%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM529+3 : 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 : n014.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 2.98s 0.84s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 21 unt; 0 def)
% Number of atoms : 148 ( 71 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 164 ( 61 ~; 69 |; 26 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 8 !; 3 ?)
% 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(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)
| ( ! [W3] :
( ( doDivides0(W3,W2)
& ? [W4] :
( W2 = sdtasdt0(W3,W4)
& aNaturalNumber0(W4) )
& aNaturalNumber0(W3) )
=> ( W3 = W2
| W3 = sz10 ) )
& W2 != sz10 ) ) ) ) ),
file('theBenchmark.p',m__2963) ).
fof(m__3025,axiom,
( isPrime0(xp)
& ! [W0] :
( ( ( doDivides0(W0,xp)
| ? [W1] :
( xp = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xp
| W0 = sz10 ) )
& xp != sz10 ),
file('theBenchmark.p',m__3025) ).
fof(m__3059,axiom,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('theBenchmark.p',m__3059) ).
fof(m__3124,axiom,
( sdtlseqdt0(xm,xn)
& ? [W0] :
( sdtpldt0(xm,W0) = xn
& aNaturalNumber0(W0) )
& xm != xn ),
file('theBenchmark.p',m__3124) ).
cnf(c_55,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]) ).
cnf(c_56,plain,
isPrime0(xp),
inference(clausify,[status(thm)],[m__3025]) ).
cnf(c_64,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_56,c_55]) ).
cnf(c_65,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_64]) ).
cnf(c_99,plain,
sdtlseqdt0(xm,xn),
inference(clausify,[status(thm)],[m__3124]) ).
cnf(c_102,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_103,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(clausify,[status(thm)],[m__3082]) ).
cnf(c_104,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xm,xm),
inference(copy,[status(thm)],[c_103]) ).
cnf(c_106,plain,
sdtasdt0(xp,xq) = xn,
inference(clausify,[status(thm)],[m__3059]) ).
cnf(c_107,plain,
aNaturalNumber0(xq),
inference(clausify,[status(thm)],[m__3059]) ).
cnf(c_130,plain,
xp != sz00,
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_131,plain,
xm != sz00,
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_132,plain,
xn != sz00,
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_133,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_134,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_135,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__2987]) ).
cnf(c_150,plain,
( iLess0(A,B)
| ~ sdtlseqdt0(A,B)
| B = A
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mIH_03]) ).
cnf(c_186,plain,
( sdtasdt0(A,sz00) = sz00
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m_MulZero]) ).
cnf(c_3023,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_133,c_65]) ).
cnf(c_262,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_130,c_3023]) ).
cnf(c_3024,plain,
( iLess0(xm,xn)
| xn = xm
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolve,[status(thm)],[c_150,c_99]) ).
cnf(c_3025,plain,
( iLess0(xm,xn)
| xm = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(copy,[status(thm)],[c_3024]) ).
cnf(c_3026,plain,
( iLess0(xm,xn)
| xm = xn
| ~ aNaturalNumber0(xn) ),
inference(resolve,[status(thm)],[c_134,c_3025]) ).
cnf(c_3027,plain,
( iLess0(xm,xn)
| xm = xn ),
inference(resolve,[status(thm)],[c_135,c_3026]) ).
cnf(c_1667,plain,
iLess0(xm,xn),
inference(resolve,[status(thm)],[c_102,c_3027]) ).
cnf(c_2226,plain,
sdtasdt0(xp,sz00) = sz00,
inference(resolve,[status(thm)],[c_186,c_133]) ).
cnf(c_3028,plain,
( ~ iLess0(xm,xn)
| sz00 = xq
| sz00 = xm
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xm) ),
inference(resolve,[status(thm)],[c_262,c_104]) ).
cnf(c_3029,plain,
( ~ iLess0(xm,xn)
| sz00 = xq
| xm = sz00
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xm) ),
inference(copy,[status(thm)],[c_3028]) ).
cnf(c_3030,plain,
( ~ iLess0(xm,xn)
| xq = sz00
| xm = sz00
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xm) ),
inference(copy,[status(thm)],[c_3029]) ).
cnf(c_3031,plain,
( ~ iLess0(xm,xn)
| xq = sz00
| xm = sz00
| ~ aNaturalNumber0(xq) ),
inference(resolve,[status(thm)],[c_134,c_3030]) ).
cnf(c_3032,plain,
( ~ iLess0(xm,xn)
| xq = sz00
| xm = sz00 ),
inference(resolve,[status(thm)],[c_107,c_3031]) ).
cnf(c_3033,plain,
( ~ iLess0(xm,xn)
| xq = sz00 ),
inference(resolve,[status(thm)],[c_131,c_3032]) ).
cnf(c_3013,plain,
xq = sz00,
inference(resolve,[status(thm)],[c_1667,c_3033]) ).
cnf(c_3034,plain,
sdtasdt0(xp,sz00) = xn,
inference(paramod,[status(thm)],[c_3013,c_106]) ).
cnf(c_3035,plain,
sz00 = xn,
inference(paramod,[status(thm)],[c_2226,c_3034]) ).
cnf(c_3036,plain,
xn = sz00,
inference(copy,[status(thm)],[c_3035]) ).
cnf(c_3022,plain,
$false,
inference(resolve,[status(thm)],[c_132,c_3036]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM529+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n014.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 03:07:32 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2010217 was started by sandbox2 on n014,
% 0.17/0.43 % Sat Sep 26 03:07:32 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 2.98/0.84
% 2.98/0.84 % SZS status Theorem for theBenchmark
% 2.98/0.84
% 2.98/0.84 % Proof 1 at 0.31 (+ 0.08) seconds.
% 2.98/0.84 % Length of proof is 30.
% 2.98/0.84 % Level of proof is 6.
% 2.98/0.84 % Maximum clause weight is 44.000.
% 2.98/0.84 % Given clauses 165.
% 2.98/0.84
% 2.98/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------