%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM294+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 08:16:24 AM UTC 2026
% Result : Theorem 14.32s 2.51s
% Output : CNFRefutation 14.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 7 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 6 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn_positive_less_multi_digit_high,axiom,
! [Ds,Os,Db,Ob] :
( rdn_positive_less(Os,Ob)
=> rdn_positive_less(rdn(rdnn(Ds),Os),rdn(rdnn(Db),Ob)) ),
file('theBenchmark.p',rdn_positive_less_multi_digit_high) ).
fof(less_entry_point_pos_pos,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_positive_less(RDN_X,RDN_Y)
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_pos(RDN_X)) )
=> less(X,Y) ),
file('theBenchmark.p',less_entry_point_pos_pos) ).
fof(n12_less_something,conjecture,
? [X] : less(n12,X),
file('theBenchmark.p',n12_less_something) ).
fof(n12_less_something_neg,negated_conjecture,
~ ? [X] : less(n12,X),
inference(assume_negation,[status(cth)],[n12_less_something]) ).
fof(rdn29,axiom,
rdn_translate(n29,rdn_pos(rdn(rdnn(n9),rdnn(n2)))),
file('theBenchmark.p',rdn29) ).
cnf(c_47,plain,
rdn_translate(n29,rdn_pos(rdn(rdnn(n9),rdnn(n2)))),
inference(clausify,[status(thm)],[rdn29]) ).
fof(rdn12,axiom,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
file('theBenchmark.p',rdn12) ).
cnf(c_290,plain,
rdn_translate(n12,rdn_pos(rdn(rdnn(n2),rdnn(n1)))),
inference(clausify,[status(thm)],[rdn12]) ).
fof(rdn_positive_less12,axiom,
rdn_positive_less(rdnn(n1),rdnn(n2)),
file('theBenchmark.p',rdn_positive_less12) ).
cnf(c_301,plain,
rdn_positive_less(rdnn(n1),rdnn(n2)),
inference(clausify,[status(thm)],[rdn_positive_less12]) ).
cnf(c_310,plain,
( rdn_positive_less(rdn(rdnn(C),A),rdn(rdnn(D),B))
| ~ rdn_positive_less(A,B) ),
inference(clausify,[status(thm)],[rdn_positive_less_multi_digit_high]) ).
cnf(c_315,plain,
( less(A,C)
| ~ rdn_positive_less(B,D)
| ~ rdn_translate(C,rdn_pos(D))
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(clausify,[status(thm)],[less_entry_point_pos_pos]) ).
cnf(c_435,negated_conjecture,
~ less(n12,A),
inference(clausify,[status(thm)],[n12_less_something_neg]) ).
cnf(c_1537,plain,
rdn_positive_less(rdn(rdnn(A),rdnn(n1)),rdn(rdnn(B),rdnn(n2))),
inference(resolve,[status(thm)],[c_310,c_301]) ).
cnf(c_8747,plain,
( less(n12,A)
| ~ rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),B)
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(resolve,[status(thm)],[c_315,c_290]) ).
cnf(c_1564,negated_conjecture,
( ~ rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),B)
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(resolve,[status(thm)],[c_435,c_8747]) ).
cnf(c_8748,plain,
~ rdn_positive_less(rdn(rdnn(n2),rdnn(n1)),rdn(rdnn(n9),rdnn(n2))),
inference(resolve,[status(thm)],[c_1564,c_47]) ).
cnf(c_8746,plain,
$false,
inference(resolve,[status(thm)],[c_1537,c_8748]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM294+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n001.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 02:30:12 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 710426 was started by sandbox2 on n001,
% 0.17/0.44 % Sat Sep 26 02:30:12 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SInE: 153 to sos, 248 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 14.32/2.51
% 14.32/2.51 % given #500 (F,wt=8): 1396 nn128 != n33. [resolve(969,a,319,a),flip(a)].
% 14.32/2.51
% 14.32/2.51 % given #1000 (W,wt=8): 6460 less(nn127,n44). [resolve(625,a,62,a)].
% 14.32/2.51
% 14.32/2.51 % SZS status Theorem for theBenchmark
% 14.32/2.51
% 14.32/2.51 % Proof 1 at 1.69 (+ 0.27) seconds.
% 14.32/2.51 % Length of proof is 12.
% 14.32/2.51 % Level of proof is 3.
% 14.32/2.51 % Maximum clause weight is 127.000.
% 14.32/2.51 % Given clauses 1454.
% 14.32/2.51
% 14.32/2.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------