4.78 % SZS status Theorem for theBenchmark.p
% 6.86/4.78 % SZS output start CNFRefutation
% See solution above
% 6.95/4.81 % Total time : 3.373s
%------------------------------------------------------------------------------