%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM521+3 : 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 : 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 08:17:16 AM UTC 2026
% Result : Theorem 13.11s 3.95s
% Output : CNFRefutation 13.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 82 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 81 ( 32 ~; 37 |; 11 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 2 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mLETotal,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& W1 != W0 )
| sdtlseqdt0(W0,W1) ) ),
file('theBenchmark.p',mLETotal) ).
fof(m__1837,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('theBenchmark.p',m__1837) ).
fof(m__1870,axiom,
~ ( sdtlseqdt0(xp,xn)
| ? [W0] :
( sdtpldt0(xp,W0) = xn
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__1870) ).
fof(m__2075,axiom,
~ ( sdtlseqdt0(xp,xm)
| ? [W0] :
( sdtpldt0(xp,W0) = xm
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__2075) ).
fof(m__2287,axiom,
~ ( ( sdtlseqdt0(xm,xp)
| ? [W0] :
( sdtpldt0(xm,W0) = xp
& aNaturalNumber0(W0) ) )
& xm != xp
& ( sdtlseqdt0(xn,xp)
| ? [W0] :
( sdtpldt0(xn,W0) = xp
& aNaturalNumber0(W0) ) )
& xn != xp ),
file('theBenchmark.p',m__2287) ).
cnf(c_274,plain,
( ~ sdtlseqdt0(xm,xp)
| xp = xm
| ~ sdtlseqdt0(xn,xp)
| xp = xn ),
inference(clausify,[status(thm)],[m__2287]) ).
cnf(c_4639,plain,
( ~ sdtlseqdt0(xm,xp)
| xp = xm
| ~ sdtlseqdt0(xn,xp)
| xn = xp ),
inference(copy,[status(thm)],[c_274]) ).
cnf(c_275,plain,
( ~ sdtlseqdt0(xm,xp)
| xm = xp
| ~ sdtlseqdt0(xn,xp)
| xn = xp ),
inference(copy,[status(thm)],[c_4639]) ).
cnf(c_282,plain,
~ sdtlseqdt0(xp,xm),
inference(clausify,[status(thm)],[m__2075]) ).
cnf(c_284,plain,
~ sdtlseqdt0(xp,xn),
inference(clausify,[status(thm)],[m__1870]) ).
cnf(c_512,plain,
aNaturalNumber0(xp),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_513,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_514,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1837]) ).
cnf(c_540,plain,
( sdtlseqdt0(B,A)
| sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLETotal]) ).
cnf(c_541,plain,
( B != A
| sdtlseqdt0(A,B)
| ~ aNaturalNumber0(B)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[mLETotal]) ).
cnf(c_2657,plain,
( sdtlseqdt0(A,xn)
| sdtlseqdt0(xn,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_540,c_514]) ).
cnf(c_2658,plain,
( sdtlseqdt0(A,xm)
| sdtlseqdt0(xm,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_540,c_513]) ).
cnf(c_4640,plain,
( A != xp
| sdtlseqdt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(resolve,[status(thm)],[c_541,c_512]) ).
cnf(c_2667,plain,
( xp != A
| sdtlseqdt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(copy,[status(thm)],[c_4640]) ).
cnf(c_4641,plain,
( sdtlseqdt0(xp,xn)
| sdtlseqdt0(xn,xp) ),
inference(resolve,[status(thm)],[c_2657,c_512]) ).
cnf(c_3503,plain,
sdtlseqdt0(xn,xp),
inference(resolve,[status(thm)],[c_284,c_4641]) ).
cnf(c_3506,plain,
( ~ sdtlseqdt0(xm,xp)
| xm = xp
| xn = xp ),
inference(resolve,[status(thm)],[c_3503,c_275]) ).
cnf(c_4642,plain,
( sdtlseqdt0(xp,xm)
| sdtlseqdt0(xm,xp) ),
inference(resolve,[status(thm)],[c_2658,c_512]) ).
cnf(c_3729,plain,
sdtlseqdt0(xm,xp),
inference(resolve,[status(thm)],[c_282,c_4642]) ).
cnf(c_3731,plain,
( xm = xp
| xn = xp ),
inference(resolve,[status(thm)],[c_3729,c_3506]) ).
cnf(c_4643,plain,
( xp != xn
| sdtlseqdt0(xp,xn) ),
inference(resolve,[status(thm)],[c_2667,c_514]) ).
cnf(c_4644,plain,
( xn != xp
| sdtlseqdt0(xp,xn) ),
inference(copy,[status(thm)],[c_4643]) ).
cnf(c_4629,plain,
xn != xp,
inference(resolve,[status(thm)],[c_284,c_4644]) ).
cnf(c_4645,plain,
( xp != xm
| sdtlseqdt0(xp,xm) ),
inference(resolve,[status(thm)],[c_2667,c_513]) ).
cnf(c_4646,plain,
( xm != xp
| sdtlseqdt0(xp,xm) ),
inference(copy,[status(thm)],[c_4645]) ).
cnf(c_4630,plain,
xm != xp,
inference(resolve,[status(thm)],[c_282,c_4646]) ).
cnf(c_4647,plain,
xm = xp,
inference(resolve,[status(thm)],[c_4629,c_3731]) ).
cnf(c_4638,plain,
$false,
inference(resolve,[status(thm)],[c_4630,c_4647]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM521+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.42 % Computer : n014.cluster.edu
% 0.08/0.42 % Model : x86_64 x86_64
% 0.08/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.42 % Memory : 8046.5625MB
% 0.08/0.42 % OS : Linux 6.8.0-71-generic
% 0.08/0.42 % CPULimit : 300
% 0.08/0.42 % WCLimit : 300
% 0.08/0.42 % DateTime : Sat Sep 26 03:05:46 UTC 2026
% 0.08/0.42 % CPUTime :
% 0.08/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.42 % Process 2003779 was started by sandbox on n014,
% 0.08/0.42 % Sat Sep 26 03:05:46 2026
% 0.08/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.46
% 0.08/0.46 % From the command line: assign(max_seconds, 300).
% 13.11/3.95
% 13.11/3.95 % given #500 (I,wt=60): 884 -aNaturalNumber0(A) | -aNaturalNumber0(B) | -aNaturalNumber0(C) | sdtasdt0(C,B) != sdtasdt0(A,B) | -iLess0(sdtpldt0(sdtpldt0(A,B),C),sdtpldt0(sdtpldt0(xn,xm),xp)) | sdtasdt0(C,f7(A,B,C)) = A | doDivides0(C,B) | sz00 = C | sz10 = C | f3(C) != sz10. [factor(207,b,d)].
% 13.11/3.95
% 13.11/3.95 % given #1000 (I,wt=49): 1519 -aNaturalNumber0(A) | -aNaturalNumber0(B) | -aNaturalNumber0(C) | sdtasdt0(xp,C) != sdtasdt0(A,B) | -iLess0(sdtpldt0(sdtpldt0(A,B),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) | aNaturalNumber0(f7(A,B,xp)) | aNaturalNumber0(f8(A,B,xp)). [back_unit_del(76),unit_del(c,512)].
% 13.11/3.95
% 13.11/3.95 % given #1500 (I,wt=59): 2177 -aNaturalNumber0(A) | -aNaturalNumber0(B) | sz00 = B | sz10 = B | f5(A,A,B) != sz10 | sdtasdt0(B,A) != sdtasdt0(A,A) | -iLess0(sdtpldt0(sdtpldt0(A,A),B),sdtpldt0(sdtpldt0(xn,xm),xp)) | aNaturalNumber0(f7(A,A,B)) | aNaturalNumber0(f8(A,A,B)). [factor(1204,a,f)].
% 13.11/3.95
% 13.11/3.95 % SZS status Theorem for theBenchmark
% 13.11/3.95
% 13.11/3.95 % Proof 1 at 1.53 (+ 0.14) seconds.
% 13.11/3.95 % Length of proof is 24.
% 13.11/3.95 % Level of proof is 6.
% 13.11/3.95 % Maximum clause weight is 17.000.
% 13.11/3.95 % Given clauses 1904.
% 13.11/3.95
% 13.11/3.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------