%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM300+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 : n001.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 0.13s 0.44s
% Output : CNFRefutation 0.13s
% 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 : 5 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 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(something_less_n0,conjecture,
? [X] : less(X,n0),
file('theBenchmark.p',something_less_n0) ).
fof(something_less_n0_neg,negated_conjecture,
~ ? [X] : less(X,n0),
inference(assume_negation,[status(cth)],[something_less_n0]) ).
fof(rdnn128,axiom,
rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))),
file('theBenchmark.p',rdnn128) ).
cnf(c_274,plain,
rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))),
inference(clausify,[status(thm)],[rdnn128]) ).
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('theBenchmark.p',rdn0) ).
cnf(c_281,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(clausify,[status(thm)],[rdn0]) ).
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(A,n0),
inference(clausify,[status(thm)],[something_less_n0_neg]) ).
cnf(c_643,plain,
( less(A,n0)
| ~ rdn_translate(A,rdn_neg(B)) ),
inference(resolve,[status(thm)],[c_316,c_281]) ).
cnf(c_641,negated_conjecture,
~ rdn_translate(A,rdn_neg(B)),
inference(resolve,[status(thm)],[c_435,c_643]) ).
cnf(c_642,plain,
$false,
inference(resolve,[status(thm)],[c_641,c_274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM300+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 02:31:11 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 713944 was started by sandbox2 on n001,
% 0.08/0.36 % Sat Sep 26 02:31:11 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 0.08/0.39
% 0.08/0.39 % SInE: 152 to sos, 249 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.13/0.44 % Length of proof is 8.
% 0.13/0.44 % Level of proof is 3.
% 0.13/0.44 % Maximum clause weight is 21.000.
% 0.13/0.44 % Given clauses 108.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------