%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM529+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:17:17 AM UTC 2026
% Result : Theorem 3.00s 0.81s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 26 unt; 0 def)
% Number of atoms : 192 ( 84 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 218 ( 88 ~; 103 |; 18 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m_MulZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',m_MulZero) ).
fof(mIH_03,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W0,W1)
& W0 != W1 )
=> iLess0(W0,W1) ) ),
file('theBenchmark.p',mIH_03) ).
fof(mDefQuot,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( doDivides0(W0,W1)
& W0 != sz00 )
=> ! [W2] :
( W2 = sdtsldt0(W1,W0)
<=> ( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ) ),
file('theBenchmark.p',mDefQuot) ).
fof(m__2987,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__2987) ).
fof(m__2963,axiom,
! [W0,W1,W2] :
( ( W2 != sz00
& W1 != sz00
& W0 != sz00
& aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(W2,sdtasdt0(W1,W1)) = sdtasdt0(W0,W0)
=> ( iLess0(W0,xn)
=> ~ isPrime0(W2) ) ) ),
file('theBenchmark.p',m__2963) ).
fof(m__3046,axiom,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('theBenchmark.p',m__3046) ).
fof(m__3124,axiom,
( sdtlseqdt0(xm,xn)
& xm != xn ),
file('theBenchmark.p',m__3124) ).
cnf(c_53,plain,
( ~ isPrime0(C)
| ~ iLess0(A,xn)
| sdtasdt0(C,sdtasdt0(B,B)) != sdtasdt0(A,A)
| C = sz00
| B = sz00
| sz00 = A
| ~ aNaturalNumber0(C)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m__2963]) ).
fof(m__3025,axiom,
isPrime0(xp),
file('theBenchmark.p',m__3025) ).
cnf(c_54,plain,
isPrime0(xp),
inference(clausify,[status(thm)],[m__3025]) ).
cnf(c_62,plain,
( ~ iLess0(A,xn)
| sdtasdt0(xp,sdtasdt0(B,B)) != sdtasdt0(A,A)
| xp = sz00
| B = sz00
| sz00 = A
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_54,c_53]) ).
cnf(c_63,plain,
( ~ iLess0(A,xn)
| sdtasdt0(xp,sdtasdt0(B,B)) != sdtasdt0(A,A)
| xp = sz00
| sz00 = B
| sz00 = A
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_97,plain,
sdtlseqdt0(xm,xn),
inference(clausify,[status(thm)],[m__3124]) ).
cnf(c_98,plain,
xm != xn,
inference(clausify,[status(thm)],[m__3124]) ).
fof(m__3082,axiom,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('theBenchmark.p',m__3082) ).
cnf(c_99,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(clausify,[status(thm)],[m__3082]) ).
cnf(c_100,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xm,xm),
inference(copy,[status(thm)],[c_99]) ).
fof(m__3059,axiom,
xq = sdtsldt0(xn,xp),
file('theBenchmark.p',m__3059) ).
cnf(c_101,plain,
xq = sdtsldt0(xn,xp),
inference(clausify,[status(thm)],[m__3059]) ).
cnf(c_102,plain,
sdtsldt0(xn,xp) = xq,
inference(copy,[status(thm)],[c_101]) ).
cnf(c_103,plain,
doDivides0(xp,xn),
inference(clausify,[status(thm)],[m__3046]) ).
cnf(c_106,plain,
xp != sz00,
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_107,plain,
xm != sz00,
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_108,plain,
xn != sz00,
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_109,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_110,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_111,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_121,plain,
( sdtasdt0(A,C) = B
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_122,plain,
( aNaturalNumber0(C)
| sdtsldt0(B,A) != C
| ~ doDivides0(A,B)
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mDefQuot]) ).
cnf(c_126,plain,
( iLess0(A,B)
| ~ sdtlseqdt0(A,B)
| B = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mIH_03]) ).
cnf(c_162,plain,
( sdtasdt0(A,sz00) = sz00
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulZero]) ).
cnf(c_1496,plain,
( ~ iLess0(A,xn)
| sdtasdt0(xp,sdtasdt0(B,B)) != sdtasdt0(A,A)
| xp = sz00
| sz00 = B
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_109,c_63]) ).
cnf(c_219,plain,
( ~ iLess0(A,xn)
| sdtasdt0(xp,sdtasdt0(B,B)) != sdtasdt0(A,A)
| sz00 = B
| sz00 = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_106,c_1496]) ).
cnf(c_1497,plain,
( sdtasdt0(xp,xq) = xn
| ~ doDivides0(xp,xn)
| sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_121,c_102]) ).
cnf(c_1498,plain,
( sdtasdt0(xp,xq) = xn
| ~ doDivides0(xp,xn)
| xp = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_1497]) ).
cnf(c_1499,plain,
( sdtasdt0(xp,xq) = xn
| ~ doDivides0(xp,xn)
| xp = sz00
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_109,c_1498]) ).
cnf(c_1500,plain,
( sdtasdt0(xp,xq) = xn
| ~ doDivides0(xp,xn)
| xp = sz00 ),
inference(resolve,[status(thm)],[c_111,c_1499]) ).
cnf(c_1501,plain,
( sdtasdt0(xp,xq) = xn
| ~ doDivides0(xp,xn) ),
inference(resolve,[status(thm)],[c_106,c_1500]) ).
cnf(c_618,plain,
sdtasdt0(xp,xq) = xn,
inference(resolve,[status(thm)],[c_103,c_1501]) ).
cnf(c_1502,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xp,xn)
| sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolve,[status(thm)],[c_122,c_102]) ).
cnf(c_1503,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xp,xn)
| xp = sz00
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(copy,[status(thm)],[c_1502]) ).
cnf(c_1504,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xp,xn)
| xp = sz00
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_109,c_1503]) ).
cnf(c_1505,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xp,xn)
| xp = sz00 ),
inference(resolve,[status(thm)],[c_111,c_1504]) ).
cnf(c_1506,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xp,xn) ),
inference(resolve,[status(thm)],[c_106,c_1505]) ).
cnf(c_629,plain,
aNaturalNumber0(xq),
inference(resolve,[status(thm)],[c_103,c_1506]) ).
cnf(c_1507,plain,
( iLess0(xm,xn)
| xn = xm
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolve,[status(thm)],[c_126,c_97]) ).
cnf(c_1508,plain,
( iLess0(xm,xn)
| xm = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(copy,[status(thm)],[c_1507]) ).
cnf(c_1509,plain,
( iLess0(xm,xn)
| xm = xn
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_110,c_1508]) ).
cnf(c_1510,plain,
( iLess0(xm,xn)
| xm = xn ),
inference(resolve,[status(thm)],[c_111,c_1509]) ).
cnf(c_693,plain,
iLess0(xm,xn),
inference(resolve,[status(thm)],[c_98,c_1510]) ).
cnf(c_997,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolve,[status(thm)],[c_162,c_109]) ).
cnf(c_1511,plain,
( ~ iLess0(xm,xn)
| sz00 = xq
| sz00 = xm
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xm) ),
inference(resolve,[status(thm)],[c_219,c_100]) ).
cnf(c_1512,plain,
( ~ iLess0(xm,xn)
| sz00 = xq
| xm = sz00
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xm) ),
inference(copy,[status(thm)],[c_1511]) ).
cnf(c_1513,plain,
( ~ iLess0(xm,xn)
| xq = sz00
| xm = sz00
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xm) ),
inference(copy,[status(thm)],[c_1512]) ).
cnf(c_1514,plain,
( ~ iLess0(xm,xn)
| xq = sz00
| xm = sz00
| ~ aNaturalNumber0(xq) ),
inference(resolve,[status(thm)],[c_110,c_1513]) ).
cnf(c_1515,plain,
( ~ iLess0(xm,xn)
| xq = sz00
| xm = sz00 ),
inference(resolve,[status(thm)],[c_629,c_1514]) ).
cnf(c_1516,plain,
( ~ iLess0(xm,xn)
| xq = sz00 ),
inference(resolve,[status(thm)],[c_107,c_1515]) ).
cnf(c_1489,plain,
xq = sz00,
inference(resolve,[status(thm)],[c_693,c_1516]) ).
cnf(c_1517,plain,
sdtasdt0(xp,sz00) = xn,
inference(paramod,[status(thm)],[c_1489,c_618]) ).
cnf(c_1518,plain,
sz00 = xn,
inference(paramod,[status(thm)],[c_997,c_1517]) ).
cnf(c_1519,plain,
xn = sz00,
inference(copy,[status(thm)],[c_1518]) ).
cnf(c_1495,plain,
$false,
inference(resolve,[status(thm)],[c_108,c_1519]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM529+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 03:05:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2657290 was started by sandbox2 on n007,
% 0.11/0.37 % Sat Sep 26 03:05:54 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 3.00/0.81
% 3.00/0.81 % SZS status Theorem for theBenchmark
% 3.00/0.81
% 3.00/0.81 % Proof 1 at 0.30 (+ 0.05) seconds.
% 3.00/0.81 % Length of proof is 35.
% 3.00/0.81 % Level of proof is 6.
% 3.00/0.81 % Maximum clause weight is 35.000.
% 3.00/0.81 % Given clauses 129.
% 3.00/0.81
% 3.00/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------