%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM291+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 : n020.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 29.16s 9.16s
% Output : CNFRefutation 29.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 30 ( 1 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 7 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 15 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('theBenchmark.p',less_property) ).
fof(n3_not_less_n2,conjecture,
~ less(n3,n2),
file('theBenchmark.p',n3_not_less_n2) ).
fof(n3_not_less_n2_neg,negated_conjecture,
~ ~ less(n3,n2),
inference(assume_negation,[status(cth)],[n3_not_less_n2]) ).
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('theBenchmark.p',rdn2) ).
cnf(c_283,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(clausify,[status(thm)],[rdn2]) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('theBenchmark.p',rdn3) ).
cnf(c_284,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(clausify,[status(thm)],[rdn3]) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('theBenchmark.p',rdn_positive_less23) ).
cnf(c_302,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(clausify,[status(thm)],[rdn_positive_less23]) ).
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_318,plain,
( ~ less(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_435,negated_conjecture,
less(n3,n2),
inference(clausify,[status(thm)],[n3_not_less_n2_neg]) ).
cnf(c_489,plain,
~ less(n2,n3),
inference(resolve,[status(thm)],[c_435,c_318]) ).
cnf(c_565,plain,
( less(A,B)
| ~ rdn_translate(B,rdn_pos(rdnn(n3)))
| ~ rdn_translate(A,rdn_pos(rdnn(n2))) ),
inference(resolve,[status(thm)],[c_315,c_302]) ).
cnf(c_2561,plain,
( less(n2,A)
| ~ rdn_translate(A,rdn_pos(rdnn(n3))) ),
inference(resolve,[status(thm)],[c_565,c_283]) ).
cnf(c_16407,plain,
less(n2,n3),
inference(resolve,[status(thm)],[c_2561,c_284]) ).
cnf(c_16406,plain,
$false,
inference(resolve,[status(thm)],[c_489,c_16407]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM291+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.40 % Computer : n020.cluster.edu
% 0.11/5.40 % Model : x86_64 x86_64
% 0.11/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.40 % Memory : 8046.5625MB
% 0.11/5.40 % OS : Linux 6.8.0-71-generic
% 0.11/5.41 % CPULimit : 300
% 0.11/5.41 % WCLimit : 300
% 0.11/5.41 % DateTime : Sat Sep 26 02:25:39 UTC 2026
% 0.11/5.41 % CPUTime :
% 0.11/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.41 % Process 402896 was started by sandbox2 on n020,
% 0.11/5.41 % Sat Sep 26 02:25:39 2026
% 0.11/5.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.44
% 0.11/5.44 % From the command line: assign(max_seconds, 300).
% 0.11/5.44
% 0.11/5.44 % SInE: 152 to sos, 249 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 29.16/9.16
% 29.16/9.16 % given #500 (A,wt=24): 464 -rdn_translate(A,rdn_neg(B)) | -rdn_add_with_carry(rdnn(n0),B,B,B) | sum(A,A,A). [factor(442,a,c)].
% 29.16/9.16
% 29.16/9.16 % given #1000 (A,wt=17): 605 -rdn_translate(A,rdn_pos(B)) | less(nn91,A). [resolve(316,a,237,a)].
% 29.16/9.16
% 29.16/9.16 % given #1500 (T,wt=8): 2769 less(nn125,n99). [resolve(571,a,118,a)].
% 29.16/9.16
% 29.16/9.16 % given #2000 (A,wt=28): 835 -rdn_translate(A,rdn_pos(rdnn(n6))) | -rdn_translate(B,rdn_pos(rdnn(n8))) | less(A,B). [resolve(526,a,315,c)].
% 29.16/9.16
% 29.16/9.16 % given #2500 (F,wt=8): 9443 -less(n8,nn125). [resolve(2732,a,318,b)].
% 29.16/9.16
% 29.16/9.16 % given #3000 (W,wt=8): 3476 less(nn120,n50). [resolve(576,a,69,a)].
% 29.16/9.16
% 29.16/9.16 % given #3500 (F,wt=8): 9833 nn124 != n110. [resolve(2886,a,319,a),flip(a)].
% 29.16/9.16
% 29.16/9.16 % given #4000 (W,wt=8): 3961 less(nn116,n113). [resolve(580,a,132,a)].
% 29.16/9.16
% 29.16/9.16 % given #4500 (F,wt=8): 10293 -less(n85,nn123). [resolve(3039,a,318,b)].
% 29.16/9.16
% 29.16/9.16 % given #5000 (T,wt=8): 4434 less(nn113,n42). [resolve(583,a,61,a)].
% 29.16/9.16
% 29.16/9.16 % given #5500 (F,wt=8): 10760 nn122 != n59. [resolve(3211,a,319,a),flip(a)].
% 29.16/9.16
% 29.16/9.16 % given #6000 (T,wt=8): 4907 less(nn109,n99). [resolve(587,a,118,a)].
% 29.16/9.16
% 29.16/9.16 % given #6500 (A,wt=26): 2420 rdn_positive_less(rdn(rdnn(A),rdnn(n0)),rdn(rdnn(B),rdnn(n7))). [resolve(2386,a,310,a)].
% 29.16/9.16
% 29.16/9.16 % SZS status Theorem for theBenchmark
% 29.16/9.16
% 29.16/9.16 % Proof 1 at 2.99 (+ 0.68) seconds.
% 29.16/9.16 % Length of proof is 13.
% 29.16/9.16 % Level of proof is 4.
% 29.16/9.16 % Maximum clause weight is 115.000.
% 29.16/9.16 % Given clauses 6537.
% 29.16/9.16
% 29.16/9.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------