%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM292+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 : n026.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 40.32s 6.20s
% Output : CNFRefutation 40.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 8 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 4 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdn_extra_digits_positive_less,axiom,
! [D,Db,Ob] :
( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
file('theBenchmark.p',rdn_extra_digits_positive_less) ).
fof(rdn_non_zero_by_digit,axiom,
! [X] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('theBenchmark.p',rdn_non_zero_by_digit) ).
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(n2_less_n13,conjecture,
less(n2,n13),
file('theBenchmark.p',n2_less_n13) ).
fof(n2_less_n13_neg,negated_conjecture,
~ less(n2,n13),
inference(assume_negation,[status(cth)],[n2_less_n13]) ).
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('theBenchmark.p',rdn2) ).
cnf(c_282,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(clausify,[status(thm)],[rdn2]) ).
fof(rdn13,axiom,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
file('theBenchmark.p',rdn13) ).
cnf(c_290,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(clausify,[status(thm)],[rdn13]) ).
fof(rdn_digit1,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('theBenchmark.p',rdn_digit1) ).
cnf(c_291,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(clausify,[status(thm)],[rdn_digit1]) ).
cnf(c_312,plain,
( rdn_positive_less(rdnn(B),rdn(rdnn(C),A))
| ~ rdn_non_zero(A) ),
inference(clausify,[status(thm)],[rdn_extra_digits_positive_less]) ).
cnf(c_313,plain,
( rdn_non_zero(rdnn(A))
| ~ rdn_non_zero_digit(rdnn(A)) ),
inference(clausify,[status(thm)],[rdn_non_zero_by_digit]) ).
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(n2,n13),
inference(clausify,[status(thm)],[n2_less_n13_neg]) ).
cnf(c_1565,plain,
rdn_non_zero(rdnn(n1)),
inference(resolve,[status(thm)],[c_313,c_291]) ).
cnf(c_1574,plain,
( less(n2,A)
| ~ rdn_positive_less(rdnn(n2),B)
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(resolve,[status(thm)],[c_315,c_282]) ).
cnf(c_7270,plain,
rdn_positive_less(rdnn(A),rdn(rdnn(B),rdnn(n1))),
inference(resolve,[status(thm)],[c_1565,c_312]) ).
cnf(c_23617,plain,
( less(n2,n13)
| ~ rdn_positive_less(rdnn(n2),rdn(rdnn(n3),rdnn(n1))) ),
inference(resolve,[status(thm)],[c_1574,c_290]) ).
cnf(c_23618,plain,
less(n2,n13),
inference(resolve,[status(thm)],[c_7270,c_23617]) ).
cnf(c_23616,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_435,c_23618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM292+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 02:27:10 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 4097656 was started by sandbox2 on n026,
% 0.08/0.36 % Sat Sep 26 02:27:10 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SInE: 153 to sos, 248 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 40.32/6.20
% 40.32/6.20 % given #500 (F,wt=8): 1338 -less(n52,nn128). [resolve(959,a,318,b)].
% 40.32/6.20
% 40.32/6.20 % given #1000 (W,wt=8): 7371 less(nn127,n74). [resolve(626,a,92,a)].
% 40.32/6.20
% 40.32/6.20 % given #1500 (F,wt=41): 516 -rdn_positive_less(rdn(rdnn(n8),rdn(rdnn(n0),rdnn(n1))),rdn(rdnn(n8),rdn(rdnn(n0),rdnn(n1)))). [resolve(461,a,253,a)].
% 40.32/6.20
% 40.32/6.20 % given #2000 (W,wt=8): 11129 -less(n68,nn126). [resolve(10790,a,318,b)].
% 40.32/6.20
% 40.32/6.20 % given #2500 (F,wt=8): 16038 -less(n91,nn125). [resolve(11352,a,318,b)].
% 40.32/6.20
% 40.32/6.20 % given #3000 (W,wt=8): 11833 less(nn122,n58). [resolve(631,a,76,a)].
% 40.32/6.20
% 40.32/6.20 % given #3500 (F,wt=8): 19475 nn124 != n37. [resolve(11558,a,319,a),flip(a)].
% 40.32/6.20
% 40.32/6.20 % given #4000 (T,wt=8): 12378 less(nn118,n25). [resolve(635,a,43,a)].
% 40.32/6.20
% 40.32/6.20 % given #4500 (F,wt=8): 20127 -less(n112,nn122). [resolve(11779,a,318,b)].
% 40.32/6.20
% 40.32/6.20 % given #5000 (T,wt=8): 12923 less(nn113,n120). [resolve(640,a,138,a)].
% 40.32/6.20
% 40.32/6.20 % SZS status Theorem for theBenchmark
% 40.32/6.20
% 40.32/6.20 % Proof 1 at 4.68 (+ 1.03) seconds.
% 40.32/6.20 % Length of proof is 15.
% 40.32/6.20 % Level of proof is 4.
% 40.32/6.20 % Maximum clause weight is 413.000.
% 40.32/6.20 % Given clauses 5092.
% 40.32/6.20
% 40.32/6.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------