TSTP Solution File: NUM506+1 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : NUM506+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.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 19:07:27 EDT 2023
% Result : Theorem 403.20s 52.56s
% Output : CNFRefutation 403.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 30
% Syntax : Number of formulae : 166 ( 43 unt; 0 def)
% Number of atoms : 637 ( 166 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 804 ( 333 ~; 354 |; 77 &)
% ( 5 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 222 ( 1 sgn; 100 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mDefPrime) ).
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.g0wlylGOIo/E---3.1_1844.p',mDefQuot) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m__1860) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m__1837) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m__2306) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mSortsB_02) ).
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.g0wlylGOIo/E---3.1_1844.p',mDivMin) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m_AddZero) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mSortsC) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mMonMul2) ).
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.g0wlylGOIo/E---3.1_1844.p',mDefDiv) ).
fof(m__2362,hypothesis,
( sdtlseqdt0(xr,xk)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m__2362) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m__2342) ).
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.g0wlylGOIo/E---3.1_1844.p',mDefLE) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mLEAsym) ).
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.g0wlylGOIo/E---3.1_1844.p',mDivTrans) ).
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.g0wlylGOIo/E---3.1_1844.p',mAMDistr) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m_MulUnit) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mSortsC_01) ).
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.g0wlylGOIo/E---3.1_1844.p',mDefDiff) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mMulComm) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mSortsB) ).
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.g0wlylGOIo/E---3.1_1844.p',mLETran) ).
fof(m__2377,hypothesis,
( xk != xp
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m__2377) ).
fof(m__,conjecture,
( doDivides0(xr,xn)
| doDivides0(xr,xm) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m__) ).
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.g0wlylGOIo/E---3.1_1844.p',mMonAdd) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mLETotal) ).
fof(m__1799,hypothesis,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( isPrime0(X3)
& doDivides0(X3,sdtasdt0(X1,X2)) )
=> ( iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X3,X1)
| doDivides0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',m__1799) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p',mIH_03) ).
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.g0wlylGOIo/E---3.1_1844.p',mAddCanc) ).
fof(c_0_30,plain,
! [X81,X82] :
( ( X81 != sz00
| ~ isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( X81 != sz10
| ~ isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( ~ aNaturalNumber0(X82)
| ~ doDivides0(X82,X81)
| X82 = sz10
| X82 = X81
| ~ isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( aNaturalNumber0(esk3_1(X81))
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( doDivides0(esk3_1(X81),X81)
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( esk3_1(X81) != sz10
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( esk3_1(X81) != X81
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
fof(c_0_31,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_32,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_35,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_31]) ).
cnf(c_0_36,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_37,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_38,hypothesis,
xp != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
fof(c_0_39,plain,
! [X6,X7] :
( ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X7)
| aNaturalNumber0(sdtasdt0(X6,X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_40,hypothesis,
( sdtasdt0(xn,xm) = sdtasdt0(xp,X1)
| X1 != 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_35,c_0_36]),c_0_37]),c_0_34])]),c_0_38]) ).
cnf(c_0_41,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_42,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_44,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])]) ).
fof(c_0_45,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_46,hypothesis,
( sdtasdt0(xn,xm) = sdtasdt0(xp,X1)
| X1 != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_47,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_44]) ).
cnf(c_0_48,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_50,hypothesis,
( aNaturalNumber0(sdtasdt0(xp,X1))
| X1 != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_46]),c_0_42]),c_0_43])]) ).
fof(c_0_51,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])]) ).
fof(c_0_52,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])])])])]) ).
cnf(c_0_53,plain,
( doDivides0(X1,sz00)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ 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_54,hypothesis,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__2362]) ).
cnf(c_0_55,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_56,hypothesis,
( aNaturalNumber0(sdtasdt0(xn,xm))
| X1 != xk ),
inference(spm,[status(thm)],[c_0_50,c_0_46]) ).
fof(c_0_57,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])])])])]) ).
cnf(c_0_58,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_60,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,hypothesis,
( doDivides0(xr,sz00)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]) ).
cnf(c_0_62,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(er,[status(thm)],[c_0_56]) ).
fof(c_0_63,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_64,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_66,plain,
( esk2_2(X1,X2) = sz00
| sdtlseqdt0(X1,X2)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_67,hypothesis,
doDivides0(xr,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).
fof(c_0_68,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_69,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_70,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])])]) ).
fof(c_0_71,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_72,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_73,plain,
( sdtlseqdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_49])])]) ).
cnf(c_0_74,hypothesis,
( esk2_2(xr,sz00) = sz00
| sdtlseqdt0(xr,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_55]),c_0_49])]) ).
cnf(c_0_75,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_76,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,hypothesis,
doDivides0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_78,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_69]) ).
cnf(c_0_79,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_70]) ).
cnf(c_0_80,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_81,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_82,plain,
( X1 = sz00
| ~ sdtlseqdt0(X1,sz00)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_49])]) ).
cnf(c_0_83,hypothesis,
( sdtasdt0(xr,sz00) = sz00
| sdtlseqdt0(xr,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_74]),c_0_67]),c_0_55]),c_0_49])]) ).
cnf(c_0_84,hypothesis,
xr != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_75]),c_0_55])]) ).
cnf(c_0_85,hypothesis,
( doDivides0(X1,xk)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_55])]) ).
cnf(c_0_86,hypothesis,
aNaturalNumber0(xk),
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_78,c_0_37]),c_0_36]),c_0_34]),c_0_62])]),c_0_38]) ).
cnf(c_0_87,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_88,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_89,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_90,hypothesis,
sdtasdt0(xr,sz00) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_55])]),c_0_84]) ).
cnf(c_0_91,hypothesis,
( doDivides0(X1,xk)
| ~ doDivides0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]) ).
cnf(c_0_92,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_81])])]) ).
cnf(c_0_93,hypothesis,
sdtasdt0(xr,sdtpldt0(sz00,sz10)) = sdtpldt0(sz00,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_49]),c_0_55])]) ).
fof(c_0_94,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_95,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_96,hypothesis,
doDivides0(sz10,xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_81]),c_0_55])]) ).
cnf(c_0_97,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_98,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_31]) ).
fof(c_0_99,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_100,hypothesis,
sdtpldt0(sz00,xr) = sdtasdt0(xr,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_65]),c_0_81])]) ).
cnf(c_0_101,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_94]) ).
fof(c_0_102,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_103,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_104,hypothesis,
sdtasdt0(sz10,sdtsldt0(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_95,c_0_96]),c_0_81]),c_0_86])]),c_0_97]) ).
cnf(c_0_105,hypothesis,
aNaturalNumber0(sdtsldt0(xk,sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_96]),c_0_81]),c_0_86])]),c_0_97]) ).
cnf(c_0_106,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[c_0_98,c_0_87]) ).
cnf(c_0_107,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_108,hypothesis,
sdtasdt0(xr,sz10) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_100]),c_0_55])]) ).
cnf(c_0_109,plain,
( X1 = sdtmndt0(X2,X3)
| sdtpldt0(X3,X1) != X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[c_0_101,c_0_64]) ).
cnf(c_0_110,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_111,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_112,hypothesis,
sdtlseqdt0(xk,xp),
inference(split_conjunct,[status(thm)],[m__2377]) ).
cnf(c_0_113,hypothesis,
sdtsldt0(xk,sz10) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_104]),c_0_105])]) ).
cnf(c_0_114,hypothesis,
( aNaturalNumber0(X1)
| X1 != 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_69,c_0_36]),c_0_37]),c_0_34])]),c_0_38]) ).
cnf(c_0_115,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_106]),c_0_41]) ).
cnf(c_0_116,hypothesis,
sdtasdt0(sz10,xr) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_81]),c_0_55])]) ).
cnf(c_0_117,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_87]),c_0_41]) ).
cnf(c_0_118,plain,
( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_109]),c_0_110]) ).
cnf(c_0_119,hypothesis,
sdtpldt0(sz00,xr) = xr,
inference(rw,[status(thm)],[c_0_100,c_0_108]) ).
cnf(c_0_120,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_64]),c_0_110]) ).
cnf(c_0_121,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_34])]) ).
cnf(c_0_122,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_107]) ).
cnf(c_0_123,hypothesis,
( sdtasdt0(sz10,X1) = xk
| X1 != xk ),
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_35,c_0_113]),c_0_96]),c_0_81]),c_0_86])]),c_0_97]) ).
cnf(c_0_124,hypothesis,
( aNaturalNumber0(X1)
| X1 != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_125,hypothesis,
sdtlseqdt0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2362]) ).
cnf(c_0_126,hypothesis,
sdtsldt0(xr,sz10) = xr,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_81]),c_0_55])]),c_0_97]) ).
cnf(c_0_127,hypothesis,
doDivides0(sz10,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_116]),c_0_81]),c_0_55])]) ).
cnf(c_0_128,plain,
( aNaturalNumber0(X1)
| X1 != sdtmndt0(X2,X3)
| ~ sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_129,hypothesis,
sdtmndt0(xr,sz00) = xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_49]),c_0_55])]) ).
cnf(c_0_130,hypothesis,
sdtlseqdt0(sz00,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_119]),c_0_49]),c_0_55])]) ).
fof(c_0_131,negated_conjecture,
~ ( doDivides0(xr,xn)
| doDivides0(xr,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_132,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])])])]) ).
fof(c_0_133,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_134,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xk)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_86])]) ).
cnf(c_0_135,hypothesis,
( sdtlseqdt0(X1,xk)
| X1 != xk ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_81])]),c_0_97]),c_0_124]) ).
cnf(c_0_136,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_111,c_0_125]),c_0_55])]) ).
cnf(c_0_137,hypothesis,
( sdtasdt0(sz10,X1) = xr
| X1 != xr ),
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_35,c_0_126]),c_0_127]),c_0_81]),c_0_55])]),c_0_97]) ).
cnf(c_0_138,hypothesis,
( aNaturalNumber0(X1)
| X1 != xr ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]),c_0_49]),c_0_55])]) ).
fof(c_0_139,hypothesis,
! [X86,X87,X88] :
( ~ aNaturalNumber0(X86)
| ~ aNaturalNumber0(X87)
| ~ aNaturalNumber0(X88)
| ~ isPrime0(X88)
| ~ doDivides0(X88,sdtasdt0(X86,X87))
| ~ iLess0(sdtpldt0(sdtpldt0(X86,X87),X88),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X88,X86)
| doDivides0(X88,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1799])]) ).
fof(c_0_140,negated_conjecture,
( ~ doDivides0(xr,xn)
& ~ doDivides0(xr,xm) ),
inference(fof_nnf,[status(thm)],[c_0_131]) ).
fof(c_0_141,plain,
! [X58,X59] :
( ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X59)
| X58 = X59
| ~ sdtlseqdt0(X58,X59)
| iLess0(X58,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).
cnf(c_0_142,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| X2 = X3
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_143,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
fof(c_0_144,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_145,hypothesis,
( sdtlseqdt0(X1,xp)
| X1 != xk ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_124]) ).
cnf(c_0_146,hypothesis,
( sdtlseqdt0(X1,xk)
| ~ sdtlseqdt0(X1,xr)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_86])]) ).
cnf(c_0_147,hypothesis,
( sdtlseqdt0(X1,xr)
| X1 != xr ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_137]),c_0_81])]),c_0_97]),c_0_138]) ).
cnf(c_0_148,hypothesis,
( doDivides0(X3,X1)
| doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ isPrime0(X3)
| ~ doDivides0(X3,sdtasdt0(X1,X2))
| ~ iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_149,negated_conjecture,
~ doDivides0(xr,xm),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_150,negated_conjecture,
~ doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[c_0_140]) ).
cnf(c_0_151,plain,
( X1 = X2
| iLess0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_152,plain,
( X1 = X2
| sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_153,plain,
( X2 = X3
| sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_154,hypothesis,
( xp = X1
| X1 != xk
| ~ sdtlseqdt0(xp,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_145]),c_0_34])]),c_0_124]) ).
cnf(c_0_155,hypothesis,
( sdtlseqdt0(X1,xk)
| X1 != xr ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_138]) ).
cnf(c_0_156,hypothesis,
xk != xp,
inference(split_conjunct,[status(thm)],[m__2377]) ).
cnf(c_0_157,hypothesis,
( sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_125]),c_0_55])]) ).
cnf(c_0_158,hypothesis,
~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
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_148,c_0_54]),c_0_75]),c_0_55]),c_0_42]),c_0_43])]),c_0_149]),c_0_150]) ).
cnf(c_0_159,plain,
( X1 = X2
| iLess0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_110]),c_0_110]),c_0_153]) ).
cnf(c_0_160,hypothesis,
xr != xp,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_156]) ).
cnf(c_0_161,hypothesis,
( xr = xp
| ~ sdtlseqdt0(xp,xr)
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_157]),c_0_55]),c_0_34])]) ).
cnf(c_0_162,hypothesis,
( sdtlseqdt0(xp,xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_34]),c_0_55])]),c_0_160]) ).
cnf(c_0_163,hypothesis,
( xr = xp
| ~ sdtlseqdt0(xp,xr) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_161,c_0_86])]) ).
cnf(c_0_164,hypothesis,
sdtlseqdt0(xp,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_110]),c_0_42]),c_0_43])]) ).
cnf(c_0_165,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164])]),c_0_160]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM506+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n025.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 2400
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Oct 2 14:12:51 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.42 Running first-order model finding
% 0.16/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.g0wlylGOIo/E---3.1_1844.p
% 403.20/52.56 # Version: 3.1pre001
% 403.20/52.56 # Preprocessing class: FSLSSMSSSSSNFFN.
% 403.20/52.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 403.20/52.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 403.20/52.56 # Starting new_bool_3 with 300s (1) cores
% 403.20/52.56 # Starting new_bool_1 with 300s (1) cores
% 403.20/52.56 # Starting sh5l with 300s (1) cores
% 403.20/52.56 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1928 completed with status 0
% 403.20/52.56 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 403.20/52.56 # Preprocessing class: FSLSSMSSSSSNFFN.
% 403.20/52.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 403.20/52.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 403.20/52.56 # No SInE strategy applied
% 403.20/52.56 # Search class: FGHSF-FFMM21-SFFFFFNN
% 403.20/52.56 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 403.20/52.56 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 403.20/52.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 403.20/52.56 # Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 403.20/52.56 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 403.20/52.56 # Starting G----_Z1014__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 403.20/52.56 # G-E--_208_C18_F1_AE_CS_SP_PS_S3S with pid 1936 completed with status 0
% 403.20/52.56 # Result found by G-E--_208_C18_F1_AE_CS_SP_PS_S3S
% 403.20/52.56 # Preprocessing class: FSLSSMSSSSSNFFN.
% 403.20/52.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 403.20/52.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 403.20/52.56 # No SInE strategy applied
% 403.20/52.56 # Search class: FGHSF-FFMM21-SFFFFFNN
% 403.20/52.56 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 403.20/52.56 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 811s (1) cores
% 403.20/52.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 403.20/52.56 # Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 403.20/52.56 # Preprocessing time : 0.002 s
% 403.20/52.56 # Presaturation interreduction done
% 403.20/52.56
% 403.20/52.56 # Proof found!
% 403.20/52.56 # SZS status Theorem
% 403.20/52.56 # SZS output start CNFRefutation
% See solution above
% 403.20/52.56 # Parsed axioms : 51
% 403.20/52.56 # Removed by relevancy pruning/SinE : 0
% 403.20/52.56 # Initial clauses : 96
% 403.20/52.56 # Removed in clause preprocessing : 3
% 403.20/52.56 # Initial clauses in saturation : 93
% 403.20/52.56 # Processed clauses : 60895
% 403.20/52.56 # ...of these trivial : 1247
% 403.20/52.56 # ...subsumed : 52443
% 403.20/52.56 # ...remaining for further processing : 7205
% 403.20/52.56 # Other redundant clauses eliminated : 7326
% 403.20/52.56 # Clauses deleted for lack of memory : 19360
% 403.20/52.56 # Backward-subsumed : 671
% 403.20/52.56 # Backward-rewritten : 540
% 403.20/52.56 # Generated clauses : 1996859
% 403.20/52.56 # ...of the previous two non-redundant : 1932412
% 403.20/52.56 # ...aggressively subsumed : 0
% 403.20/52.56 # Contextual simplify-reflections : 3091
% 403.20/52.56 # Paramodulations : 1988871
% 403.20/52.56 # Factorizations : 29
% 403.20/52.56 # NegExts : 0
% 403.20/52.56 # Equation resolutions : 7937
% 403.20/52.56 # Total rewrite steps : 1366893
% 403.20/52.56 # Propositional unsat checks : 0
% 403.20/52.56 # Propositional check models : 0
% 403.20/52.56 # Propositional check unsatisfiable : 0
% 403.20/52.56 # Propositional clauses : 0
% 403.20/52.56 # Propositional clauses after purity: 0
% 403.20/52.56 # Propositional unsat core size : 0
% 403.20/52.56 # Propositional preprocessing time : 0.000
% 403.20/52.56 # Propositional encoding time : 0.000
% 403.20/52.56 # Propositional solver time : 0.000
% 403.20/52.56 # Success case prop preproc time : 0.000
% 403.20/52.56 # Success case prop encoding time : 0.000
% 403.20/52.56 # Success case prop solver time : 0.000
% 403.20/52.56 # Current number of processed clauses : 5885
% 403.20/52.56 # Positive orientable unit clauses : 520
% 403.20/52.56 # Positive unorientable unit clauses: 0
% 403.20/52.56 # Negative unit clauses : 465
% 403.20/52.56 # Non-unit-clauses : 4900
% 403.20/52.56 # Current number of unprocessed clauses: 959781
% 403.20/52.56 # ...number of literals in the above : 5938810
% 403.20/52.56 # Current number of archived formulas : 0
% 403.20/52.56 # Current number of archived clauses : 1319
% 403.20/52.56 # Clause-clause subsumption calls (NU) : 8564190
% 403.20/52.56 # Rec. Clause-clause subsumption calls : 1036118
% 403.20/52.56 # Non-unit clause-clause subsumptions : 14464
% 403.20/52.56 # Unit Clause-clause subsumption calls : 333338
% 403.20/52.56 # Rewrite failures with RHS unbound : 0
% 403.20/52.56 # BW rewrite match attempts : 177
% 403.20/52.56 # BW rewrite match successes : 139
% 403.20/52.56 # Condensation attempts : 0
% 403.20/52.56 # Condensation successes : 0
% 403.20/52.56 # Termbank termtop insertions : 47827288
% 403.20/52.56
% 403.20/52.56 # -------------------------------------------------
% 403.20/52.56 # User time : 49.012 s
% 403.20/52.56 # System time : 1.339 s
% 403.20/52.56 # Total time : 50.351 s
% 403.20/52.56 # Maximum resident set size: 2000 pages
% 403.20/52.56
% 403.20/52.56 # -------------------------------------------------
% 403.20/52.56 # User time : 245.286 s
% 403.20/52.56 # System time : 5.851 s
% 403.20/52.56 # Total time : 251.137 s
% 403.20/52.56 # Maximum resident set size: 1736 pages
% 403.20/52.56 % E---3.1 exiting
%------------------------------------------------------------------------------