%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM302+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 08:16:25 AM UTC 2026
% Result : Theorem 0.15s 0.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 3 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 15 ( 6 sgn 4 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(less_entry_point_neg_pos,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> less(X,Y) ),
file('theBenchmark.p',less_entry_point_neg_pos) ).
fof(nn2_less_something,conjecture,
? [X] : less(nn2,X),
file('theBenchmark.p',nn2_less_something) ).
fof(nn2_less_something_neg,negated_conjecture,
~ ? [X] : less(nn2,X),
inference(assume_negation,[status(cth)],[nn2_less_something]) ).
fof(rdn9,axiom,
rdn_translate(n9,rdn_pos(rdnn(n9))),
file('theBenchmark.p',rdn9) ).
cnf(c_289,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(clausify,[status(thm)],[rdn9]) ).
fof(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('theBenchmark.p',rdnn2) ).
cnf(c_290,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(clausify,[status(thm)],[rdnn2]) ).
cnf(c_316,plain,
( less(A,C)
| ~ rdn_translate(C,rdn_pos(D))
| ~ rdn_translate(A,rdn_neg(B)) ),
inference(clausify,[status(thm)],[less_entry_point_neg_pos]) ).
cnf(c_435,negated_conjecture,
~ less(nn2,A),
inference(clausify,[status(thm)],[nn2_less_something_neg]) ).
cnf(c_495,plain,
( less(nn2,A)
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(resolve,[status(thm)],[c_316,c_290]) ).
cnf(c_493,negated_conjecture,
~ rdn_translate(A,rdn_pos(B)),
inference(resolve,[status(thm)],[c_435,c_495]) ).
cnf(c_494,plain,
$false,
inference(resolve,[status(thm)],[c_493,c_289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM302+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n005.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 02:25:02 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 1020378 was started by sandbox2 on n005,
% 0.15/0.44 % Sat Sep 26 02:25:02 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.47
% 0.15/0.47 % From the command line: assign(max_seconds, 300).
% 0.15/0.47
% 0.15/0.47 % SInE: 153 to sos, 248 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.15/0.51
% 0.15/0.51 % SZS status Theorem for theBenchmark
% 0.15/0.51
% 0.15/0.51 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/0.51 % Length of proof is 8.
% 0.15/0.51 % Level of proof is 3.
% 0.15/0.51 % Maximum clause weight is 105.000.
% 0.15/0.51 % Given clauses 16.
% 0.15/0.51
% 0.15/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------