%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM496+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:17:11 AM UTC 2026
% Result : Theorem 3.76s 0.90s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 20 unt; 0 def)
% Number of atoms : 129 ( 26 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 141 ( 63 ~; 59 |; 11 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('theBenchmark.p',mSortsC_01) ).
fof(m_MulUnit,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',m_MulUnit) ).
fof(mDefDiff,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefDiff) ).
fof(mDefDiv,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('theBenchmark.p',mDefDiv) ).
fof(mDivSum,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W2)
& doDivides0(W0,W1) )
=> doDivides0(W0,sdtpldt0(W1,W2)) ) ),
file('theBenchmark.p',mDivSum) ).
fof(m__1837,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__1837) ).
fof(m__,conjecture,
( doDivides0(xp,xm)
| doDivides0(xp,xn) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( doDivides0(xp,xm)
| doDivides0(xp,xn) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_83,negated_conjecture,
~ doDivides0(xp,xm),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_84,negated_conjecture,
~ doDivides0(xp,xn),
inference(clausify,[status(thm)],[m___neg]) ).
fof(m__2027,axiom,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
file('theBenchmark.p',m__2027) ).
cnf(c_85,plain,
( doDivides0(xp,xm)
| doDivides0(xp,xr) ),
inference(clausify,[status(thm)],[m__2027]) ).
cnf(c_86,negated_conjecture,
doDivides0(xp,xr),
inference(resolve,[status(thm)],[c_83,c_85]) ).
fof(m__1883,axiom,
xr = sdtmndt0(xn,xp),
file('theBenchmark.p',m__1883) ).
cnf(c_90,plain,
xr = sdtmndt0(xn,xp),
inference(clausify,[status(thm)],[m__1883]) ).
fof(m__1870,axiom,
sdtlseqdt0(xp,xn),
file('theBenchmark.p',m__1870) ).
cnf(c_91,plain,
sdtlseqdt0(xp,xn),
inference(clausify,[status(thm)],[m__1870]) ).
cnf(c_93,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_95,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_102,plain,
( doDivides0(A,sdtpldt0(B,C))
| ~ doDivides0(A,C)
| ~ doDivides0(A,B)
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDivSum]) ).
cnf(c_107,plain,
( sdtasdt0(A,C) != B
| ~ aNaturalNumber0(C)
| doDivides0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiv]) ).
cnf(c_127,plain,
( sdtpldt0(A,C) = B
| sdtmndt0(B,A) != C
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_128,plain,
( aNaturalNumber0(C)
| sdtmndt0(B,A) != C
| ~ sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefDiff]) ).
cnf(c_146,plain,
( sdtasdt0(A,sz10) = A
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulUnit]) ).
cnf(c_156,plain,
aNaturalNumber0(sz10),
inference(clausify,[status(thm)],[mSortsC_01]) ).
cnf(c_184,negated_conjecture,
doDivides0(xp,sdtmndt0(xn,xp)),
inference(paramod,[status(thm)],[c_90,c_86]) ).
cnf(c_194,plain,
( doDivides0(A,sdtpldt0(A,B))
| ~ doDivides0(A,B)
| ~ doDivides0(A,A)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(factor,[status(thm)],[c_102]) ).
cnf(c_203,plain,
( sdtasdt0(A,B) != A
| ~ aNaturalNumber0(B)
| doDivides0(A,A)
| ~ aNaturalNumber0(A) ),
inference(factor,[status(thm)],[c_107]) ).
cnf(c_1701,plain,
sdtmndt0(xn,xp) = xr,
inference(copy,[status(thm)],[c_90]) ).
cnf(c_1702,plain,
( sdtpldt0(xp,xr) = xn
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_127,c_1701]) ).
cnf(c_1703,plain,
( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(paramod,[status(thm)],[c_90,c_1702]) ).
cnf(c_1704,plain,
( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_93,c_1703]) ).
cnf(c_1705,plain,
( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn
| ~ sdtlseqdt0(xp,xn) ),
inference(resolve,[status(thm)],[c_95,c_1704]) ).
cnf(c_635,plain,
sdtpldt0(xp,sdtmndt0(xn,xp)) = xn,
inference(resolve,[status(thm)],[c_91,c_1705]) ).
cnf(c_1706,plain,
sdtmndt0(xn,xp) = xr,
inference(copy,[status(thm)],[c_90]) ).
cnf(c_1707,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_128,c_1706]) ).
cnf(c_1708,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(paramod,[status(thm)],[c_90,c_1707]) ).
cnf(c_1709,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_93,c_1708]) ).
cnf(c_1710,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
| ~ sdtlseqdt0(xp,xn) ),
inference(resolve,[status(thm)],[c_95,c_1709]) ).
cnf(c_645,plain,
aNaturalNumber0(sdtmndt0(xn,xp)),
inference(resolve,[status(thm)],[c_91,c_1710]) ).
cnf(c_787,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolve,[status(thm)],[c_146,c_93]) ).
cnf(c_1711,plain,
( doDivides0(xp,sdtpldt0(xp,sdtmndt0(xn,xp)))
| ~ doDivides0(xp,xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_194,c_184]) ).
cnf(c_1712,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xp) ),
inference(paramod,[status(thm)],[c_635,c_1711]) ).
cnf(c_1713,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,xp)
| ~ aNaturalNumber0(sdtmndt0(xn,xp)) ),
inference(resolve,[status(thm)],[c_93,c_1712]) ).
cnf(c_1714,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,xp) ),
inference(resolve,[status(thm)],[c_645,c_1713]) ).
cnf(c_1320,negated_conjecture,
~ doDivides0(xp,xp),
inference(resolve,[status(thm)],[c_84,c_1714]) ).
cnf(c_1715,plain,
( sdtasdt0(xp,A) != xp
| ~ aNaturalNumber0(A)
| doDivides0(xp,xp) ),
inference(resolve,[status(thm)],[c_203,c_93]) ).
cnf(c_1716,plain,
( sdtasdt0(xp,A) != xp
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_1715,c_1320]) ).
cnf(c_1717,plain,
sdtasdt0(xp,sz10) != xp,
inference(resolve,[status(thm)],[c_1716,c_156]) ).
cnf(c_1718,plain,
xp != xp,
inference(paramod,[status(thm)],[c_787,c_1717]) ).
cnf(c_1700,plain,
$false,
inference(copy,[status(thm)],[c_1718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM496+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 03:01:54 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 4144717 was started by sandbox on n026,
% 0.09/0.35 % Sat Sep 26 03:01:54 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 3.76/0.90
% 3.76/0.90 % SZS status Theorem for theBenchmark
% 3.76/0.90
% 3.76/0.90 % Proof 1 at 0.38 (+ 0.07) seconds.
% 3.76/0.90 % Length of proof is 29.
% 3.76/0.90 % Level of proof is 5.
% 3.76/0.90 % Maximum clause weight is 21.000.
% 3.76/0.90 % Given clauses 201.
% 3.76/0.90
% 3.76/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------