TSTP Solution File: NUM510+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : NUM510+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n013.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 09:33:14 EDT 2022
% Result : Theorem 0.23s 1.42s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 100 ( 24 unt; 0 def)
% Number of atoms : 417 ( 146 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 528 ( 211 ~; 236 |; 56 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 121 ( 1 sgn 56 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLETotal) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefDiv) ).
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/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefQuot) ).
fof(m__2487,hypothesis,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2487) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2342) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1837) ).
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/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefPrime) ).
fof(m__,conjecture,
( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMonMul) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLEAsym) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMonMul2) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB_02) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m_MulZero) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMulComm) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsC) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2315) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1860) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMulCanc) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m_MulUnit) ).
fof(mDivLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X1,X2)
& X2 != sz00 )
=> sdtlseqdt0(X1,X2) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDivLE) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2306) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsC_01) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2287) ).
fof(c_0_23,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])])]) ).
fof(c_0_24,plain,
! [X4,X5,X7] :
( ( aNaturalNumber0(esk2_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( X5 = sdtasdt0(X4,esk2_2(X4,X5))
| ~ doDivides0(X4,X5)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5) )
& ( ~ aNaturalNumber0(X7)
| X5 != sdtasdt0(X4,X7)
| doDivides0(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)],[mDefDiv])])])])])])]) ).
cnf(c_0_25,plain,
( sdtlseqdt0(X2,X1)
| sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,plain,
( aNaturalNumber0(esk2_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_27,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_28,plain,
( sdtlseqdt0(esk2_2(X1,X2),X3)
| sdtlseqdt0(X3,esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,hypothesis,
doDivides0(xr,xn),
inference(split_conjunct,[status(thm)],[m__2487]) ).
cnf(c_0_30,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
cnf(c_0_31,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_32,plain,
( X2 = sz00
| X3 = sdtsldt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( doDivides0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X1 != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_34,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_35,negated_conjecture,
~ ( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_36,hypothesis,
( sdtlseqdt0(X1,esk2_2(xr,xn))
| sdtlseqdt0(esk2_2(xr,xn),X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_31])]) ).
cnf(c_0_37,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_39,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,hypothesis,
isPrime0(xr),
inference(split_conjunct,[status(thm)],[m__2342]) ).
fof(c_0_41,plain,
! [X4,X5,X6] :
( ( sdtasdt0(X4,X5) != sdtasdt0(X4,X6)
| X4 = sz00
| X5 = X6
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtlseqdt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
| X4 = sz00
| X5 = X6
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtasdt0(X5,X4) != sdtasdt0(X6,X4)
| X4 = sz00
| X5 = X6
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) )
& ( sdtlseqdt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
| X4 = sz00
| X5 = X6
| ~ sdtlseqdt0(X5,X6)
| ~ aNaturalNumber0(X4)
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_42,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_27]) ).
cnf(c_0_43,plain,
( X2 = sz00
| aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X1)
| X3 != sdtsldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_44,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(fof_nnf,[status(thm)],[c_0_35]) ).
cnf(c_0_45,hypothesis,
( sdtlseqdt0(esk2_2(xr,xn),xn)
| sdtlseqdt0(xn,esk2_2(xr,xn)) ),
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_46,plain,
( esk2_2(X1,X2) = sdtsldt0(X2,X1)
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38])]),c_0_26]) ).
cnf(c_0_47,hypothesis,
sz00 != xr,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_30])]) ).
fof(c_0_48,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_49,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| X3 = sz00
| sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
fof(c_0_50,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_51,plain,
( X2 = X1
| X3 = sz00
| sdtlseqdt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_53,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_54,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,hypothesis,
( sdtlseqdt0(xn,sdtsldt0(xn,xr))
| sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
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_45,c_0_46]),c_0_29]),c_0_30]),c_0_31])]),c_0_47]) ).
fof(c_0_56,plain,
! [X2] :
( ( sdtasdt0(X2,sz00) = sz00
| ~ aNaturalNumber0(X2) )
& ( sz00 = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_57,plain,
( X1 = X2
| ~ sdtlseqdt0(X2,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_58,plain,
( sdtlseqdt0(X1,sdtasdt0(X1,X2))
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_60,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_61,plain,
( sdtsldt0(X1,X2) = X3
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X2,X3),X1)
| ~ doDivides0(X2,X1)
| ~ sdtlseqdt0(X3,sdtsldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_65,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_66,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_67,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_68,plain,
! [X4,X5,X6] :
( ( sdtasdt0(X4,X5) != sdtasdt0(X4,X6)
| X5 = X6
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| X4 = sz00
| ~ aNaturalNumber0(X4) )
& ( sdtasdt0(X5,X4) != sdtasdt0(X6,X4)
| X5 = X6
| ~ aNaturalNumber0(X5)
| ~ aNaturalNumber0(X6)
| X4 = sz00
| ~ aNaturalNumber0(X4) ) ),
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)],[mMulCanc])])])])])]) ).
fof(c_0_69,plain,
! [X2] :
( ( sdtasdt0(X2,sz10) = X2
| ~ aNaturalNumber0(X2) )
& ( X2 = sdtasdt0(sz10,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
cnf(c_0_70,plain,
( sdtasdt0(X1,X2) = X1
| X2 = sz00
| ~ sdtlseqdt0(sdtasdt0(X1,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_71,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_72,negated_conjecture,
( sdtsldt0(xn,xr) = xn
| sdtlseqdt0(sdtasdt0(xr,xn),xn) ),
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_61,c_0_62]),c_0_29]),c_0_30]),c_0_31])]),c_0_47]) ).
fof(c_0_73,plain,
! [X3,X4] :
( ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X4)
| ~ doDivides0(X3,X4)
| X4 = sz00
| sdtlseqdt0(X3,X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).
cnf(c_0_74,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_75,plain,
( sdtsldt0(X1,X2) = sz00
| X2 = sz00
| X1 != sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_63]),c_0_64])]) ).
cnf(c_0_76,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_77,hypothesis,
sz00 != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_66]),c_0_67])]) ).
cnf(c_0_78,plain,
( X1 = sz00
| X3 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| sdtasdt0(X3,X1) != sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_79,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_80,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_81,plain,
( sdtasdt0(X1,X2) = X2
| X1 = sz00
| ~ sdtlseqdt0(sdtasdt0(X1,X2),X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_82,negated_conjecture,
( sdtasdt0(xr,xn) = xn
| sdtlseqdt0(sdtasdt0(xr,xn),xn) ),
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_52,c_0_72]),c_0_29]),c_0_30]),c_0_31])]),c_0_47]) ).
cnf(c_0_83,plain,
( ~ aNaturalNumber0(X1)
| ~ isPrime0(X1)
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_84,plain,
( sdtlseqdt0(X1,X2)
| X2 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_85,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_86,hypothesis,
( sdtasdt0(xn,xm) != sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_67])]),c_0_76]),c_0_77]) ).
cnf(c_0_87,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_88,plain,
( X1 = sz10
| X2 = sz00
| sdtasdt0(X1,X2) != X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
cnf(c_0_89,negated_conjecture,
sdtasdt0(xr,xn) = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_31]),c_0_30])]),c_0_47]) ).
cnf(c_0_90,hypothesis,
xr != sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_40]),c_0_30])]) ).
cnf(c_0_91,hypothesis,
( sdtasdt0(xn,xm) = sz00
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_67])]) ).
cnf(c_0_92,hypothesis,
sdtasdt0(xn,xm) != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_59]),c_0_87]),c_0_31])]) ).
cnf(c_0_93,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_94,negated_conjecture,
sz00 = xn,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_30]),c_0_31])]),c_0_90]) ).
cnf(c_0_95,hypothesis,
( sdtasdt0(xn,xm) = xp
| ~ sdtlseqdt0(sdtasdt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_91]),c_0_67])]),c_0_92]) ).
cnf(c_0_96,plain,
( sdtasdt0(xn,X1) = xn
| ~ aNaturalNumber0(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_94]) ).
cnf(c_0_97,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_98,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_99,hypothesis,
$false,
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_95,c_0_96]),c_0_97]),c_0_31]),c_0_87])]),c_0_98]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM510+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 5 21:30:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.23/1.42 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.23/1.42 # Preprocessing time : 0.019 s
% 0.23/1.42
% 0.23/1.42 # Proof found!
% 0.23/1.42 # SZS status Theorem
% 0.23/1.42 # SZS output start CNFRefutation
% See solution above
% 0.23/1.42 # Proof object total steps : 100
% 0.23/1.42 # Proof object clause steps : 61
% 0.23/1.42 # Proof object formula steps : 39
% 0.23/1.42 # Proof object conjectures : 9
% 0.23/1.42 # Proof object clause conjectures : 6
% 0.23/1.42 # Proof object formula conjectures : 3
% 0.23/1.42 # Proof object initial clauses used : 34
% 0.23/1.42 # Proof object initial formulas used : 23
% 0.23/1.42 # Proof object generating inferences : 25
% 0.23/1.42 # Proof object simplifying inferences : 60
% 0.23/1.42 # Training examples: 0 positive, 0 negative
% 0.23/1.42 # Parsed axioms : 53
% 0.23/1.42 # Removed by relevancy pruning/SinE : 0
% 0.23/1.42 # Initial clauses : 97
% 0.23/1.42 # Removed in clause preprocessing : 3
% 0.23/1.42 # Initial clauses in saturation : 94
% 0.23/1.42 # Processed clauses : 3352
% 0.23/1.42 # ...of these trivial : 82
% 0.23/1.42 # ...subsumed : 1822
% 0.23/1.42 # ...remaining for further processing : 1448
% 0.23/1.42 # Other redundant clauses eliminated : 238
% 0.23/1.42 # Clauses deleted for lack of memory : 0
% 0.23/1.42 # Backward-subsumed : 164
% 0.23/1.42 # Backward-rewritten : 666
% 0.23/1.42 # Generated clauses : 51064
% 0.23/1.42 # ...of the previous two non-trivial : 48954
% 0.23/1.42 # Contextual simplify-reflections : 2002
% 0.23/1.42 # Paramodulations : 50707
% 0.23/1.42 # Factorizations : 2
% 0.23/1.42 # Equation resolutions : 331
% 0.23/1.42 # Current number of processed clauses : 597
% 0.23/1.42 # Positive orientable unit clauses : 62
% 0.23/1.42 # Positive unorientable unit clauses: 0
% 0.23/1.42 # Negative unit clauses : 28
% 0.23/1.42 # Non-unit-clauses : 507
% 0.23/1.42 # Current number of unprocessed clauses: 22088
% 0.23/1.42 # ...number of literals in the above : 174370
% 0.23/1.42 # Current number of archived formulas : 0
% 0.23/1.42 # Current number of archived clauses : 848
% 0.23/1.42 # Clause-clause subsumption calls (NU) : 355625
% 0.23/1.42 # Rec. Clause-clause subsumption calls : 77502
% 0.23/1.42 # Non-unit clause-clause subsumptions : 3629
% 0.23/1.42 # Unit Clause-clause subsumption calls : 8139
% 0.23/1.42 # Rewrite failures with RHS unbound : 0
% 0.23/1.42 # BW rewrite match attempts : 29
% 0.23/1.42 # BW rewrite match successes : 27
% 0.23/1.42 # Condensation attempts : 0
% 0.23/1.42 # Condensation successes : 0
% 0.23/1.42 # Termbank termtop insertions : 1183399
% 0.23/1.42
% 0.23/1.42 # -------------------------------------------------
% 0.23/1.42 # User time : 0.913 s
% 0.23/1.42 # System time : 0.026 s
% 0.23/1.42 # Total time : 0.939 s
% 0.23/1.42 # Maximum resident set size: 40300 pages
% 0.23/23.41 eprover: CPU time limit exceeded, terminating
% 0.23/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.42 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.48 eprover: No such file or directory
% 0.23/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.48 eprover: No such file or directory
%------------------------------------------------------------------------------