%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM290+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 : n018.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 08:16:23 AM UTC 2026
% Result : Theorem 25.89s 3.79s
% Output : CNFRefutation 25.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 6 |; 2 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn 4 !; 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(n2_less_n3,conjecture,
less(n2,n3),
file('theBenchmark.p',n2_less_n3) ).
fof(n2_less_n3_neg,negated_conjecture,
~ less(n2,n3),
inference(assume_negation,[status(cth)],[n2_less_n3]) ).
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_435,negated_conjecture,
~ less(n2,n3),
inference(clausify,[status(thm)],[n2_less_n3_neg]) ).
cnf(c_695,plain,
( less(n2,A)
| ~ rdn_positive_less(rdnn(n2),B)
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(resolve,[status(thm)],[c_315,c_283]) ).
cnf(c_11482,plain,
( less(n2,n3)
| ~ rdn_positive_less(rdnn(n2),rdnn(n3)) ),
inference(resolve,[status(thm)],[c_695,c_284]) ).
cnf(c_11483,plain,
less(n2,n3),
inference(resolve,[status(thm)],[c_302,c_11482]) ).
cnf(c_11481,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_435,c_11483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM290+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 02:26:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3502016 was started by sandbox2 on n018,
% 0.10/0.37 % Sat Sep 26 02:26:51 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SInE: 152 to sos, 249 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 25.89/3.79
% 25.89/3.79 % given #500 (F,wt=8): 7061 nn128 != n84. [resolve(1271,a,319,a),flip(a)].
% 25.89/3.79
% 25.89/3.79 % given #1000 (W,wt=12): 7667 -sum(A,n1,n31) | less_or_equal(nn128,A). [resolve(1324,a,278,b)].
% 25.89/3.79
% 25.89/3.79 % SZS status Theorem for theBenchmark
% 25.89/3.79
% 25.89/3.79 % Proof 1 at 2.91 (+ 0.42) seconds.
% 25.89/3.79 % Length of proof is 9.
% 25.89/3.79 % Level of proof is 3.
% 25.89/3.79 % Maximum clause weight is 115.000.
% 25.89/3.79 % Given clauses 1106.
% 25.89/3.79
% 25.89/3.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------