TSTP Solution File: NUM502+1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : NUM502+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:56:04 EDT 2023
% Result : Theorem 553.17s 70.75s
% Output : CNFRefutation 553.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 40
% Syntax : Number of formulae : 396 ( 156 unt; 0 def)
% Number of atoms : 1151 ( 395 equ)
% Maximal formula atoms : 28 ( 2 avg)
% Number of connectives : 1309 ( 554 ~; 605 |; 97 &)
% ( 4 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 396 ( 0 sgn; 140 !; 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/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.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/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mDefQuot) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m_MulUnit) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mSortsC_01) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mSortsB) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mZeroMul) ).
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/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mLETran) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m_AddZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mSortsC) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m__1837) ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mMonAdd) ).
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/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mDivSum) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mMonMul2) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mAddComm) ).
fof(mAddCanc,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
| sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mAddCanc) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mDivLE) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m__1860) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m__2306) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mZeroAdd) ).
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/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mDivTrans) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m__2342) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m_MulZero) ).
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/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mDivMin) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mMulComm) ).
fof(m__2362,hypothesis,
( sdtlseqdt0(xr,xk)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m__2362) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mLEAsym) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
=> ! [X3] :
( X3 = sdtmndt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mDefDiff) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m__2315) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mAMDistr) ).
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/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mMulCanc) ).
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/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mMulAsso) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mLETotal) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mAddAsso) ).
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/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mMonMul) ).
fof(m__,conjecture,
( xk != xp
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m__) ).
fof(mDivAsso,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',mDivAsso) ).
fof(m__1870,hypothesis,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p',m__1870) ).
fof(c_0_40,plain,
! [X60,X61,X63] :
( ( aNaturalNumber0(esk2_2(X60,X61))
| ~ doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) )
& ( X61 = sdtasdt0(X60,esk2_2(X60,X61))
| ~ doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) )
& ( ~ aNaturalNumber0(X63)
| X61 != sdtasdt0(X60,X63)
| doDivides0(X60,X61)
| ~ aNaturalNumber0(X60)
| ~ aNaturalNumber0(X61) ) ),
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_41,plain,
! [X6,X7] :
( ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X7)
| aNaturalNumber0(sdtasdt0(X6,X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_42,plain,
! [X64,X65,X66] :
( ( aNaturalNumber0(X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( X65 = sdtasdt0(X64,X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( ~ aNaturalNumber0(X66)
| X65 != sdtasdt0(X64,X66)
| X66 = sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_43,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_45,plain,
! [X19] :
( ( sdtasdt0(X19,sz10) = X19
| ~ aNaturalNumber0(X19) )
& ( X19 = sdtasdt0(sz10,X19)
| ~ aNaturalNumber0(X19) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_46,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_42]) ).
cnf(c_0_47,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_50,plain,
! [X34,X35,X37] :
( ( aNaturalNumber0(esk1_2(X34,X35))
| ~ sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) )
& ( sdtpldt0(X34,esk1_2(X34,X35)) = X35
| ~ sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) )
& ( ~ aNaturalNumber0(X37)
| sdtpldt0(X34,X37) != X35
| sdtlseqdt0(X34,X35)
| ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35) ) ),
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_51,plain,
! [X4,X5] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| aNaturalNumber0(sdtpldt0(X4,X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_52,plain,
! [X32,X33] :
( ~ aNaturalNumber0(X32)
| ~ aNaturalNumber0(X33)
| sdtasdt0(X32,X33) != sz00
| X32 = sz00
| X33 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_53,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_54,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_55,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_56,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_57,plain,
! [X44,X45,X46] :
( ~ aNaturalNumber0(X44)
| ~ aNaturalNumber0(X45)
| ~ aNaturalNumber0(X46)
| ~ sdtlseqdt0(X44,X45)
| ~ sdtlseqdt0(X45,X46)
| sdtlseqdt0(X44,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_58,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_60,plain,
! [X13] :
( ( sdtpldt0(X13,sz00) = X13
| ~ aNaturalNumber0(X13) )
& ( X13 = sdtpldt0(sz00,X13)
| ~ aNaturalNumber0(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_61,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,plain,
( sdtasdt0(sz10,sdtsldt0(X1,sz10)) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_49])]),c_0_55]) ).
cnf(c_0_63,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_64,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_65,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_66,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_67,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_68,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_69,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_58]),c_0_59]) ).
cnf(c_0_70,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_71,plain,
! [X49,X50,X51] :
( ( sdtpldt0(X51,X49) != sdtpldt0(X51,X50)
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(sdtpldt0(X51,X49),sdtpldt0(X51,X50))
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtpldt0(X49,X51) != sdtpldt0(X50,X51)
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(sdtpldt0(X49,X51),sdtpldt0(X50,X51))
| ~ aNaturalNumber0(X51)
| X49 = X50
| ~ sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
cnf(c_0_72,plain,
( sdtsldt0(sz00,sz10) = sz00
| ~ aNaturalNumber0(sdtsldt0(sz00,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_49])]),c_0_55])]),c_0_63])]) ).
cnf(c_0_73,plain,
( aNaturalNumber0(sdtsldt0(X1,sz10))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_54]),c_0_49])]),c_0_55]) ).
cnf(c_0_74,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[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_68])]) ).
cnf(c_0_75,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_63])]) ).
cnf(c_0_76,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X3,X2))
| X1 = X3
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_77,hypothesis,
xm != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_78,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_63])]) ).
cnf(c_0_79,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_80,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_63]),c_0_68])]) ).
cnf(c_0_81,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_82,hypothesis,
( sdtlseqdt0(sdtpldt0(xm,X1),sdtpldt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_66]),c_0_67]),c_0_68])]),c_0_77]) ).
cnf(c_0_83,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_84,plain,
! [X70,X71,X72] :
( ~ aNaturalNumber0(X70)
| ~ aNaturalNumber0(X71)
| ~ aNaturalNumber0(X72)
| ~ doDivides0(X70,X71)
| ~ doDivides0(X70,X72)
| doDivides0(X70,sdtpldt0(X71,X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_85,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_78]),c_0_63])]) ).
cnf(c_0_86,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_67]),c_0_63])]) ).
cnf(c_0_87,hypothesis,
aNaturalNumber0(esk1_2(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_80]),c_0_67]),c_0_63])]) ).
cnf(c_0_88,hypothesis,
sdtlseqdt0(sdtpldt0(xm,sz00),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_63]),c_0_67])]) ).
fof(c_0_89,plain,
! [X56,X57] :
( ~ aNaturalNumber0(X56)
| ~ aNaturalNumber0(X57)
| X56 = sz00
| sdtlseqdt0(X57,sdtasdt0(X57,X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
cnf(c_0_90,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_84]) ).
cnf(c_0_91,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_85]),c_0_49]),c_0_63])]) ).
fof(c_0_92,plain,
! [X8,X9] :
( ~ aNaturalNumber0(X8)
| ~ aNaturalNumber0(X9)
| sdtpldt0(X8,X9) = sdtpldt0(X9,X8) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(c_0_93,plain,
! [X24,X25,X26] :
( ( sdtpldt0(X24,X25) != sdtpldt0(X24,X26)
| X25 = X26
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26) )
& ( sdtpldt0(X25,X24) != sdtpldt0(X26,X24)
| X25 = X26
| ~ aNaturalNumber0(X24)
| ~ aNaturalNumber0(X25)
| ~ aNaturalNumber0(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_94,hypothesis,
esk1_2(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_86]),c_0_87])]) ).
cnf(c_0_95,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_88]),c_0_67])]) ).
cnf(c_0_96,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_97,plain,
( 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_90,c_0_91]),c_0_63]),c_0_49])]),c_0_54]) ).
cnf(c_0_98,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_99,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_100,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_86,c_0_94]) ).
cnf(c_0_101,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_59]),c_0_63]),c_0_68])]) ).
cnf(c_0_102,plain,
( X1 = sz00
| sdtlseqdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_48]),c_0_49])]) ).
fof(c_0_103,plain,
! [X76,X77] :
( ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| ~ doDivides0(X76,X77)
| X77 = sz00
| sdtlseqdt0(X76,X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_104,plain,
( doDivides0(sz10,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_63])]) ).
cnf(c_0_105,hypothesis,
( xp = X1
| sdtpldt0(sz00,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_67]),c_0_63])]) ).
cnf(c_0_106,hypothesis,
( sdtpldt0(xm,sz00) = sz00
| sdtlseqdt0(sz10,xp)
| ~ aNaturalNumber0(sdtpldt0(xm,sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_49])]) ).
cnf(c_0_107,plain,
( X2 = sz00
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_100]),c_0_67])]) ).
cnf(c_0_109,hypothesis,
( xp = X1
| sdtpldt0(X1,sz00) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_98]),c_0_63])]) ).
cnf(c_0_110,hypothesis,
( sdtpldt0(xm,sz00) = sz00
| sdtlseqdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_59]),c_0_63]),c_0_68])]) ).
cnf(c_0_111,hypothesis,
( xp = sz00
| sdtlseqdt0(sz10,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_67]),c_0_49])]) ).
cnf(c_0_112,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_113,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
fof(c_0_114,plain,
! [X30,X31] :
( ( X30 = sz00
| sdtpldt0(X30,X31) != sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) )
& ( X31 = sz00
| sdtpldt0(X30,X31) != sz00
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_115,hypothesis,
sdtlseqdt0(sz10,xp),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_68])]),c_0_77]),c_0_111]) ).
fof(c_0_116,plain,
! [X67,X68,X69] :
( ~ aNaturalNumber0(X67)
| ~ aNaturalNumber0(X68)
| ~ aNaturalNumber0(X69)
| ~ doDivides0(X67,X68)
| ~ doDivides0(X68,X69)
| doDivides0(X67,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivTrans])]) ).
cnf(c_0_117,hypothesis,
( xp = sz00
| aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_112]),c_0_113]),c_0_67])]) ).
cnf(c_0_118,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_119,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_120,hypothesis,
sdtpldt0(sz10,esk1_2(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_115]),c_0_67]),c_0_49])]) ).
cnf(c_0_121,hypothesis,
aNaturalNumber0(esk1_2(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_115]),c_0_67]),c_0_49])]) ).
cnf(c_0_122,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_123,hypothesis,
( xp = sz00
| aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_44]),c_0_68]),c_0_118])]) ).
cnf(c_0_124,hypothesis,
xp != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_121]),c_0_49])]),c_0_55]) ).
cnf(c_0_125,plain,
( doDivides0(X1,sdtasdt0(X2,X3))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_47]),c_0_44]) ).
cnf(c_0_126,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_127,hypothesis,
aNaturalNumber0(xk),
inference(sr,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_128,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
fof(c_0_129,plain,
! [X20] :
( ( sdtasdt0(X20,sz00) = sz00
| ~ aNaturalNumber0(X20) )
& ( sz00 = sdtasdt0(sz00,X20)
| ~ aNaturalNumber0(X20) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_130,hypothesis,
( doDivides0(xr,sdtasdt0(xk,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]),c_0_128])]) ).
cnf(c_0_131,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
fof(c_0_132,plain,
! [X73,X74,X75] :
( ~ aNaturalNumber0(X73)
| ~ aNaturalNumber0(X74)
| ~ aNaturalNumber0(X75)
| ~ doDivides0(X73,X74)
| ~ doDivides0(X73,sdtpldt0(X74,X75))
| doDivides0(X73,X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
cnf(c_0_133,hypothesis,
doDivides0(xr,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_63]),c_0_127])]) ).
cnf(c_0_134,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_135,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_132]) ).
cnf(c_0_136,hypothesis,
( doDivides0(xr,sdtpldt0(X1,sz00))
| ~ doDivides0(xr,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_133]),c_0_63]),c_0_128])]) ).
cnf(c_0_137,plain,
( doDivides0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_134]),c_0_49])]) ).
fof(c_0_138,plain,
! [X14,X15] :
( ~ aNaturalNumber0(X14)
| ~ aNaturalNumber0(X15)
| sdtasdt0(X14,X15) = sdtasdt0(X15,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_139,plain,
( doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X2,X3))
| ~ doDivides0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_135,c_0_98]) ).
cnf(c_0_140,hypothesis,
doDivides0(xr,sdtpldt0(xr,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_128])]) ).
cnf(c_0_141,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_138]) ).
cnf(c_0_142,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_143,hypothesis,
doDivides0(xr,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_133]),c_0_128]),c_0_63])]) ).
cnf(c_0_144,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_145,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_141]) ).
cnf(c_0_146,hypothesis,
sdtasdt0(xr,esk2_2(xr,xr)) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_128])]) ).
cnf(c_0_147,hypothesis,
aNaturalNumber0(esk2_2(xr,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_143]),c_0_128])]) ).
cnf(c_0_148,hypothesis,
sdtasdt0(sz10,esk2_2(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_108]),c_0_49]),c_0_67])]) ).
cnf(c_0_149,hypothesis,
aNaturalNumber0(esk2_2(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_108]),c_0_67]),c_0_49])]) ).
cnf(c_0_150,hypothesis,
sdtlseqdt0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2362]) ).
cnf(c_0_151,hypothesis,
doDivides0(esk2_2(xr,xr),xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]),c_0_128])]) ).
cnf(c_0_152,hypothesis,
esk2_2(sz10,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_148]),c_0_149])]) ).
cnf(c_0_153,hypothesis,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_150]),c_0_128])]) ).
cnf(c_0_154,hypothesis,
( doDivides0(X1,xr)
| ~ doDivides0(X1,esk2_2(xr,xr))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_151]),c_0_128]),c_0_147])]) ).
cnf(c_0_155,hypothesis,
sdtasdt0(sz10,xp) = xp,
inference(rw,[status(thm)],[c_0_148,c_0_152]) ).
cnf(c_0_156,hypothesis,
( xp = sz00
| sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_153,c_0_123]) ).
cnf(c_0_157,hypothesis,
doDivides0(sz10,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_54]),c_0_49]),c_0_147])]) ).
cnf(c_0_158,hypothesis,
doDivides0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_155]),c_0_67]),c_0_49])]) ).
cnf(c_0_159,hypothesis,
( xp = sz00
| sdtlseqdt0(sz00,xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_75]),c_0_63]),c_0_128])]) ).
cnf(c_0_160,hypothesis,
sdtasdt0(sz10,esk2_2(sz10,xr)) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_157]),c_0_49]),c_0_128])]) ).
cnf(c_0_161,hypothesis,
aNaturalNumber0(esk2_2(sz10,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_157]),c_0_128]),c_0_49])]) ).
fof(c_0_162,plain,
! [X42,X43] :
( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X43)
| ~ sdtlseqdt0(X42,X43)
| ~ sdtlseqdt0(X43,X42)
| X42 = X43 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_163,hypothesis,
( doDivides0(xp,sdtasdt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_158]),c_0_67])]) ).
fof(c_0_164,plain,
! [X38,X39,X40] :
( ( aNaturalNumber0(X40)
| X40 != sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) )
& ( sdtpldt0(X38,X40) = X39
| X40 != sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) )
& ( ~ aNaturalNumber0(X40)
| sdtpldt0(X38,X40) != X39
| X40 = sdtmndt0(X39,X38)
| ~ sdtlseqdt0(X38,X39)
| ~ aNaturalNumber0(X38)
| ~ aNaturalNumber0(X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).
cnf(c_0_165,hypothesis,
( sdtpldt0(sz00,esk1_2(sz00,xk)) = xk
| xp = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_159]),c_0_63])]),c_0_123]) ).
cnf(c_0_166,hypothesis,
( xp = sz00
| aNaturalNumber0(esk1_2(sz00,xk)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_159]),c_0_63])]),c_0_123]) ).
fof(c_0_167,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_168,hypothesis,
esk2_2(sz10,xr) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_160]),c_0_161])]) ).
cnf(c_0_169,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_162]) ).
cnf(c_0_170,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_131]),c_0_63]),c_0_67])]) ).
cnf(c_0_171,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_42]) ).
cnf(c_0_172,plain,
( sdtpldt0(X1,X2) = X3
| X2 != sdtmndt0(X3,X1)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_173,hypothesis,
( xp = sz00
| doDivides0(sz10,xk) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_165]),c_0_166]) ).
cnf(c_0_174,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_175,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_176,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_141]) ).
cnf(c_0_177,hypothesis,
sdtasdt0(sz10,xr) = xr,
inference(rw,[status(thm)],[c_0_160,c_0_168]) ).
cnf(c_0_178,plain,
( X1 = sdtmndt0(X3,X2)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_179,plain,
( sdtasdt0(X1,X2) = X1
| X2 = sz00
| ~ sdtlseqdt0(sdtasdt0(X1,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_96]),c_0_44]) ).
cnf(c_0_180,hypothesis,
sdtasdt0(xp,esk2_2(xp,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_170]),c_0_67]),c_0_63])]) ).
cnf(c_0_181,hypothesis,
aNaturalNumber0(esk2_2(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_170]),c_0_63]),c_0_67])]) ).
cnf(c_0_182,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_171]),c_0_44]),c_0_47]) ).
cnf(c_0_183,plain,
( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_172]) ).
cnf(c_0_184,hypothesis,
( xp = sz00
| sdtlseqdt0(sz10,xk) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_173]),c_0_49])]),c_0_174]),c_0_123]) ).
cnf(c_0_185,plain,
( aNaturalNumber0(sdtmndt0(X1,X2))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[c_0_175]) ).
cnf(c_0_186,hypothesis,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_112]),c_0_113]),c_0_67])]),c_0_124]) ).
cnf(c_0_187,hypothesis,
sdtlseqdt0(xr,xr),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_128]),c_0_49])]),c_0_55]) ).
cnf(c_0_188,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_85]),c_0_63]),c_0_49])]) ).
fof(c_0_189,plain,
! [X21,X22,X23] :
( ( sdtasdt0(X21,sdtpldt0(X22,X23)) = sdtpldt0(sdtasdt0(X21,X22),sdtasdt0(X21,X23))
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X23) )
& ( sdtasdt0(sdtpldt0(X22,X23),X21) = sdtpldt0(sdtasdt0(X22,X21),sdtasdt0(X23,X21))
| ~ aNaturalNumber0(X21)
| ~ aNaturalNumber0(X22)
| ~ aNaturalNumber0(X23) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_190,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_178]),c_0_59]),c_0_69]) ).
cnf(c_0_191,hypothesis,
sdtpldt0(xm,esk1_2(xm,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_66]),c_0_67]),c_0_68])]) ).
cnf(c_0_192,hypothesis,
aNaturalNumber0(esk1_2(xm,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_66]),c_0_67]),c_0_68])]) ).
cnf(c_0_193,hypothesis,
esk2_2(xp,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_179,c_0_180]),c_0_80]),c_0_67]),c_0_181])]),c_0_124]) ).
cnf(c_0_194,plain,
( sdtsldt0(X1,X1) = sz10
| X1 = sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_134]),c_0_49])]) ).
fof(c_0_195,plain,
! [X27,X28,X29] :
( ( sdtasdt0(X27,X28) != sdtasdt0(X27,X29)
| X28 = X29
| ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X29)
| X27 = sz00
| ~ aNaturalNumber0(X27) )
& ( sdtasdt0(X28,X27) != sdtasdt0(X29,X27)
| X28 = X29
| ~ aNaturalNumber0(X28)
| ~ aNaturalNumber0(X29)
| X27 = sz00
| ~ aNaturalNumber0(X27) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_196,hypothesis,
( sdtpldt0(sz10,sdtmndt0(xk,sz10)) = xk
| xp = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_49])]),c_0_123]) ).
cnf(c_0_197,hypothesis,
( xp = sz00
| aNaturalNumber0(sdtmndt0(xk,sz10)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_184]),c_0_49])]),c_0_123]) ).
cnf(c_0_198,plain,
( X1 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_199,hypothesis,
( sdtasdt0(sz10,esk2_2(sz10,xk)) = xk
| xp = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_173]),c_0_49])]),c_0_123]) ).
cnf(c_0_200,plain,
( aNaturalNumber0(esk2_2(X1,sdtasdt0(X1,X2)))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_47]),c_0_44]) ).
cnf(c_0_201,hypothesis,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__2362]) ).
cnf(c_0_202,hypothesis,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_44]),c_0_68]),c_0_118])]) ).
cnf(c_0_203,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_83]),c_0_63])]) ).
cnf(c_0_204,hypothesis,
sdtpldt0(xr,esk1_2(xr,xr)) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_187]),c_0_128])]) ).
cnf(c_0_205,hypothesis,
aNaturalNumber0(esk1_2(xr,xr)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_187]),c_0_128])]) ).
fof(c_0_206,plain,
! [X16,X17,X18] :
( ~ aNaturalNumber0(X16)
| ~ aNaturalNumber0(X17)
| ~ aNaturalNumber0(X18)
| sdtasdt0(sdtasdt0(X16,X17),X18) = sdtasdt0(X16,sdtasdt0(X17,X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_207,plain,
sdtlseqdt0(sz00,sz00),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_188]),c_0_63]),c_0_49])]),c_0_55]) ).
cnf(c_0_208,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_209,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_210,hypothesis,
esk1_2(xm,xp) = sdtmndt0(xp,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_68]),c_0_192])]) ).
cnf(c_0_211,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(rw,[status(thm)],[c_0_180,c_0_193]) ).
cnf(c_0_212,plain,
( sdtpldt0(X1,esk1_2(X1,sdtasdt0(X1,X2))) = sdtasdt0(X1,X2)
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_96]),c_0_44]) ).
cnf(c_0_213,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_194]),c_0_49])]),c_0_55]) ).
cnf(c_0_214,plain,
( X1 = sz00
| aNaturalNumber0(esk1_2(X2,sdtasdt0(X2,X1)))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_96]),c_0_44]) ).
cnf(c_0_215,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_195]) ).
cnf(c_0_216,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_217,hypothesis,
sdtpldt0(sz10,sdtmndt0(xk,sz10)) = xk,
inference(sr,[status(thm)],[c_0_196,c_0_124]) ).
cnf(c_0_218,hypothesis,
aNaturalNumber0(sdtmndt0(xk,sz10)),
inference(sr,[status(thm)],[c_0_197,c_0_124]) ).
fof(c_0_219,plain,
! [X47,X48] :
( ( X48 != X47
| sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) )
& ( sdtlseqdt0(X48,X47)
| sdtlseqdt0(X47,X48)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_220,plain,
( sdtlseqdt0(X1,sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_98]) ).
cnf(c_0_221,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_70]),c_0_63])]) ).
cnf(c_0_222,hypothesis,
( esk2_2(sz10,xk) = xk
| xp = sz00
| ~ aNaturalNumber0(esk2_2(sz10,xk)) ),
inference(spm,[status(thm)],[c_0_48,c_0_199]) ).
cnf(c_0_223,plain,
( aNaturalNumber0(esk2_2(sz10,X1))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_62]),c_0_49])]),c_0_73]) ).
cnf(c_0_224,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_189]) ).
cnf(c_0_225,hypothesis,
( sdtasdt0(xr,esk2_2(xr,sdtasdt0(xn,xm))) = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_201]),c_0_128])]) ).
cnf(c_0_226,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_202]),c_0_68]),c_0_118])]) ).
cnf(c_0_227,hypothesis,
esk1_2(xr,xr) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_205]),c_0_128])]) ).
cnf(c_0_228,hypothesis,
doDivides0(xr,sdtasdt0(xp,xk)),
inference(rw,[status(thm)],[c_0_201,c_0_202]) ).
cnf(c_0_229,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_206]) ).
cnf(c_0_230,plain,
doDivides0(sz00,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_188]),c_0_63]),c_0_49])]) ).
cnf(c_0_231,plain,
( X1 = sz00
| sdtpldt0(X2,X1) != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_232,plain,
sdtpldt0(sz00,esk1_2(sz00,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_207]),c_0_63])]) ).
cnf(c_0_233,plain,
aNaturalNumber0(esk1_2(sz00,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_207]),c_0_63])]) ).
cnf(c_0_234,plain,
( sdtpldt0(sdtasdt0(sz00,X1),sz00) = sdtasdt0(sz00,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_63])]) ).
cnf(c_0_235,hypothesis,
sdtpldt0(xm,sdtmndt0(xp,xm)) = xp,
inference(rw,[status(thm)],[c_0_191,c_0_210]) ).
cnf(c_0_236,hypothesis,
sdtasdt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_211]),c_0_63]),c_0_67])]) ).
cnf(c_0_237,hypothesis,
aNaturalNumber0(sdtmndt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_66]),c_0_68]),c_0_67])]) ).
cnf(c_0_238,plain,
sdtpldt0(sz10,esk1_2(sz10,sz10)) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_49])]),c_0_55]) ).
cnf(c_0_239,plain,
aNaturalNumber0(esk1_2(sz10,sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_213]),c_0_49])]),c_0_55]) ).
cnf(c_0_240,hypothesis,
( xp = sz00
| sz10 = X1
| sdtasdt0(X1,xp) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_155]),c_0_67]),c_0_49])]) ).
cnf(c_0_241,hypothesis,
sdtpldt0(xn,esk1_2(xn,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_216]),c_0_67]),c_0_118])]) ).
cnf(c_0_242,hypothesis,
aNaturalNumber0(esk1_2(xn,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_216]),c_0_67]),c_0_118])]) ).
cnf(c_0_243,hypothesis,
( X1 = sz10
| sdtpldt0(X1,sdtmndt0(xk,sz10)) != xk
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_217]),c_0_49]),c_0_218])]) ).
cnf(c_0_244,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_219]) ).
cnf(c_0_245,hypothesis,
sdtlseqdt0(sdtmndt0(xk,sz10),xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_217]),c_0_218]),c_0_49])]) ).
cnf(c_0_246,hypothesis,
sdtmndt0(xk,sz10) != xk,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_217]),c_0_218]),c_0_49])]),c_0_55]) ).
cnf(c_0_247,hypothesis,
( esk2_2(sz10,xk) = xk
| xp = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_123]) ).
cnf(c_0_248,plain,
( sdtpldt0(sdtasdt0(X1,X2),sz00) = sdtasdt0(sdtpldt0(X1,sz00),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_209]),c_0_63])]) ).
cnf(c_0_249,hypothesis,
sdtasdt0(xr,esk2_2(xr,sdtasdt0(xp,xk))) = sdtasdt0(xp,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_225,c_0_202]),c_0_202]),c_0_202]),c_0_226])]) ).
cnf(c_0_250,hypothesis,
sdtpldt0(xr,sz00) = xr,
inference(rw,[status(thm)],[c_0_204,c_0_227]) ).
cnf(c_0_251,hypothesis,
aNaturalNumber0(esk2_2(xr,sdtasdt0(xp,xk))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_228]),c_0_226]),c_0_128])]) ).
cnf(c_0_252,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_209]),c_0_63])]) ).
cnf(c_0_253,plain,
sdtasdt0(sz00,esk2_2(sz00,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_230]),c_0_63])]) ).
cnf(c_0_254,plain,
aNaturalNumber0(esk2_2(sz00,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_230]),c_0_63])]) ).
cnf(c_0_255,plain,
esk1_2(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_63]),c_0_233])]) ).
cnf(c_0_256,hypothesis,
sdtpldt0(sdtasdt0(sz00,xm),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_235]),c_0_236]),c_0_237]),c_0_68])]) ).
cnf(c_0_257,plain,
esk1_2(sz10,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_238]),c_0_239]),c_0_49])]) ).
cnf(c_0_258,hypothesis,
( xp = sz00
| sz10 = X1
| sdtasdt0(xp,X1) != xp
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_141]),c_0_67])]) ).
cnf(c_0_259,hypothesis,
sdtasdt0(xp,esk2_2(xp,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_158]),c_0_67])]) ).
cnf(c_0_260,hypothesis,
aNaturalNumber0(esk2_2(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_158]),c_0_67])]) ).
cnf(c_0_261,hypothesis,
esk1_2(xn,xp) = sdtmndt0(xp,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_241]),c_0_118]),c_0_242])]) ).
fof(c_0_262,plain,
! [X10,X11,X12] :
( ~ aNaturalNumber0(X10)
| ~ aNaturalNumber0(X11)
| ~ aNaturalNumber0(X12)
| sdtpldt0(sdtpldt0(X10,X11),X12) = sdtpldt0(X10,sdtpldt0(X11,X12)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_263,hypothesis,
( X1 = sz10
| sdtpldt0(sdtmndt0(xk,sz10),X1) != xk
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_98]),c_0_218])]) ).
cnf(c_0_264,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_244]) ).
cnf(c_0_265,hypothesis,
aNaturalNumber0(esk1_2(sdtmndt0(xk,sz10),xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_245]),c_0_127]),c_0_218])]) ).
cnf(c_0_266,hypothesis,
~ sdtlseqdt0(xk,sdtmndt0(xk,sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_245]),c_0_218]),c_0_127])]),c_0_246]) ).
cnf(c_0_267,hypothesis,
( sdtasdt0(sz10,xk) = xk
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_199,c_0_247]) ).
cnf(c_0_268,plain,
( sdtpldt0(sz00,sdtasdt0(X1,sz00)) = sdtasdt0(sdtpldt0(X2,X1),sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_131]),c_0_63])]) ).
cnf(c_0_269,hypothesis,
sdtpldt0(sdtasdt0(xp,xk),sz00) = sdtasdt0(xp,xk),
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_248,c_0_249]),c_0_250]),c_0_249]),c_0_251]),c_0_128])]) ).
cnf(c_0_270,plain,
sdtasdt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_253]),c_0_254]),c_0_63])]) ).
cnf(c_0_271,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(rw,[status(thm)],[c_0_232,c_0_255]) ).
cnf(c_0_272,hypothesis,
( sdtasdt0(sz00,xm) = sz00
| ~ aNaturalNumber0(sdtasdt0(sz00,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_256]),c_0_63])]) ).
cnf(c_0_273,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(rw,[status(thm)],[c_0_238,c_0_257]) ).
cnf(c_0_274,hypothesis,
esk2_2(xp,xp) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_260])]),c_0_124]) ).
cnf(c_0_275,hypothesis,
sdtpldt0(xn,sdtmndt0(xp,xn)) = xp,
inference(rw,[status(thm)],[c_0_241,c_0_261]) ).
cnf(c_0_276,hypothesis,
aNaturalNumber0(sdtmndt0(xp,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_216]),c_0_118]),c_0_67])]) ).
cnf(c_0_277,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_278,hypothesis,
esk1_2(sdtmndt0(xk,sz10),xk) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_263,c_0_264]),c_0_218])])]),c_0_265]),c_0_127])]),c_0_266]) ).
cnf(c_0_279,plain,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,X3)))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_229]),c_0_44]) ).
cnf(c_0_280,hypothesis,
( aNaturalNumber0(esk2_2(xr,xk))
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_126]),c_0_128])]) ).
cnf(c_0_281,hypothesis,
( doDivides0(X1,sdtasdt0(xn,xm))
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_112]),c_0_67])]) ).
cnf(c_0_282,hypothesis,
sdtasdt0(sz10,xk) = xk,
inference(sr,[status(thm)],[c_0_267,c_0_124]) ).
fof(c_0_283,plain,
! [X52,X53,X54] :
( ( sdtasdt0(X52,X53) != sdtasdt0(X52,X54)
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) )
& ( sdtlseqdt0(sdtasdt0(X52,X53),sdtasdt0(X52,X54))
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) )
& ( sdtasdt0(X53,X52) != sdtasdt0(X54,X52)
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) )
& ( sdtlseqdt0(sdtasdt0(X53,X52),sdtasdt0(X54,X52))
| X52 = sz00
| X53 = X54
| ~ sdtlseqdt0(X53,X54)
| ~ aNaturalNumber0(X52)
| ~ aNaturalNumber0(X53)
| ~ aNaturalNumber0(X54) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_284,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X3,X1)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(spm,[status(thm)],[c_0_65,c_0_244]) ).
cnf(c_0_285,hypothesis,
sdtlseqdt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_100]),c_0_67]),c_0_63])]) ).
cnf(c_0_286,plain,
( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_134]),c_0_49])]) ).
cnf(c_0_287,hypothesis,
sdtasdt0(sdtasdt0(xp,xk),sz00) = sz00,
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_268,c_0_269]),c_0_270]),c_0_271]),c_0_63]),c_0_226])]) ).
fof(c_0_288,negated_conjecture,
~ ( xk != xp
& sdtlseqdt0(xk,xp) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_289,plain,
( sdtpldt0(sdtasdt0(X1,X2),X2) = sdtasdt0(sdtpldt0(X1,sz10),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_48]),c_0_49])]) ).
cnf(c_0_290,hypothesis,
sdtasdt0(sz00,xm) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_44]),c_0_68]),c_0_63])]) ).
cnf(c_0_291,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_273]),c_0_63]),c_0_49])]) ).
fof(c_0_292,plain,
! [X78,X79,X80] :
( ~ aNaturalNumber0(X78)
| ~ aNaturalNumber0(X79)
| X78 = sz00
| ~ doDivides0(X78,X79)
| ~ aNaturalNumber0(X80)
| sdtasdt0(X80,sdtsldt0(X79,X78)) = sdtsldt0(sdtasdt0(X80,X79),X78) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivAsso])])]) ).
cnf(c_0_293,hypothesis,
sdtasdt0(xp,sz10) = xp,
inference(rw,[status(thm)],[c_0_259,c_0_274]) ).
cnf(c_0_294,hypothesis,
sdtpldt0(sdtasdt0(sz00,xn),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_275]),c_0_236]),c_0_276]),c_0_118])]) ).
cnf(c_0_295,plain,
( X1 = sz00
| sdtpldt0(X2,sdtpldt0(X3,X1)) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_277]),c_0_59]) ).
cnf(c_0_296,hypothesis,
sdtpldt0(sdtmndt0(xk,sz10),sz10) = xk,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_278]),c_0_127]),c_0_218])]),c_0_266]) ).
cnf(c_0_297,plain,
( aNaturalNumber0(sdtasdt0(X1,sz10))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_213]),c_0_49])]) ).
cnf(c_0_298,hypothesis,
( sdtasdt0(xr,esk2_2(xr,xk)) = xk
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_126]),c_0_128])]) ).
cnf(c_0_299,hypothesis,
( xp = sz00
| aNaturalNumber0(esk2_2(xr,xk)) ),
inference(spm,[status(thm)],[c_0_280,c_0_123]) ).
cnf(c_0_300,hypothesis,
( doDivides0(X1,sdtasdt0(xp,xk))
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_281,c_0_202]),c_0_202]),c_0_226])]) ).
cnf(c_0_301,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_48]),c_0_49])]) ).
cnf(c_0_302,hypothesis,
( sz10 = X1
| sdtasdt0(X1,xk) != xk
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_282]),c_0_127]),c_0_49])]),c_0_174]) ).
cnf(c_0_303,hypothesis,
doDivides0(xk,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_282]),c_0_127]),c_0_49])]) ).
cnf(c_0_304,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X3,X2))
| X2 = sz00
| X1 = X3
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_283]) ).
cnf(c_0_305,hypothesis,
( sdtlseqdt0(xp,X1)
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_285]),c_0_67])]) ).
cnf(c_0_306,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X2,sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_229,c_0_141]) ).
cnf(c_0_307,hypothesis,
sdtasdt0(sdtasdt0(xp,xk),sz10) = sdtasdt0(xp,xk),
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_286,c_0_287]),c_0_269]),c_0_273]),c_0_63]),c_0_226])]) ).
fof(c_0_308,negated_conjecture,
( xk = xp
| ~ sdtlseqdt0(xk,xp) ),
inference(fof_nnf,[status(thm)],[c_0_288]) ).
cnf(c_0_309,hypothesis,
sdtpldt0(sz00,xm) = sdtasdt0(sz10,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_290]),c_0_291]),c_0_68]),c_0_63])]) ).
cnf(c_0_310,plain,
( sdtsldt0(sdtasdt0(X1,X2),X2) = X1
| X2 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_182,c_0_141]) ).
cnf(c_0_311,plain,
( sdtasdt0(X1,sdtsldt0(sdtasdt0(X1,X2),X1)) = sdtasdt0(X1,X2)
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_47]),c_0_44]) ).
cnf(c_0_312,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(sdtasdt0(X1,X2),X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_47]),c_0_44]) ).
cnf(c_0_313,plain,
( X1 = sz00
| sdtasdt0(X3,sdtsldt0(X2,X1)) = sdtsldt0(sdtasdt0(X3,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_292]) ).
cnf(c_0_314,hypothesis,
sdtsldt0(xp,xp) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_293]),c_0_67]),c_0_49])]),c_0_124]) ).
cnf(c_0_315,hypothesis,
( sdtasdt0(sz00,xn) = sz00
| ~ aNaturalNumber0(sdtasdt0(sz00,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_294]),c_0_63])]) ).
cnf(c_0_316,hypothesis,
( sdtpldt0(X1,xk) != sz00
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_295,c_0_296]),c_0_49]),c_0_218])]),c_0_55]) ).
cnf(c_0_317,plain,
( sdtpldt0(sdtasdt0(sz10,X1),X2) = sdtasdt0(sz10,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_48]),c_0_49])]) ).
cnf(c_0_318,plain,
( aNaturalNumber0(sdtasdt0(sz10,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_141]),c_0_49])]) ).
cnf(c_0_319,hypothesis,
sdtasdt0(xr,esk2_2(xr,xk)) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_298,c_0_127])]) ).
cnf(c_0_320,hypothesis,
aNaturalNumber0(esk2_2(xr,xk)),
inference(sr,[status(thm)],[c_0_299,c_0_124]) ).
cnf(c_0_321,hypothesis,
doDivides0(sz10,sdtasdt0(xp,xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_300,c_0_54]),c_0_49]),c_0_67])]) ).
cnf(c_0_322,plain,
( sdtasdt0(X1,X2) = sz00
| X3 = sz00
| sdtasdt0(X1,sdtasdt0(X2,X3)) != sz00
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_229]),c_0_44]) ).
cnf(c_0_323,hypothesis,
sdtasdt0(sz10,sdtasdt0(xp,xk)) = sdtasdt0(xp,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_249]),c_0_251]),c_0_128])]) ).
cnf(c_0_324,hypothesis,
( sz10 = X1
| sdtasdt0(xk,X1) != xk
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_302,c_0_141]),c_0_127])]) ).
cnf(c_0_325,hypothesis,
sdtasdt0(xk,esk2_2(xk,xk)) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_303]),c_0_127])]) ).
cnf(c_0_326,hypothesis,
aNaturalNumber0(esk2_2(xk,xk)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_303]),c_0_127])]) ).
cnf(c_0_327,hypothesis,
( xp = X1
| X2 = sz00
| sdtlseqdt0(sdtasdt0(xp,X2),sdtasdt0(X1,X2))
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_304,c_0_305]),c_0_67])]) ).
cnf(c_0_328,hypothesis,
sdtasdt0(xk,xp) = sdtasdt0(xp,xk),
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_306,c_0_307]),c_0_293]),c_0_49]),c_0_67]),c_0_127])]) ).
cnf(c_0_329,negated_conjecture,
( xk = xp
| ~ sdtlseqdt0(xk,xp) ),
inference(split_conjunct,[status(thm)],[c_0_308]) ).
cnf(c_0_330,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_283]) ).
cnf(c_0_331,hypothesis,
sdtasdt0(sz10,xm) = xm,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_309]),c_0_68])]) ).
cnf(c_0_332,plain,
( sdtsldt0(sdtasdt0(X1,X2),sdtsldt0(sdtasdt0(X1,X2),X1)) = X1
| sdtsldt0(sdtasdt0(X1,X2),X1) = sz00
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_310,c_0_311]),c_0_312]) ).
cnf(c_0_333,hypothesis,
( sdtsldt0(sdtasdt0(X1,xp),xp) = sdtasdt0(X1,sz10)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_158]),c_0_67])]),c_0_124]),c_0_314]) ).
cnf(c_0_334,hypothesis,
sdtasdt0(sz00,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_315,c_0_44]),c_0_118]),c_0_63])]) ).
cnf(c_0_335,hypothesis,
( sdtasdt0(sz10,sdtpldt0(X1,xk)) != sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_317]),c_0_127])]),c_0_318]) ).
cnf(c_0_336,hypothesis,
( aNaturalNumber0(sdtasdt0(X1,xk))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_319]),c_0_320]),c_0_128])]) ).
cnf(c_0_337,hypothesis,
( sdtasdt0(xp,xk) = sz00
| sdtlseqdt0(sz10,sdtasdt0(xp,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_321]),c_0_226]),c_0_49])]) ).
cnf(c_0_338,hypothesis,
sdtasdt0(xp,xk) != sz00,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[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_322,c_0_323]),c_0_155]),c_0_127]),c_0_67]),c_0_49])]),c_0_124]),c_0_174]) ).
cnf(c_0_339,hypothesis,
esk2_2(xk,xk) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_325]),c_0_326])]) ).
cnf(c_0_340,hypothesis,
( xk = xp
| sdtlseqdt0(sdtasdt0(xp,xp),sdtasdt0(xp,xk)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_327,c_0_328]),c_0_127]),c_0_67])]),c_0_124]),c_0_329]) ).
cnf(c_0_341,hypothesis,
( X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,xm),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330,c_0_66]),c_0_67]),c_0_68])]),c_0_77]) ).
cnf(c_0_342,hypothesis,
( aNaturalNumber0(sdtasdt0(X1,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_331]),c_0_68]),c_0_49])]) ).
cnf(c_0_343,hypothesis,
( aNaturalNumber0(sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_293]),c_0_49]),c_0_67])]) ).
cnf(c_0_344,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_345,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = sz00
| X1 = sz00
| X1 = X3
| sdtasdt0(X3,sdtsldt0(sdtasdt0(X1,X2),X1)) != sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_311]),c_0_312]) ).
cnf(c_0_346,hypothesis,
sdtsldt0(sdtasdt0(xp,xp),xp) = xp,
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_332,c_0_333]),c_0_293]),c_0_293]),c_0_67])]),c_0_124]) ).
cnf(c_0_347,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_141,c_0_229]),c_0_44]) ).
cnf(c_0_348,hypothesis,
sdtpldt0(sz00,xn) = sdtasdt0(sz10,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_334]),c_0_291]),c_0_118]),c_0_63])]) ).
cnf(c_0_349,hypothesis,
( sdtasdt0(sz10,sdtasdt0(sdtpldt0(X1,sz10),xk)) != sz00
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_335,c_0_289]),c_0_127])]),c_0_336]) ).
cnf(c_0_350,hypothesis,
sdtlseqdt0(sz10,sdtasdt0(xp,xk)),
inference(sr,[status(thm)],[c_0_337,c_0_338]) ).
cnf(c_0_351,hypothesis,
sdtasdt0(xk,sz10) = xk,
inference(rw,[status(thm)],[c_0_325,c_0_339]) ).
cnf(c_0_352,hypothesis,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xp)
| xk = xp
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xp))
| ~ aNaturalNumber0(sdtasdt0(xp,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_340]),c_0_226])]) ).
cnf(c_0_353,hypothesis,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,xp))
| ~ sdtlseqdt0(X2,sdtasdt0(X1,xm))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_341]),c_0_342]),c_0_343]) ).
cnf(c_0_354,hypothesis,
( X1 = sz00
| sdtlseqdt0(sdtasdt0(xn,X1),sdtasdt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_304,c_0_216]),c_0_67]),c_0_118])]),c_0_344]) ).
cnf(c_0_355,hypothesis,
( xp = X1
| sdtasdt0(X1,xp) != sdtasdt0(xp,xp)
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_345,c_0_346]),c_0_67])]),c_0_124]) ).
cnf(c_0_356,plain,
( sdtpldt0(sdtasdt0(X1,sz00),sz00) = sdtasdt0(sdtpldt0(X1,X2),sz00)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_131]),c_0_63])]) ).
cnf(c_0_357,hypothesis,
( sdtasdt0(xp,sdtasdt0(sz10,X1)) = sdtasdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_347,c_0_293]),c_0_49]),c_0_67])]) ).
cnf(c_0_358,hypothesis,
sdtasdt0(sz10,xn) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_348]),c_0_118])]) ).
fof(c_0_359,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(fof_simplification,[status(thm)],[m__1870]) ).
cnf(c_0_360,hypothesis,
( sdtasdt0(sz10,sdtasdt0(sdtpldt0(sz10,X1),xk)) != sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_349,c_0_98]),c_0_49])]) ).
cnf(c_0_361,hypothesis,
sdtpldt0(sz10,esk1_2(sz10,sdtasdt0(xp,xk))) = sdtasdt0(xp,xk),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_323]),c_0_49]),c_0_226])]),c_0_338]) ).
cnf(c_0_362,hypothesis,
aNaturalNumber0(esk1_2(sz10,sdtasdt0(xp,xk))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_350]),c_0_226]),c_0_49])]) ).
cnf(c_0_363,hypothesis,
( sdtasdt0(xk,sdtasdt0(sz10,X1)) = sdtasdt0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_347,c_0_351]),c_0_49]),c_0_127])]) ).
cnf(c_0_364,hypothesis,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xp)
| xk = xp
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_352,c_0_44]),c_0_67])]) ).
cnf(c_0_365,hypothesis,
( xm = sz00
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xp)) ),
inference(sr,[status(thm)],[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_353,c_0_354]),c_0_202]),c_0_202]),c_0_226]),c_0_67]),c_0_68])]),c_0_124]) ).
cnf(c_0_366,hypothesis,
( xk = xp
| sdtasdt0(xp,xk) != sdtasdt0(xp,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_355,c_0_328]),c_0_127])]) ).
cnf(c_0_367,plain,
( sdtpldt0(sdtasdt0(X1,X2),sz00) = sdtasdt0(X1,sdtpldt0(X2,sz00))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_131]),c_0_63])]) ).
cnf(c_0_368,hypothesis,
sdtpldt0(sdtasdt0(xn,sz00),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_356,c_0_275]),c_0_211]),c_0_276]),c_0_118])]) ).
cnf(c_0_369,hypothesis,
( X1 = xp
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(xp,X2))
| sdtlseqdt0(xp,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_304,c_0_305]),c_0_67])]) ).
cnf(c_0_370,hypothesis,
sdtasdt0(xn,xp) = sdtasdt0(xp,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_357,c_0_358]),c_0_118])]) ).
cnf(c_0_371,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_359]) ).
cnf(c_0_372,hypothesis,
( aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,xp)))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_343,c_0_229]),c_0_67])]),c_0_44]) ).
cnf(c_0_373,hypothesis,
( sdtasdt0(xp,sdtasdt0(sz10,X1)) = sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_293]),c_0_49]),c_0_67])]) ).
cnf(c_0_374,hypothesis,
sdtasdt0(sz10,sdtasdt0(sdtasdt0(xp,xk),xk)) != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_360,c_0_361]),c_0_362])]) ).
cnf(c_0_375,hypothesis,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xn,sdtasdt0(xm,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_202]),c_0_68]),c_0_118])]) ).
cnf(c_0_376,hypothesis,
sdtasdt0(xm,xk) = sdtasdt0(xk,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_363,c_0_331]),c_0_68])]) ).
cnf(c_0_377,hypothesis,
( xm = sz00
| xk = xp ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_364,c_0_365]),c_0_366]) ).
cnf(c_0_378,hypothesis,
sdtasdt0(xn,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_367,c_0_368]),c_0_271]),c_0_63]),c_0_118])]) ).
cnf(c_0_379,hypothesis,
sdtlseqdt0(sdtasdt0(xp,xn),sdtasdt0(xp,xp)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_369,c_0_370]),c_0_67]),c_0_118])]),c_0_344]),c_0_124]),c_0_371]) ).
cnf(c_0_380,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_370]),c_0_67]),c_0_118])]) ).
cnf(c_0_381,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_372,c_0_373]),c_0_49]),c_0_67])]) ).
cnf(c_0_382,hypothesis,
sdtasdt0(xp,xn) != sdtasdt0(xp,xp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_355,c_0_370]),c_0_118])]),c_0_344]) ).
cnf(c_0_383,hypothesis,
sdtasdt0(xm,xp) = sdtasdt0(xp,xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_357,c_0_331]),c_0_68])]) ).
cnf(c_0_384,hypothesis,
sdtasdt0(sz10,sdtasdt0(xn,sdtasdt0(xk,xm))) != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_374,c_0_375]),c_0_376]),c_0_127])]) ).
cnf(c_0_385,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_347,c_0_48]),c_0_49])]) ).
cnf(c_0_386,hypothesis,
aNaturalNumber0(sdtasdt0(xk,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_376]),c_0_127]),c_0_68])]) ).
cnf(c_0_387,hypothesis,
( xn = sz00
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xn)) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_202]),c_0_118])]),c_0_370]) ).
cnf(c_0_388,hypothesis,
xk = xp,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_377]),c_0_378]),c_0_338]) ).
cnf(c_0_389,hypothesis,
~ sdtlseqdt0(sdtasdt0(xp,xp),sdtasdt0(xp,xn)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_379]),c_0_380]),c_0_381])]),c_0_382]) ).
cnf(c_0_390,hypothesis,
sdtasdt0(sz00,sdtasdt0(xp,xm)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_383]),c_0_236]),c_0_67]),c_0_68])]) ).
cnf(c_0_391,hypothesis,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_383]),c_0_67]),c_0_68])]) ).
cnf(c_0_392,hypothesis,
sdtasdt0(sdtasdt0(xk,xm),xn) != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_384,c_0_385]),c_0_386]),c_0_118])]) ).
cnf(c_0_393,hypothesis,
xn = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_387,c_0_388]),c_0_389]) ).
cnf(c_0_394,hypothesis,
sdtasdt0(sdtasdt0(xp,xm),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_385,c_0_390]),c_0_85]),c_0_391]),c_0_63])]) ).
cnf(c_0_395,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_392,c_0_388]),c_0_393]),c_0_394])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM502+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 2400
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Oct 2 14:21:41 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.SmByGyR8wS/E---3.1_25811.p
% 553.17/70.75 # Version: 3.1pre001
% 553.17/70.75 # Preprocessing class: FSLSSMSSSSSNFFN.
% 553.17/70.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 553.17/70.75 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 553.17/70.75 # Starting new_bool_3 with 300s (1) cores
% 553.17/70.75 # Starting new_bool_1 with 300s (1) cores
% 553.17/70.75 # Starting sh5l with 300s (1) cores
% 553.17/70.75 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 25891 completed with status 0
% 553.17/70.75 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 553.17/70.75 # Preprocessing class: FSLSSMSSSSSNFFN.
% 553.17/70.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 553.17/70.75 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 553.17/70.75 # No SInE strategy applied
% 553.17/70.75 # Search class: FGHSF-FFMM21-SFFFFFNN
% 553.17/70.75 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 553.17/70.75 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 553.17/70.75 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 553.17/70.75 # Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 553.17/70.75 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 553.17/70.75 # Starting G----_Z1014__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 553.17/70.75 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 25896 completed with status 0
% 553.17/70.75 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 553.17/70.75 # Preprocessing class: FSLSSMSSSSSNFFN.
% 553.17/70.75 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 553.17/70.75 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 553.17/70.75 # No SInE strategy applied
% 553.17/70.75 # Search class: FGHSF-FFMM21-SFFFFFNN
% 553.17/70.75 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 553.17/70.75 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 553.17/70.75 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 553.17/70.75 # Preprocessing time : 0.002 s
% 553.17/70.75 # Presaturation interreduction done
% 553.17/70.75
% 553.17/70.75 # Proof found!
% 553.17/70.75 # SZS status Theorem
% 553.17/70.75 # SZS output start CNFRefutation
% See solution above
% 553.17/70.75 # Parsed axioms : 50
% 553.17/70.75 # Removed by relevancy pruning/SinE : 0
% 553.17/70.75 # Initial clauses : 93
% 553.17/70.75 # Removed in clause preprocessing : 3
% 553.17/70.75 # Initial clauses in saturation : 90
% 553.17/70.75 # Processed clauses : 78591
% 553.17/70.75 # ...of these trivial : 2900
% 553.17/70.75 # ...subsumed : 62117
% 553.17/70.75 # ...remaining for further processing : 13574
% 553.17/70.75 # Other redundant clauses eliminated : 2627
% 553.17/70.75 # Clauses deleted for lack of memory : 62832
% 553.17/70.75 # Backward-subsumed : 846
% 553.17/70.75 # Backward-rewritten : 5652
% 553.17/70.75 # Generated clauses : 2563243
% 553.17/70.75 # ...of the previous two non-redundant : 2450735
% 553.17/70.75 # ...aggressively subsumed : 0
% 553.17/70.75 # Contextual simplify-reflections : 3459
% 553.17/70.75 # Paramodulations : 2560377
% 553.17/70.75 # Factorizations : 48
% 553.17/70.75 # NegExts : 0
% 553.17/70.75 # Equation resolutions : 2754
% 553.17/70.75 # Total rewrite steps : 2484286
% 553.17/70.75 # Propositional unsat checks : 2
% 553.17/70.75 # Propositional check models : 0
% 553.17/70.75 # Propositional check unsatisfiable : 0
% 553.17/70.75 # Propositional clauses : 0
% 553.17/70.75 # Propositional clauses after purity: 0
% 553.17/70.75 # Propositional unsat core size : 0
% 553.17/70.75 # Propositional preprocessing time : 0.000
% 553.17/70.75 # Propositional encoding time : 2.743
% 553.17/70.75 # Propositional solver time : 1.342
% 553.17/70.75 # Success case prop preproc time : 0.000
% 553.17/70.75 # Success case prop encoding time : 0.000
% 553.17/70.75 # Success case prop solver time : 0.000
% 553.17/70.75 # Current number of processed clauses : 6918
% 553.17/70.75 # Positive orientable unit clauses : 1395
% 553.17/70.75 # Positive unorientable unit clauses: 0
% 553.17/70.75 # Negative unit clauses : 1068
% 553.17/70.75 # Non-unit-clauses : 4455
% 553.17/70.75 # Current number of unprocessed clauses: 1440425
% 553.17/70.75 # ...number of literals in the above : 7696748
% 553.17/70.75 # Current number of archived formulas : 0
% 553.17/70.75 # Current number of archived clauses : 6645
% 553.17/70.75 # Clause-clause subsumption calls (NU) : 7958186
% 553.17/70.75 # Rec. Clause-clause subsumption calls : 2146113
% 553.17/70.75 # Non-unit clause-clause subsumptions : 27150
% 553.17/70.75 # Unit Clause-clause subsumption calls : 1645194
% 553.17/70.75 # Rewrite failures with RHS unbound : 0
% 553.17/70.75 # BW rewrite match attempts : 2692
% 553.17/70.75 # BW rewrite match successes : 596
% 553.17/70.75 # Condensation attempts : 0
% 553.17/70.75 # Condensation successes : 0
% 553.17/70.75 # Termbank termtop insertions : 73448763
% 553.17/70.75
% 553.17/70.75 # -------------------------------------------------
% 553.17/70.75 # User time : 66.974 s
% 553.17/70.75 # System time : 1.592 s
% 553.17/70.75 # Total time : 68.566 s
% 553.17/70.75 # Maximum resident set size: 2000 pages
% 553.17/70.75
% 553.17/70.75 # -------------------------------------------------
% 553.17/70.75 # User time : 336.763 s
% 553.17/70.75 # System time : 6.949 s
% 553.17/70.75 # Total time : 343.712 s
% 553.17/70.75 # Maximum resident set size: 1732 pages
% 553.17/70.75 % E---3.1 exiting
% 553.17/70.75 % E---3.1 exiting
%------------------------------------------------------------------------------