TSTP Solution File: NUM506+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM506+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n012.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 09:33:11 EDT 2022
% Result : Theorem 1.16s 158.33s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 85 ( 23 unt; 0 def)
% Number of atoms : 352 ( 85 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 447 ( 180 ~; 194 |; 49 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 106 ( 2 sgn 59 !; 0 ?)
% 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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefQuot) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1860) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1837) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2306) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB_02) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMulComm) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLETran) ).
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.mepo_128.in',mIH_03) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMonAdd) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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.mepo_128.in',mAddCanc) ).
fof(m__2377,hypothesis,
( xk != xp
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2377) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLEAsym) ).
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.mepo_128.in',m__1799) ).
fof(m__2362,hypothesis,
( sdtlseqdt0(xr,xk)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2362) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2342) ).
fof(m__,conjecture,
( doDivides0(xr,xn)
| doDivides0(xr,xm) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLETotal) ).
fof(c_0_19,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])])])])])])]) ).
fof(c_0_20,plain,
! [X4,X5,X6,X6] :
( ( aNaturalNumber0(X6)
| X6 != sdtsldt0(X5,X4)
| X4 = sz00
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( X5 = sdtasdt0(X4,X6)
| X6 != sdtsldt0(X5,X4)
| X4 = sz00
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X6)
| X5 != sdtasdt0(X4,X6)
| X6 = sdtsldt0(X5,X4)
| X4 = sz00
| ~ doDivides0(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)],[mDefQuot])])])])])]) ).
cnf(c_0_21,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_23,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_24,plain,
( X2 = sz00
| X1 = sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_26,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_27,hypothesis,
sz00 != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_28,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtasdt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_29,plain,
( X2 = sz00
| aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_30,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_31,hypothesis,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| 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_24,c_0_25]),c_0_26]),c_0_23])]),c_0_27]) ).
cnf(c_0_32,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_34,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_35,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_29,c_0_25]),c_0_26]),c_0_23])]),c_0_27]) ).
cnf(c_0_36,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,hypothesis,
( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
| X1 != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_38,hypothesis,
( aNaturalNumber0(X1)
| X1 != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_32]),c_0_33]),c_0_34])]) ).
cnf(c_0_39,hypothesis,
( sdtasdt0(xn,xm) = sdtasdt0(X1,xp)
| X1 != xk ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_23])]),c_0_38]) ).
fof(c_0_40,plain,
! [X4,X5,X6] :
( ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| ~ sdtlseqdt0(X4,X5)
| ~ sdtlseqdt0(X5,X6)
| sdtlseqdt0(X4,X6) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_41,hypothesis,
( aNaturalNumber0(sdtasdt0(X1,xp))
| X1 != xk ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_33]),c_0_34])]) ).
fof(c_0_42,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])]) ).
fof(c_0_43,plain,
! [X4,X5,X6] :
( ( sdtpldt0(X6,X4) != sdtpldt0(X6,X5)
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtpldt0(X4,X6) != sdtpldt0(X5,X6)
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ sdtlseqdt0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
| ~ aNaturalNumber0(X6)
| X4 = X5
| ~ 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)],[mMonAdd])])])])])]) ).
fof(c_0_44,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| aNaturalNumber0(sdtpldt0(X3,X4)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
fof(c_0_45,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_46,plain,
( sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X3,X2)
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,hypothesis,
sdtlseqdt0(xk,xp),
inference(split_conjunct,[status(thm)],[m__2377]) ).
cnf(c_0_48,hypothesis,
( aNaturalNumber0(sdtasdt0(xn,xm))
| X1 != xk ),
inference(spm,[status(thm)],[c_0_41,c_0_39]) ).
fof(c_0_49,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ sdtlseqdt0(X3,X4)
| ~ sdtlseqdt0(X4,X3)
| X3 = X4 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
fof(c_0_50,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_51,plain,
( iLess0(X1,X2)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,plain,
( X2 = X1
| sdtlseqdt0(sdtpldt0(X3,X2),sdtpldt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_53,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,plain,
( X2 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,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_46,c_0_47]),c_0_23])]) ).
cnf(c_0_56,hypothesis,
sdtlseqdt0(xr,xk),
inference(split_conjunct,[status(thm)],[m__2362]) ).
cnf(c_0_57,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_58,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_59,hypothesis,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(er,[status(thm)],[c_0_48]) ).
fof(c_0_60,negated_conjecture,
~ ( doDivides0(xr,xn)
| doDivides0(xr,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_61,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_62,hypothesis,
xk != xp,
inference(split_conjunct,[status(thm)],[m__2377]) ).
cnf(c_0_63,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_50]) ).
cnf(c_0_64,plain,
( X1 = X2
| iLess0(sdtpldt0(X3,X2),sdtpldt0(X3,X1))
| ~ sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_53]),c_0_54]) ).
cnf(c_0_65,hypothesis,
( sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_66,hypothesis,
aNaturalNumber0(xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_25]),c_0_26]),c_0_23])]),c_0_27]),c_0_59])]) ).
fof(c_0_67,negated_conjecture,
( ~ doDivides0(xr,xn)
& ~ doDivides0(xr,xm) ),
inference(fof_nnf,[status(thm)],[c_0_60]) ).
fof(c_0_68,plain,
! [X3,X4] :
( ( X4 != X3
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) )
& ( sdtlseqdt0(X4,X3)
| sdtlseqdt0(X3,X4)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_69,hypothesis,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_47]),c_0_23])]),c_0_62]) ).
cnf(c_0_70,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_46,c_0_56]),c_0_57])]) ).
cnf(c_0_71,hypothesis,
( xp = X1
| doDivides0(X1,xn)
| doDivides0(X1,xm)
| ~ isPrime0(X1)
| ~ doDivides0(X1,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_34]),c_0_33]),c_0_23])]) ).
cnf(c_0_72,hypothesis,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__2362]) ).
cnf(c_0_73,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_74,hypothesis,
sdtlseqdt0(xr,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_75,negated_conjecture,
~ doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_76,negated_conjecture,
~ doDivides0(xr,xm),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_78,hypothesis,
( ~ sdtlseqdt0(xp,xr)
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_23])]) ).
cnf(c_0_79,hypothesis,
( xr = xp
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
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(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74]),c_0_57])]),c_0_75]),c_0_76]) ).
cnf(c_0_80,hypothesis,
( sdtlseqdt0(xp,X1)
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_23]) ).
cnf(c_0_81,hypothesis,
~ sdtlseqdt0(xp,xr),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_66])]) ).
cnf(c_0_82,hypothesis,
xr = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_53]),c_0_33]),c_0_34])]) ).
cnf(c_0_83,hypothesis,
sdtlseqdt0(xp,xp),
inference(spm,[status(thm)],[c_0_80,c_0_23]) ).
cnf(c_0_84,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_83])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM506+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 07:41:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.36/23.41 eprover: CPU time limit exceeded, terminating
% 0.36/23.41 eprover: eprover: CPU time limit exceeded, terminatingCPU time limit exceeded, terminating
% 0.36/23.41
% 0.36/23.42 eprover: CPU time limit exceeded, terminating
% 0.49/46.42 eprover: CPU time limit exceeded, terminating
% 0.49/46.43 eprover: CPU time limit exceeded, terminating
% 0.49/46.43 eprover: CPU time limit exceeded, terminating
% 0.49/46.44 eprover: CPU time limit exceeded, terminating
% 0.63/69.44 eprover: CPU time limit exceeded, terminating
% 0.63/69.45 eprover: CPU time limit exceeded, terminating
% 0.63/69.45 eprover: CPU time limit exceeded, terminating
% 0.63/69.46 eprover: CPU time limit exceeded, terminating
% 0.78/92.45 eprover: CPU time limit exceeded, terminating
% 0.78/92.47 eprover: CPU time limit exceeded, terminating
% 0.78/92.48 eprover: CPU time limit exceeded, terminating
% 0.78/92.49 eprover: CPU time limit exceeded, terminating
% 0.92/115.48 eprover: CPU time limit exceeded, terminating
% 0.92/115.49 eprover: CPU time limit exceeded, terminating
% 0.92/115.49 eprover: CPU time limit exceeded, terminating
% 0.92/115.50 eprover: CPU time limit exceeded, terminating
% 1.04/138.50 eprover: CPU time limit exceeded, terminating
% 1.04/138.51 eprover: CPU time limit exceeded, terminating
% 1.04/138.52 eprover: CPU time limit exceeded, terminating
% 1.04/138.53 eprover: CPU time limit exceeded, terminating
% 1.16/158.33 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 1.16/158.33
% 1.16/158.33 # Failure: Resource limit exceeded (time)
% 1.16/158.33 # OLD status Res
% 1.16/158.33 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 1.16/158.33 # Preprocessing time : 0.019 s
% 1.16/158.33 # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 1.16/158.33
% 1.16/158.33 # Failure: Resource limit exceeded (time)
% 1.16/158.33 # OLD status Res
% 1.16/158.33 # Preprocessing time : 0.009 s
% 1.16/158.33 # Running protocol protocol_eprover_eb48853eb71ccd2a6fdade56c25b63f5692e1a0c for 23 seconds:
% 1.16/158.33
% 1.16/158.33 # Failure: Resource limit exceeded (time)
% 1.16/158.33 # OLD status Res
% 1.16/158.33 # Preprocessing time : 0.010 s
% 1.16/158.33 # Running protocol protocol_eprover_761a0d093d9701c0eed884aebb46468e8d439c31 for 23 seconds:
% 1.16/158.33
% 1.16/158.33 # Failure: Resource limit exceeded (time)
% 1.16/158.33 # OLD status Res
% 1.16/158.33 # SinE strategy is GSinE(CountFormulas,hypos,1.2,,,100,1.0)
% 1.16/158.33 # Preprocessing time : 0.018 s
% 1.16/158.33 # Running protocol protocol_eprover_bb5e3cecdbc7660bd3a6f864cadb7769d8aea26a for 23 seconds:
% 1.16/158.33
% 1.16/158.33 # Failure: Resource limit exceeded (time)
% 1.16/158.33 # OLD status Res
% 1.16/158.33 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,,500,1.0)
% 1.16/158.33 # Preprocessing time : 0.010 s
% 1.16/158.33 # Running protocol protocol_eprover_e252f7803940d118fa0ef69fc2319cb55aee23b9 for 23 seconds:
% 1.16/158.33
% 1.16/158.33 # Failure: Resource limit exceeded (time)
% 1.16/158.33 # OLD status Res
% 1.16/158.33 # SinE strategy is GSinE(CountFormulas,,1.4,,03,100,1.0)
% 1.16/158.33 # Preprocessing time : 0.019 s
% 1.16/158.33 # Running protocol protocol_eprover_b1d72019af42f5b571a6c0b233a5b6d1de064075 for 23 seconds:
% 1.16/158.33 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,500,1.0)
% 1.16/158.33 # Preprocessing time : 0.010 s
% 1.16/158.33
% 1.16/158.33 # Proof found!
% 1.16/158.33 # SZS status Theorem
% 1.16/158.33 # SZS output start CNFRefutation
% See solution above
% 1.16/158.33 # Proof object total steps : 85
% 1.16/158.33 # Proof object clause steps : 52
% 1.16/158.33 # Proof object formula steps : 33
% 1.16/158.33 # Proof object conjectures : 5
% 1.16/158.33 # Proof object clause conjectures : 2
% 1.16/158.33 # Proof object formula conjectures : 3
% 1.16/158.33 # Proof object initial clauses used : 27
% 1.16/158.33 # Proof object initial formulas used : 19
% 1.16/158.33 # Proof object generating inferences : 22
% 1.16/158.33 # Proof object simplifying inferences : 62
% 1.16/158.33 # Training examples: 0 positive, 0 negative
% 1.16/158.33 # Parsed axioms : 51
% 1.16/158.33 # Removed by relevancy pruning/SinE : 1
% 1.16/158.33 # Initial clauses : 93
% 1.16/158.33 # Removed in clause preprocessing : 3
% 1.16/158.33 # Initial clauses in saturation : 90
% 1.16/158.33 # Processed clauses : 38144
% 1.16/158.33 # ...of these trivial : 165
% 1.16/158.33 # ...subsumed : 33748
% 1.16/158.33 # ...remaining for further processing : 4231
% 1.16/158.33 # Other redundant clauses eliminated : 2782
% 1.16/158.33 # Clauses deleted for lack of memory : 850544
% 1.16/158.33 # Backward-subsumed : 359
% 1.16/158.33 # Backward-rewritten : 675
% 1.16/158.33 # Generated clauses : 1036813
% 1.16/158.33 # ...of the previous two non-trivial : 1007756
% 1.16/158.33 # Contextual simplify-reflections : 16094
% 1.16/158.33 # Paramodulations : 1033587
% 1.16/158.33 # Factorizations : 3
% 1.16/158.33 # Equation resolutions : 3105
% 1.16/158.33 # Current number of processed clauses : 3129
% 1.16/158.33 # Positive orientable unit clauses : 123
% 1.16/158.33 # Positive unorientable unit clauses: 0
% 1.16/158.33 # Negative unit clauses : 246
% 1.16/158.33 # Non-unit-clauses : 2760
% 1.16/158.33 # Current number of unprocessed clauses: 100655
% 1.16/158.33 # ...number of literals in the above : 625723
% 1.16/158.33 # Current number of archived formulas : 0
% 1.16/158.33 # Current number of archived clauses : 1071
% 1.16/158.33 # Clause-clause subsumption calls (NU) : 6096793
% 1.16/158.33 # Rec. Clause-clause subsumption calls : 1936886
% 1.16/158.33 # Non-unit clause-clause subsumptions : 27409
% 1.16/158.33 # Unit Clause-clause subsumption calls : 200563
% 1.16/158.33 # Rewrite failures with RHS unbound : 0
% 1.16/158.33 # BW rewrite match attempts : 69
% 1.16/158.33 # BW rewrite match successes : 69
% 1.16/158.33 # Condensation attempts : 0
% 1.16/158.33 # Condensation successes : 0
% 1.16/158.33 # Termbank termtop insertions : 23639942
% 1.16/158.33
% 1.16/158.33 # -------------------------------------------------
% 1.16/158.33 # User time : 18.980 s
% 1.16/158.33 # System time : 0.122 s
% 1.16/158.33 # Total time : 19.102 s
% 1.16/158.33 # Maximum resident set size: 139404 pages
% 1.16/161.51 eprover: CPU time limit exceeded, terminating
% 1.16/161.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.53 eprover: No such file or directory
% 1.16/161.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.53 eprover: No such file or directory
% 1.16/161.53 eprover: CPU time limit exceeded, terminating
% 1.16/161.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.53 eprover: No such file or directory
% 1.16/161.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.54 eprover: No such file or directory
% 1.16/161.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.54 eprover: No such file or directory
% 1.16/161.54 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.54 eprover: No such file or directory
% 1.16/161.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.55 eprover: No such file or directory
% 1.16/161.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.55 eprover: No such file or directory
% 1.16/161.55 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.55 eprover: No such file or directory
% 1.16/161.56 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.56 eprover: No such file or directory
% 1.16/161.56 eprover: CPU time limit exceeded, terminating
% 1.16/161.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.57 eprover: No such file or directory
% 1.16/161.57 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.57 eprover: No such file or directory
% 1.16/161.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.58 eprover: No such file or directory
% 1.16/161.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.58 eprover: No such file or directory
% 1.16/161.58 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.58 eprover: No such file or directory
%------------------------------------------------------------------------------