%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM298+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.18s 5.70s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 23 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 4 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 14 ( 3 sgn 6 !; 0 ?)
% 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(less_property,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('theBenchmark.p',less_property) ).
fof(n2_not_less_nn2,conjecture,
~ less(n2,nn2),
file('theBenchmark.p',n2_not_less_nn2) ).
fof(n2_not_less_nn2_neg,negated_conjecture,
~ ~ less(n2,nn2),
inference(assume_negation,[status(cth)],[n2_not_less_nn2]) ).
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(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('theBenchmark.p',rdnn2) ).
cnf(c_290,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(clausify,[status(thm)],[rdnn2]) ).
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_318,plain,
( ~ less(B,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
cnf(c_435,negated_conjecture,
less(n2,nn2),
inference(clausify,[status(thm)],[n2_not_less_nn2_neg]) ).
cnf(c_489,plain,
~ less(nn2,n2),
inference(resolve,[status(thm)],[c_435,c_318]) ).
cnf(c_494,plain,
( less(nn2,A)
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(resolve,[status(thm)],[c_316,c_290]) ).
cnf(c_758,plain,
less(nn2,n2),
inference(resolve,[status(thm)],[c_494,c_282]) ).
cnf(c_757,plain,
$false,
inference(resolve,[status(thm)],[c_489,c_758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM298+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.57 % Computer : n003.cluster.edu
% 0.13/5.57 % Model : x86_64 x86_64
% 0.13/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.57 % Memory : 8046.5625MB
% 0.13/5.57 % OS : Linux 6.8.0-71-generic
% 0.13/5.57 % CPULimit : 300
% 0.13/5.57 % WCLimit : 300
% 0.13/5.57 % DateTime : Sat Sep 26 02:27:00 UTC 2026
% 0.13/5.58 % CPUTime :
% 0.13/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.58 % Process 1823653 was started by sandbox on n003,
% 0.13/5.58 % Sat Sep 26 02:27:00 2026
% 0.13/5.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/5.61
% 0.18/5.61 % From the command line: assign(max_seconds, 300).
% 0.18/5.61
% 0.18/5.61 % SInE: 153 to sos, 248 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.18/5.70
% 0.18/5.70 % SZS status Theorem for theBenchmark
% 0.18/5.70
% 0.18/5.70 % Proof 1 at 0.07 (+ 0.01) seconds.
% 0.18/5.70 % Length of proof is 11.
% 0.18/5.70 % Level of proof is 3.
% 0.18/5.70 % Maximum clause weight is 21.000.
% 0.18/5.70 % Given clauses 63.
% 0.18/5.70
% 0.18/5.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------