%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM529+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:49:26 PM UTC 2026
% Result : ContradictoryAxioms 6.65s 1.73s
% Output : CNFRefutation 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 29
% Syntax : Number of formulae : 159 ( 58 unt; 0 def)
% Number of atoms : 536 ( 161 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 628 ( 251 ~; 241 |; 85 &)
% ( 4 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 194 ( 0 sgn 105 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(m__2987,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mDivTrans,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X2,X3)
& doDivides0(X1,X2) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m__3046,hypothesis,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(m__3082,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
fof(m__3059,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(mPDP,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X3,sdtasdt0(X1,X2))
& isPrime0(X3) )
=> ( doDivides0(X3,X2)
| doDivides0(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPDP) ).
fof(m__3025,hypothesis,
isPrime0(xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(mDivAsso,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( sdtpldt0(X1,X3) = X2
& aNaturalNumber0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(m__3124,hypothesis,
( sdtlseqdt0(xm,xn)
& xm != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3124) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X3)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(m__2963,hypothesis,
! [X1,X2,X3] :
( ( X3 != sz00
& X2 != sz00
& X1 != sz00
& aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X3,sdtasdt0(X2,X2)) = sdtasdt0(X1,X1)
=> ( iLess0(X1,xn)
=> ~ isPrime0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2963) ).
fof(m__3014,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X2,X1)
& sdtlseqdt0(X1,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_29,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( X2 = sdtasdt0(X1,X3)
& aNaturalNumber0(X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[mDefQuot]) ).
fof(c_0_30,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_simplification,[status(thm)],[m__2987]) ).
fof(c_0_31,plain,
! [X63,X64,X66] :
( ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| doDivides0(X63,X64)
| X64 != sdtasdt0(X63,X66)
| ~ aNaturalNumber0(X66) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| X64 = sdtasdt0(X63,esk2_2(X63,X64)) )
& ( ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X63)
| ~ doDivides0(X63,X64)
| aNaturalNumber0(esk2_2(X63,X64)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_32,plain,
! [X7,X8] :
( aNaturalNumber0(sdtasdt0(X7,X8))
| ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).
fof(c_0_33,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_simplification,[status(thm)],[mSortsC_01]) ).
fof(c_0_34,plain,
! [X67,X68,X69] :
( ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 = sdtsldt0(X68,X67)
| X68 != sdtasdt0(X67,X69)
| ~ aNaturalNumber0(X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| X68 = sdtasdt0(X67,X69) )
& ( ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X67)
| ~ doDivides0(X67,X68)
| X67 = sz00
| X69 != sdtsldt0(X68,X67)
| aNaturalNumber0(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])])]) ).
fof(c_0_35,plain,
! [X70,X71,X72] :
( doDivides0(X70,X72)
| ~ doDivides0(X71,X72)
| ~ doDivides0(X70,X71)
| ~ aNaturalNumber0(X72)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X70) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])])]) ).
fof(c_0_36,hypothesis,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(fof_nnf,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_39,plain,
! [X20] :
( ( ~ aNaturalNumber0(X20)
| X20 = sdtasdt0(sz10,X20) )
& ( ~ aNaturalNumber0(X20)
| sdtasdt0(X20,sz10) = X20 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])])]) ).
fof(c_0_40,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X1 != sdtsldt0(X2,X3)
| X3 = sz00
| aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( ~ doDivides0(X2,X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,hypothesis,
doDivides0(xp,xn),
inference(split_conjunct,[status(thm)],[m__3046]) ).
cnf(c_0_44,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_37]),c_0_38]) ).
cnf(c_0_47,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(split_conjunct,[status(thm)],[m__3082]) ).
cnf(c_0_50,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(sdtsldt0(X2,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_51,hypothesis,
xq = sdtsldt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__3059]) ).
cnf(c_0_52,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_53,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xp)
| doDivides0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45])]) ).
cnf(c_0_54,plain,
( ~ aNaturalNumber0(X1)
| doDivides0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_55,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2)
| X2 = sz00
| X1 = sdtasdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_56,plain,
! [X89,X90,X91] :
( doDivides0(X91,X90)
| doDivides0(X91,X89)
| ~ doDivides0(X91,sdtasdt0(X89,X90))
| ~ isPrime0(X91)
| ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X90)
| ~ aNaturalNumber0(X89) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPDP])])]) ).
cnf(c_0_57,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| doDivides0(xp,sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_49]),c_0_45])]) ).
cnf(c_0_58,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_50,c_0_43]),c_0_51]),c_0_45]),c_0_44])]),c_0_52]) ).
cnf(c_0_59,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X2)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| X3 = sz00
| X1 = sdtsldt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_60,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 = sdtasdt0(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_61,hypothesis,
doDivides0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_48]),c_0_45])]) ).
cnf(c_0_62,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| aNaturalNumber0(esk2_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_63,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X2)
| X1 = sz00
| sdtasdt0(X1,sdtsldt0(X2,X1)) = X2 ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_64,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_65,plain,
( ~ doDivides0(X3,sdtasdt0(X1,X2))
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X3,X2)
| doDivides0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,hypothesis,
doDivides0(xp,sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_38]),c_0_58])]) ).
cnf(c_0_67,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__3025]) ).
cnf(c_0_68,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_69,plain,
! [X15,X16] :
( sdtasdt0(X15,X16) = sdtasdt0(X16,X15)
| ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X15) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_70,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = sz00
| sdtsldt0(sdtasdt0(X1,X2),X1) = X2 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_59]),c_0_38]),c_0_46]) ).
cnf(c_0_71,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_60,c_0_61]),c_0_48]),c_0_44])]) ).
cnf(c_0_72,hypothesis,
aNaturalNumber0(esk2_2(sz10,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_44]),c_0_48])]) ).
cnf(c_0_73,hypothesis,
sdtasdt0(sz10,sdtsldt0(xn,sz10)) = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_61]),c_0_48]),c_0_44])]),c_0_64]) ).
cnf(c_0_74,hypothesis,
aNaturalNumber0(sdtsldt0(xn,sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_61]),c_0_48]),c_0_44])]),c_0_64]) ).
cnf(c_0_75,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_65,c_0_66]),c_0_67]),c_0_45]),c_0_68])]) ).
cnf(c_0_76,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_77,hypothesis,
esk2_2(sz10,xn) = sdtsldt0(xn,sz10),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_48]),c_0_72])]),c_0_64]) ).
cnf(c_0_78,hypothesis,
sdtsldt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_73]),c_0_74])]) ).
fof(c_0_79,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( X2 != sz00
& doDivides0(X1,X2) )
=> sdtlseqdt0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mDivLE]) ).
cnf(c_0_80,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_49]),c_0_45])]) ).
cnf(c_0_81,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xp)
| doDivides0(X1,xm) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_75]),c_0_68]),c_0_45])]) ).
fof(c_0_82,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X1,X2)
& X1 != sz00 )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
inference(fof_simplification,[status(thm)],[mDivAsso]) ).
cnf(c_0_83,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| doDivides0(X1,sdtasdt0(X2,X1)) ),
inference(spm,[status(thm)],[c_0_46,c_0_76]) ).
cnf(c_0_84,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_77]),c_0_78]) ).
fof(c_0_85,plain,
! [X79,X80] :
( sdtlseqdt0(X79,X80)
| X80 = sz00
| ~ doDivides0(X79,X80)
| ~ aNaturalNumber0(X80)
| ~ aNaturalNumber0(X79) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])]) ).
fof(c_0_86,plain,
! [X35,X36,X38] :
( ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| sdtlseqdt0(X35,X36)
| sdtpldt0(X35,X38) != X36
| ~ aNaturalNumber0(X38) )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| sdtpldt0(X35,esk1_2(X35,X36)) = X36 )
& ( ~ aNaturalNumber0(X36)
| ~ aNaturalNumber0(X35)
| ~ sdtlseqdt0(X35,X36)
| aNaturalNumber0(esk1_2(X35,X36)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_87,plain,
! [X5,X6] :
( aNaturalNumber0(sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X5) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).
fof(c_0_88,plain,
! [X17,X18,X19] :
( sdtasdt0(sdtasdt0(X17,X18),X19) = sdtasdt0(X17,sdtasdt0(X18,X19))
| ~ aNaturalNumber0(X19)
| ~ aNaturalNumber0(X18)
| ~ aNaturalNumber0(X17) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_89,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_38]),c_0_58])]) ).
cnf(c_0_90,hypothesis,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| sdtsldt0(sdtasdt0(xm,xm),xp) = sdtasdt0(xq,xq) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_49]),c_0_45])]),c_0_52]) ).
cnf(c_0_91,hypothesis,
doDivides0(sz10,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_54]),c_0_48]),c_0_45])]) ).
fof(c_0_92,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2 )
=> iLess0(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mIH_03]) ).
fof(c_0_93,hypothesis,
( sdtlseqdt0(xm,xn)
& xm != xn ),
inference(fof_simplification,[status(thm)],[m__3124]) ).
fof(c_0_94,plain,
! [X81,X82,X83] :
( sdtasdt0(X83,sdtsldt0(X82,X81)) = sdtsldt0(sdtasdt0(X83,X82),X81)
| ~ aNaturalNumber0(X83)
| ~ doDivides0(X81,X82)
| X81 = sz00
| ~ aNaturalNumber0(X82)
| ~ aNaturalNumber0(X81) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_82])])])]) ).
fof(c_0_95,plain,
! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
inference(fof_simplification,[status(thm)],[mMonMul2]) ).
cnf(c_0_96,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| doDivides0(X1,sdtasdt0(X2,X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_46]),c_0_38]) ).
cnf(c_0_97,hypothesis,
doDivides0(xn,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_44]),c_0_48])]) ).
fof(c_0_98,plain,
! [X21] :
( ( ~ aNaturalNumber0(X21)
| sz00 = sdtasdt0(sz00,X21) )
& ( ~ aNaturalNumber0(X21)
| sdtasdt0(X21,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).
fof(c_0_99,plain,
! [X45,X46,X47] :
( sdtlseqdt0(X45,X47)
| ~ sdtlseqdt0(X46,X47)
| ~ sdtlseqdt0(X45,X46)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).
cnf(c_0_100,plain,
( ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X2)
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_101,hypothesis,
xn != sz00,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_102,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_103,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_104,plain,
! [X14] :
( ( ~ aNaturalNumber0(X14)
| X14 = sdtpldt0(sz00,X14) )
& ( ~ aNaturalNumber0(X14)
| sdtpldt0(X14,sz00) = X14 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])])]) ).
fof(c_0_105,plain,
! [X33,X34] :
( X34 = sz00
| X33 = sz00
| sdtasdt0(X33,X34) != sz00
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])])]) ).
cnf(c_0_106,plain,
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_107,hypothesis,
aNaturalNumber0(sdtsldt0(sdtasdt0(xm,xm),xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_66]),c_0_45]),c_0_89])]),c_0_52]) ).
cnf(c_0_108,hypothesis,
sdtsldt0(sdtasdt0(xm,xm),xp) = sdtasdt0(xq,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_38]),c_0_58])]) ).
cnf(c_0_109,hypothesis,
sdtasdt0(sz10,esk2_2(sz10,xm)) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_91]),c_0_48]),c_0_68])]) ).
cnf(c_0_110,hypothesis,
aNaturalNumber0(esk2_2(sz10,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_91]),c_0_68]),c_0_48])]) ).
fof(c_0_111,hypothesis,
! [X1,X2,X3] :
( ( X3 != sz00
& X2 != sz00
& X1 != sz00
& aNaturalNumber0(X3)
& aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X3,sdtasdt0(X2,X2)) = sdtasdt0(X1,X1)
=> ( iLess0(X1,xn)
=> ~ isPrime0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[m__2963]) ).
fof(c_0_112,plain,
! [X61,X62] :
( iLess0(X61,X62)
| ~ sdtlseqdt0(X61,X62)
| X61 = X62
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X61) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_92])])]) ).
fof(c_0_113,hypothesis,
( sdtlseqdt0(xm,xn)
& xm != xn ),
inference(fof_nnf,[status(thm)],[c_0_93]) ).
cnf(c_0_114,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(split_conjunct,[status(thm)],[m__3014]) ).
cnf(c_0_115,plain,
( ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1)
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
fof(c_0_116,plain,
! [X43,X44] :
( X43 = X44
| ~ sdtlseqdt0(X44,X43)
| ~ sdtlseqdt0(X43,X44)
| ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X43) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).
fof(c_0_117,plain,
! [X57,X58] :
( sdtlseqdt0(X58,sdtasdt0(X58,X57))
| X57 = sz00
| ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])]) ).
cnf(c_0_118,hypothesis,
( ~ aNaturalNumber0(X1)
| doDivides0(xn,sdtasdt0(xn,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_44])]) ).
cnf(c_0_119,plain,
( ~ aNaturalNumber0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_120,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_121,plain,
( ~ sdtlseqdt0(X2,X3)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_122,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_100,c_0_43]),c_0_44]),c_0_45])]),c_0_101]) ).
cnf(c_0_123,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X1,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_102]),c_0_103]) ).
cnf(c_0_124,plain,
( ~ aNaturalNumber0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_125,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_126,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_47]),c_0_48])]) ).
cnf(c_0_127,hypothesis,
aNaturalNumber0(sdtasdt0(xq,xq)),
inference(rw,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_128,hypothesis,
esk2_2(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_109]),c_0_110])]) ).
fof(c_0_129,hypothesis,
! [X92,X93,X94] :
( ~ isPrime0(X94)
| ~ iLess0(X92,xn)
| sdtasdt0(X94,sdtasdt0(X93,X93)) != sdtasdt0(X92,X92)
| X94 = sz00
| X93 = sz00
| X92 = sz00
| ~ aNaturalNumber0(X94)
| ~ aNaturalNumber0(X93)
| ~ aNaturalNumber0(X92) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_111])])]) ).
cnf(c_0_130,plain,
( ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| iLess0(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_131,hypothesis,
sdtlseqdt0(xm,xn),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_132,hypothesis,
xm != xn,
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_133,hypothesis,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_114]),c_0_45])]),c_0_52]),c_0_89])]) ).
cnf(c_0_134,hypothesis,
( ~ aNaturalNumber0(X1)
| sdtsldt0(sdtasdt0(X1,xn),xp) = sdtasdt0(X1,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_115,c_0_43]),c_0_51]),c_0_44]),c_0_45])]),c_0_52]) ).
cnf(c_0_135,plain,
( ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_136,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_137,hypothesis,
doDivides0(xn,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_44])]) ).
cnf(c_0_138,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X1,xp)
| sdtlseqdt0(X1,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_44]),c_0_45])]) ).
cnf(c_0_139,plain,
( ~ aNaturalNumber0(X1)
| sdtlseqdt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_120])]) ).
cnf(c_0_140,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X1,sdtasdt0(X2,X3)) != sz00
| X3 = sz00
| sdtasdt0(X1,X2) = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_106]),c_0_38]) ).
cnf(c_0_141,hypothesis,
sdtasdt0(sz10,sdtasdt0(xm,xm)) = sdtasdt0(xm,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_49]),c_0_127]),c_0_45])]) ).
cnf(c_0_142,hypothesis,
sdtasdt0(sz10,xm) = xm,
inference(rw,[status(thm)],[c_0_109,c_0_128]) ).
cnf(c_0_143,hypothesis,
xm != sz00,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_144,hypothesis,
( ~ isPrime0(X3)
| ~ iLess0(X1,xn)
| sdtasdt0(X3,sdtasdt0(X2,X2)) != sdtasdt0(X1,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| X3 = sz00
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_145,hypothesis,
iLess0(xm,xn),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_44]),c_0_68])]),c_0_132]) ).
cnf(c_0_146,hypothesis,
sdtasdt0(xm,xm) = sdtasdt0(xn,xq),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_44])]) ).
cnf(c_0_147,plain,
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(sdtasdt0(X1,X2),X1)
| X2 = sz00
| sdtasdt0(X1,X2) = X1 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_38]) ).
cnf(c_0_148,hypothesis,
sdtasdt0(xn,esk2_2(xn,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_137]),c_0_44]),c_0_120])]) ).
cnf(c_0_149,hypothesis,
sdtlseqdt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_120]),c_0_45])]) ).
cnf(c_0_150,hypothesis,
aNaturalNumber0(esk2_2(xn,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_137]),c_0_120]),c_0_44])]) ).
cnf(c_0_151,hypothesis,
sdtasdt0(xm,xm) != sz00,
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_140,c_0_141]),c_0_142]),c_0_68]),c_0_48])]),c_0_143]) ).
cnf(c_0_152,hypothesis,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ isPrime0(X2)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(xn,xq)
| X2 = sz00
| X1 = sz00 ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_68])]),c_0_143]),c_0_146]) ).
cnf(c_0_153,hypothesis,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xn,xq),
inference(rw,[status(thm)],[c_0_49,c_0_146]) ).
cnf(c_0_154,hypothesis,
esk2_2(xn,sz00) = sz00,
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_147,c_0_148]),c_0_149]),c_0_44]),c_0_150])]),c_0_101]) ).
cnf(c_0_155,hypothesis,
sdtasdt0(xn,xq) != sz00,
inference(rw,[status(thm)],[c_0_151,c_0_146]) ).
cnf(c_0_156,hypothesis,
xq = sz00,
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_152,c_0_153]),c_0_67]),c_0_45]),c_0_58])]),c_0_52]) ).
cnf(c_0_157,hypothesis,
sdtasdt0(xn,sz00) = sz00,
inference(rw,[status(thm)],[c_0_148,c_0_154]) ).
cnf(c_0_158,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156]),c_0_157])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM529+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 % Computer : n006.cluster.edu
% 0.16/0.47 % Model : x86_64 x86_64
% 0.16/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.47 % Memory : 8046.5625MB
% 0.16/0.47 % OS : Linux 6.8.0-71-generic
% 0.16/0.47 % CPULimit : 300
% 0.16/0.47 % WCLimit : 300
% 0.16/0.47 % DateTime : Mon Sep 21 02:37:42 UTC 2026
% 0.16/0.48 % CPUTime :
% 0.16/0.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.56 Running first-order theorem proving
% 0.22/0.56 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.65/1.73 % Version: 3.5.1
% 6.65/1.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.65/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.65/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.65/1.73 % Starting new_bool_3 with 300s (1) cores
% 6.65/1.73 % Starting new_bool_1 with 300s (1) cores
% 6.65/1.73 % Starting sh5l with 300s (1) cores
% 6.65/1.73 % sh5l with pid 1823461 completed with status 9
% 6.65/1.73 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1823458 completed with status 0
% 6.65/1.73 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 6.65/1.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.65/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.65/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.65/1.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.65/1.73 % No SInE strategy applied
% 6.65/1.73 % Search class: FGHSF-FFMM21-SFFFFFNN
% 6.65/1.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.65/1.73 % Starting SubtermCWHack with 136s (1) cores
% 6.65/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.65/1.73 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 6.65/1.73 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 6.65/1.73 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 6.65/1.73 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1823473 completed with status 0
% 6.65/1.73 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 6.65/1.73 % Preprocessing class: FSLSSMSSSSSNFFN.
% 6.65/1.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.65/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.65/1.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.65/1.73 % No SInE strategy applied
% 6.65/1.73 % Search class: FGHSF-FFMM21-SFFFFFNN
% 6.65/1.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.65/1.73 % Starting SubtermCWHack with 136s (1) cores
% 6.65/1.73 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.65/1.73 % Preprocessing time : 0.004 s
% 6.65/1.73 % Presaturation interreduction done
% 6.65/1.73
% 6.65/1.73 % Proof found!
% 6.65/1.73 % SZS status ContradictoryAxioms
% 6.65/1.73 % SZS output start CNFRefutation
% See solution above
% 6.65/1.73 % Parsed axioms : 48
% 6.65/1.73 % Removed by relevancy pruning/SinE : 0
% 6.65/1.73 % Initial clauses : 87
% 6.65/1.73 % Removed in clause preprocessing : 4
% 6.65/1.73 % Initial clauses in saturation : 83
% 6.65/1.73 % Processed clauses : 3824
% 6.65/1.73 % ...of these trivial : 202
% 6.65/1.73 % ...subsumed : 2181
% 6.65/1.73 % ...remaining for further processing : 1441
% 6.65/1.73 % Other redundant clauses eliminated : 116
% 6.65/1.73 % Clauses deleted for lack of memory : 0
% 6.65/1.73 % Backward-subsumed : 59
% 6.65/1.73 % Backward-rewritten : 377
% 6.65/1.73 % Generated clauses : 29253
% 6.65/1.73 % ...of the previous two non-redundant : 25585
% 6.65/1.73 % ...aggressively subsumed : 0
% 6.65/1.73 % Contextual simplify-reflections : 143
% 6.65/1.73 % Paramodulations : 29126
% 6.65/1.73 % Factorizations : 4
% 6.65/1.73 % NegExts : 0
% 6.65/1.73 % Equation resolutions : 122
% 6.65/1.73 % Disequality decompositions : 0
% 6.65/1.73 % Total rewrite steps : 36950
% 6.65/1.73 % ...of those cached : 36573
% 6.65/1.73 % Propositional unsat checks : 0
% 6.65/1.73 % Propositional check models : 0
% 6.65/1.73 % Propositional check unsatisfiable : 0
% 6.65/1.73 % Propositional clauses : 0
% 6.65/1.73 % Propositional clauses after purity: 0
% 6.65/1.73 % Propositional unsat core size : 0
% 6.65/1.73 % Propositional preprocessing time : 0.000
% 6.65/1.73 % Propositional encoding time : 0.000
% 6.65/1.73 % Propositional solver time : 0.000
% 6.65/1.73 % Success case prop preproc time : 0.000
% 6.65/1.73 % Success case prop encoding time : 0.000
% 6.65/1.73 % Success case prop solver time : 0.000
% 6.65/1.73 % Current number of processed clauses : 915
% 6.65/1.73 % Positive orientable unit clauses : 294
% 6.65/1.73 % Positive unorientable unit clauses: 0
% 6.65/1.73 % Negative unit clauses : 103
% 6.65/1.73 % Non-unit-clauses : 518
% 6.65/1.73 % Current number of unprocessed clauses: 21594
% 6.65/1.73 % ...number of literals in the above : 97204
% 6.65/1.73 % Current number of archived formulas : 0
% 6.65/1.73 % Current number of archived clauses : 515
% 6.65/1.73 % Clause-clause subsumption calls (NU) : 60836
% 6.65/1.73 % Rec. Clause-clause subsumption calls : 25227
% 6.65/1.73 % Non-unit clause-clause subsumptions : 1554
% 6.65/1.73 % Unit Clause-clause subsumption calls : 10179
% 6.65/1.73 % Rewrite failures with RHS unbound : 0
% 6.65/1.73 % BW rewrite match attempts : 135
% 6.65/1.73 % BW rewrite match successes : 82
% 6.65/1.73 % Condensation attempts : 0
% 6.65/1.73 % Condensation successes : 0
% 6.65/1.73 % Termbank termtop insertions : 551261
% 6.65/1.73 % Search garbage collected termcells : 1408
% 6.65/1.73
% 6.65/1.73 % -------------------------------------------------
% 6.65/1.73 % User time : 0.952 s
% 6.65/1.73 % System time : 0.041 s
% 6.65/1.73 % Total time : 0.993 s
% 6.65/1.73 % Maximum resident set size: 3940 pages
% 6.65/1.73
% 6.65/1.73 % -------------------------------------------------
% 6.65/1.73 % User time : 5.014 s
% 6.65/1.73 % System time : 0.225 s
% 6.65/1.73 % Total time : 5.239 s
% 6.65/1.73 % Maximum resident set size: 4864 pages
% 6.65/1.73 % E exiting
%------------------------------------------------------------------------------