TSTP Solution File: NUM493+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM493+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 09:33:02 EDT 2022
% Result : Theorem 0.51s 58.68s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 112 ( 49 unt; 0 def)
% Number of atoms : 340 ( 111 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 396 ( 168 ~; 172 |; 36 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 117 ( 1 sgn 52 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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/solver/bin/../tmp/theBenchmark.p',mDefDiff) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mDefLE) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mAddComm) ).
fof(m__1870,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1870) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1837) ).
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/solver/bin/../tmp/theBenchmark.p',mAddAsso) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mMulComm) ).
fof(m__1883,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1883) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mSortsB) ).
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/solver/bin/../tmp/theBenchmark.p',mAddCanc) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m_AddZero) ).
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/solver/bin/../tmp/theBenchmark.p',mDefPrime) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1860) ).
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/solver/bin/../tmp/theBenchmark.p',m__1799) ).
fof(m__,conjecture,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mSortsC) ).
fof(m__1913,hypothesis,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',m__1913) ).
fof(mIH_03,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> iLess0(X1,X2) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',mIH_03) ).
fof(c_0_18,plain,
! [X4,X5,X6,X6] :
( ( aNaturalNumber0(X6)
| X6 != sdtmndt0(X5,X4)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,X6) = X5
| X6 != sdtmndt0(X5,X4)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| sdtpldt0(X4,X6) != X5
| X6 = sdtmndt0(X5,X4)
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])])])]) ).
fof(c_0_19,plain,
! [X4,X5,X7] :
( ( aNaturalNumber0(esk1_2(X4,X5))
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,esk1_2(X4,X5)) = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X7)
| sdtpldt0(X4,X7) != X5
| sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])])])]) ).
fof(c_0_20,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtpldt0(X3,X4) = sdtpldt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_21,plain,
( X3 = sdtmndt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X2,X3) != X1
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
( sdtpldt0(X2,esk1_2(X2,X1)) = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[m__1870]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_26,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_27,plain,
( aNaturalNumber0(esk1_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_28,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| sdtpldt0(sdtpldt0(X4,X5),X6) = sdtpldt0(X4,sdtpldt0(X5,X6)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_29,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( X1 = sdtmndt0(X2,X3)
| sdtpldt0(X3,X1) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_31,hypothesis,
sdtpldt0(xp,esk1_2(xp,xn)) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_32,hypothesis,
aNaturalNumber0(esk1_2(xp,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_33,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_35,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_36,hypothesis,
( sdtpldt0(X1,xp) = sdtpldt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_37,hypothesis,
( esk1_2(xp,xn) = sdtmndt0(X1,xp)
| xn != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_25])]),c_0_32])]) ).
cnf(c_0_38,hypothesis,
xr = sdtmndt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__1883]) ).
fof(c_0_39,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_40,hypothesis,
( sdtpldt0(sdtpldt0(X1,X2),xp) = sdtpldt0(X1,sdtpldt0(X2,xp))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
fof(c_0_41,plain,
! [X4,X5,X6] :
( ( sdtpldt0(X4,X5) != sdtpldt0(X4,X6)
| X5 = X6
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtpldt0(X5,X4) != sdtpldt0(X6,X4)
| X5 = X6
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).
cnf(c_0_42,hypothesis,
( sdtpldt0(X1,xm) = sdtpldt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_43,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,hypothesis,
( sdtpldt0(sdtpldt0(X1,X2),xm) = sdtpldt0(X1,sdtpldt0(X2,xm))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_45,hypothesis,
sdtpldt0(xp,xm) = sdtpldt0(xm,xp),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_46,hypothesis,
esk1_2(xp,xn) = xr,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_38]) ).
cnf(c_0_47,hypothesis,
sdtpldt0(esk1_2(xp,xn),xp) = xn,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_32]),c_0_31]) ).
cnf(c_0_48,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,hypothesis,
( sdtpldt0(sdtpldt0(X1,xm),xp) = sdtpldt0(X1,sdtpldt0(xm,xp))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_50,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_51,plain,
! [X2] :
( ( sdtpldt0(X2,sz00) = X2
| ~ aNaturalNumber0(X2) )
& ( X2 = sdtpldt0(sz00,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_52,plain,
! [X3,X4] :
( ( X3 != sz00
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( X3 != sz10
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( ~ aNaturalNumber0(X4)
| ~ doDivides0(X4,X3)
| X4 = sz10
| X4 = X3
| ~ isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( aNaturalNumber0(esk3_1(X3))
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( doDivides0(esk3_1(X3),X3)
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( esk3_1(X3) != sz10
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) )
& ( esk3_1(X3) != X3
| X3 = sz00
| X3 = sz10
| isPrime0(X3)
| ~ aNaturalNumber0(X3) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])])])]) ).
cnf(c_0_53,hypothesis,
sdtpldt0(esk1_2(xp,xn),xm) = sdtpldt0(xm,esk1_2(xp,xn)),
inference(spm,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_54,hypothesis,
( sdtasdt0(X1,xm) = sdtasdt0(xm,X1)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_55,hypothesis,
( sdtpldt0(sdtpldt0(X1,xp),xm) = sdtpldt0(X1,sdtpldt0(xm,xp))
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_25]),c_0_45]) ).
cnf(c_0_56,hypothesis,
aNaturalNumber0(xr),
inference(rw,[status(thm)],[c_0_32,c_0_46]) ).
cnf(c_0_57,hypothesis,
sdtpldt0(xr,xp) = xn,
inference(rw,[status(thm)],[c_0_47,c_0_46]) ).
cnf(c_0_58,hypothesis,
( aNaturalNumber0(sdtpldt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_59,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X2,X3) != sdtpldt0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_60,hypothesis,
( sdtpldt0(sdtpldt0(X1,X2),xn) = sdtpldt0(X1,sdtpldt0(X2,xn))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_61,hypothesis,
sdtpldt0(xp,xn) = sdtpldt0(xn,xp),
inference(spm,[status(thm)],[c_0_36,c_0_26]) ).
cnf(c_0_62,hypothesis,
( sdtpldt0(sdtpldt0(X1,xn),xp) = sdtpldt0(X1,sdtpldt0(xn,xp))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_63,hypothesis,
sdtpldt0(xm,xn) = sdtpldt0(xn,xm),
inference(spm,[status(thm)],[c_0_42,c_0_26]) ).
cnf(c_0_64,hypothesis,
sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,sdtpldt0(xm,xp)),
inference(spm,[status(thm)],[c_0_49,c_0_26]) ).
cnf(c_0_65,hypothesis,
( X1 = X2
| sdtpldt0(xm,X1) != sdtpldt0(xm,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_34]) ).
cnf(c_0_66,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_67,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_68,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
fof(c_0_69,hypothesis,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ isPrime0(X6)
| ~ doDivides0(X6,sdtasdt0(X4,X5))
| ~ iLess0(sdtpldt0(sdtpldt0(X4,X5),X6),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X6,X4)
| doDivides0(X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1799])]) ).
cnf(c_0_70,hypothesis,
sdtpldt0(xr,xm) = sdtpldt0(xm,xr),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_46]),c_0_46]) ).
cnf(c_0_71,hypothesis,
sdtasdt0(esk1_2(xp,xn),xm) = sdtasdt0(xm,esk1_2(xp,xn)),
inference(spm,[status(thm)],[c_0_54,c_0_32]) ).
fof(c_0_72,negated_conjecture,
~ ( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_73,hypothesis,
sdtpldt0(xr,sdtpldt0(xm,xp)) = sdtpldt0(xn,xm),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_74,hypothesis,
aNaturalNumber0(sdtpldt0(xm,xp)),
inference(spm,[status(thm)],[c_0_58,c_0_34]) ).
cnf(c_0_75,hypothesis,
( aNaturalNumber0(sdtpldt0(X1,xm))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_34]) ).
cnf(c_0_76,hypothesis,
( X1 = X2
| sdtpldt0(X1,xn) != sdtpldt0(X2,xn)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_26]) ).
cnf(c_0_77,hypothesis,
( sdtpldt0(sdtpldt0(X1,xp),xn) = sdtpldt0(X1,sdtpldt0(xn,xp))
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_25]),c_0_61]) ).
cnf(c_0_78,hypothesis,
sdtpldt0(xm,sdtpldt0(xn,xp)) = sdtpldt0(xn,sdtpldt0(xm,xp)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_34]),c_0_63]),c_0_64]) ).
cnf(c_0_79,hypothesis,
( X1 = xp
| sdtpldt0(xm,X1) != sdtpldt0(xm,xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_25]) ).
cnf(c_0_80,hypothesis,
sdtpldt0(xm,sz00) = xm,
inference(spm,[status(thm)],[c_0_66,c_0_34]) ).
cnf(c_0_81,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_82,hypothesis,
sz00 != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_25])]) ).
cnf(c_0_83,hypothesis,
( doDivides0(X1,X2)
| doDivides0(X1,X3)
| ~ iLess0(sdtpldt0(sdtpldt0(X3,X2),X1),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ doDivides0(X1,sdtasdt0(X3,X2))
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_84,hypothesis,
sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xr,sdtpldt0(xm,xp)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_56]),c_0_70]) ).
cnf(c_0_85,hypothesis,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(split_conjunct,[status(thm)],[m__1913]) ).
cnf(c_0_86,hypothesis,
sdtasdt0(xr,xm) = sdtasdt0(xm,xr),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_46]),c_0_46]) ).
fof(c_0_87,negated_conjecture,
( ~ doDivides0(xp,xr)
& ~ doDivides0(xp,xm) ),
inference(fof_nnf,[status(thm)],[c_0_72]) ).
cnf(c_0_88,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_22]),c_0_48]) ).
cnf(c_0_89,hypothesis,
( sdtpldt0(xm,xp) = sdtmndt0(X1,xr)
| sdtpldt0(xn,xm) != X1
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_73]),c_0_56])]),c_0_74])]) ).
cnf(c_0_90,hypothesis,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(spm,[status(thm)],[c_0_75,c_0_26]) ).
cnf(c_0_91,hypothesis,
( X1 = xm
| sdtpldt0(X1,xn) != sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_34]),c_0_63]) ).
cnf(c_0_92,hypothesis,
sdtpldt0(sdtpldt0(xm,xp),xn) = sdtpldt0(xn,sdtpldt0(xm,xp)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_34]),c_0_78]) ).
cnf(c_0_93,hypothesis,
sdtpldt0(xm,xp) != xm,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]),c_0_82]) ).
cnf(c_0_94,hypothesis,
( doDivides0(X1,X2)
| doDivides0(X1,X3)
| ~ isPrime0(X1)
| ~ doDivides0(X1,sdtasdt0(X2,X3))
| ~ iLess0(sdtpldt0(sdtpldt0(X2,X3),X1),sdtpldt0(xn,sdtpldt0(xm,xp)))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[c_0_83,c_0_64]) ).
cnf(c_0_95,hypothesis,
sdtpldt0(sdtpldt0(xm,xr),xp) = sdtpldt0(xn,xm),
inference(rw,[status(thm)],[c_0_84,c_0_73]) ).
cnf(c_0_96,hypothesis,
doDivides0(xp,sdtasdt0(xm,xr)),
inference(rw,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_97,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_98,negated_conjecture,
~ doDivides0(xp,xr),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
fof(c_0_99,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| X3 = X4
| ~ sdtlseqdt0(X3,X4)
| iLess0(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).
cnf(c_0_100,hypothesis,
( sdtlseqdt0(X1,sdtpldt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_25]) ).
cnf(c_0_101,hypothesis,
sdtpldt0(xm,xp) = sdtmndt0(sdtpldt0(xn,xm),xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_89]),c_0_90])]) ).
cnf(c_0_102,hypothesis,
aNaturalNumber0(sdtpldt0(xn,xp)),
inference(spm,[status(thm)],[c_0_58,c_0_26]) ).
cnf(c_0_103,hypothesis,
sdtpldt0(sdtpldt0(xn,xp),xm) = sdtpldt0(xn,sdtpldt0(xm,xp)),
inference(spm,[status(thm)],[c_0_55,c_0_26]) ).
cnf(c_0_104,hypothesis,
sdtpldt0(xn,sdtpldt0(xm,xp)) != sdtpldt0(xn,xm),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_74])]),c_0_93]) ).
cnf(c_0_105,hypothesis,
~ iLess0(sdtpldt0(xn,xm),sdtpldt0(xn,sdtpldt0(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_68]),c_0_96]),c_0_34]),c_0_56]),c_0_25])]),c_0_97]),c_0_98]) ).
cnf(c_0_106,plain,
( iLess0(X1,X2)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_107,hypothesis,
sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xn,sdtmndt0(sdtpldt0(xn,xm),xr))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_90]),c_0_64]),c_0_101]) ).
cnf(c_0_108,hypothesis,
aNaturalNumber0(sdtpldt0(xn,sdtmndt0(sdtpldt0(xn,xm),xr))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_102]),c_0_103]),c_0_101]) ).
cnf(c_0_109,hypothesis,
sdtpldt0(xn,sdtmndt0(sdtpldt0(xn,xm),xr)) != sdtpldt0(xn,xm),
inference(rw,[status(thm)],[c_0_104,c_0_101]) ).
cnf(c_0_110,hypothesis,
~ iLess0(sdtpldt0(xn,xm),sdtpldt0(xn,sdtmndt0(sdtpldt0(xn,xm),xr))),
inference(rw,[status(thm)],[c_0_105,c_0_101]) ).
cnf(c_0_111,hypothesis,
$false,
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_106,c_0_107]),c_0_108]),c_0_90])]),c_0_109]),c_0_110]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM493+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n029.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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 01:06:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.33/23.40 eprover: CPU time limit exceeded, terminating
% 0.33/23.40 eprover: CPU time limit exceeded, terminating
% 0.33/23.40 eprover: CPU time limit exceeded, terminating
% 0.33/23.41 eprover: CPU time limit exceeded, terminating
% 0.45/46.41 eprover: CPU time limit exceeded, terminating
% 0.45/46.42 eprover: CPU time limit exceeded, terminating
% 0.45/46.43 eprover: CPU time limit exceeded, terminating
% 0.45/46.43 eprover: CPU time limit exceeded, terminating
% 0.51/58.68 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.51/58.68
% 0.51/58.68 # Failure: Resource limit exceeded (time)
% 0.51/58.68 # OLD status Res
% 0.51/58.68 # Preprocessing time : 0.018 s
% 0.51/58.68 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.51/58.68
% 0.51/58.68 # Failure: Resource limit exceeded (time)
% 0.51/58.68 # OLD status Res
% 0.51/58.68 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.51/58.68 # Preprocessing time : 0.010 s
% 0.51/58.68 # Running protocol protocol_eprover_a172c605141d0894bf6fdc293a5220c6c2a32117 for 23 seconds:
% 0.51/58.68 # Preprocessing time : 0.010 s
% 0.51/58.68
% 0.51/58.68 # Proof found!
% 0.51/58.68 # SZS status Theorem
% 0.51/58.68 # SZS output start CNFRefutation
% See solution above
% 0.51/58.68 # Proof object total steps : 112
% 0.51/58.68 # Proof object clause steps : 81
% 0.51/58.68 # Proof object formula steps : 31
% 0.51/58.68 # Proof object conjectures : 5
% 0.51/58.68 # Proof object clause conjectures : 2
% 0.51/58.68 # Proof object formula conjectures : 3
% 0.51/58.68 # Proof object initial clauses used : 24
% 0.51/58.68 # Proof object initial formulas used : 18
% 0.51/58.68 # Proof object generating inferences : 47
% 0.51/58.68 # Proof object simplifying inferences : 64
% 0.51/58.68 # Training examples: 0 positive, 0 negative
% 0.51/58.68 # Parsed axioms : 46
% 0.51/58.68 # Removed by relevancy pruning/SinE : 0
% 0.51/58.68 # Initial clauses : 83
% 0.51/58.68 # Removed in clause preprocessing : 3
% 0.51/58.68 # Initial clauses in saturation : 80
% 0.51/58.68 # Processed clauses : 35594
% 0.51/58.68 # ...of these trivial : 1697
% 0.51/58.68 # ...subsumed : 10957
% 0.51/58.68 # ...remaining for further processing : 22940
% 0.51/58.68 # Other redundant clauses eliminated : 1
% 0.51/58.68 # Clauses deleted for lack of memory : 439377
% 0.51/58.68 # Backward-subsumed : 223
% 0.51/58.68 # Backward-rewritten : 4941
% 0.51/58.68 # Generated clauses : 666355
% 0.51/58.68 # ...of the previous two non-trivial : 645428
% 0.51/58.68 # Contextual simplify-reflections : 1951
% 0.51/58.68 # Paramodulations : 665009
% 0.51/58.68 # Factorizations : 2
% 0.51/58.68 # Equation resolutions : 1193
% 0.51/58.68 # Current number of processed clauses : 17624
% 0.51/58.68 # Positive orientable unit clauses : 3710
% 0.51/58.68 # Positive unorientable unit clauses: 0
% 0.51/58.68 # Negative unit clauses : 928
% 0.51/58.68 # Non-unit-clauses : 12986
% 0.51/58.68 # Current number of unprocessed clauses: 91759
% 0.51/58.68 # ...number of literals in the above : 274928
% 0.51/58.68 # Current number of archived formulas : 0
% 0.51/58.68 # Current number of archived clauses : 5315
% 0.51/58.68 # Clause-clause subsumption calls (NU) : 12187790
% 0.51/58.68 # Rec. Clause-clause subsumption calls : 9274625
% 0.51/58.68 # Non-unit clause-clause subsumptions : 10450
% 0.51/58.68 # Unit Clause-clause subsumption calls : 1491429
% 0.51/58.68 # Rewrite failures with RHS unbound : 0
% 0.51/58.68 # BW rewrite match attempts : 7698
% 0.51/58.68 # BW rewrite match successes : 499
% 0.51/58.68 # Condensation attempts : 0
% 0.51/58.68 # Condensation successes : 0
% 0.51/58.68 # Termbank termtop insertions : 17480522
% 0.51/58.68
% 0.51/58.68 # -------------------------------------------------
% 0.51/58.68 # User time : 11.966 s
% 0.51/58.68 # System time : 0.109 s
% 0.51/58.68 # Total time : 12.075 s
% 0.51/58.68 # Maximum resident set size: 156800 pages
% 0.51/69.44 eprover: CPU time limit exceeded, terminating
% 0.51/69.44 eprover: CPU time limit exceeded, terminating
% 0.51/69.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.46 eprover: No such file or directory
% 0.51/69.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.46 eprover: No such file or directory
% 0.51/69.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.46 eprover: No such file or directory
% 0.51/69.46 eprover: CPU time limit exceeded, terminating
% 0.51/69.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.46 eprover: No such file or directory
% 0.51/69.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47 eprover: No such file or directory
% 0.51/69.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47 eprover: No such file or directory
% 0.51/69.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47 eprover: No such file or directory
% 0.51/69.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.47 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.48 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.49 eprover: No such file or directory
% 0.51/69.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.50 eprover: No such file or directory
% 0.51/69.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.51/69.50 eprover: No such file or directory
% 0.51/69.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.50 eprover: No such file or directory
% 0.51/69.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.50 eprover: No such file or directory
% 0.51/69.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.51 eprover: No such file or directory
% 0.51/69.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.51/69.51 eprover: No such file or directory
%------------------------------------------------------------------------------