%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM514+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 : n015.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 08:17:14 AM UTC 2026
% Result : Theorem 4.99s 1.16s
% Output : CNFRefutation 4.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 6 unt; 0 def)
% Number of atoms : 23 ( 12 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 18 ( 5 ~; 3 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 3 ( 0 sgn 0 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2613,axiom,
( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xk,xr)) ),
file('theBenchmark.p',m__2613) ).
fof(m__,conjecture,
( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [W0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ? [W0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_307,negated_conjecture,
( sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,A)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_310,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(clausify,[status(thm)],[m__2613]) ).
cnf(c_311,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
inference(copy,[status(thm)],[c_310]) ).
cnf(c_313,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(clausify,[status(thm)],[m__2613]) ).
cnf(c_2785,negated_conjecture,
sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(resolve,[status(thm)],[c_313,c_307]) ).
cnf(c_2786,negated_conjecture,
sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm),
inference(copy,[status(thm)],[c_2785]) ).
cnf(c_2784,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_311,c_2786]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM514+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 03:06:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2975770 was started by sandbox on n015,
% 0.10/0.36 % Sat Sep 26 03:06:58 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.44
% 0.13/0.44 % From the command line: assign(max_seconds, 300).
% 4.99/1.16
% 4.99/1.16 % SZS status Theorem for theBenchmark
% 4.99/1.16
% 4.99/1.16 % Proof 1 at 0.66 (+ 0.04) seconds.
% 4.99/1.16 % Length of proof is 7.
% 4.99/1.16 % Level of proof is 3.
% 4.99/1.16 % Maximum clause weight is 26.000.
% 4.99/1.16 % Given clauses 104.
% 4.99/1.16
% 4.99/1.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------