%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM472+2 : 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 : n016.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 08:17:06 AM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 11 ( 4 ~; 3 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 3 ( 0 sgn 0 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1324,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('theBenchmark.p',m__1324) ).
fof(m__,conjecture,
( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ? [W0] :
( sdtpldt0(xm,W0) = sdtpldt0(xm,xn)
& aNaturalNumber0(W0) ) ),
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ? [W0] :
( sdtpldt0(xm,W0) = sdtpldt0(xm,xn)
& aNaturalNumber0(W0) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_39,negated_conjecture,
( sdtpldt0(xm,xn) != sdtpldt0(xm,A)
| ~ aNaturalNumber0(A) ),
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_55,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[m__1324]) ).
cnf(c_194,plain,
~ aNaturalNumber0(xn),
inference(xxres,[status(thm)],[c_39]) ).
cnf(c_193,plain,
$false,
inference(resolve,[status(thm)],[c_55,c_194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM472+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 02:58:15 UTC 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.36 % Process 4049523 was started by sandbox2 on n016,
% 0.15/0.36 % Sat Sep 26 02:58:15 2026
% 0.15/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 5.
% 0.15/0.39 % Level of proof is 2.
% 0.15/0.39 % Maximum clause weight is 19.000.
% 0.15/0.39 % Given clauses 2.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------