%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM304+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 : 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 08:16:25 AM UTC 2026
% Result : Theorem 0.26s 0.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 13 unt; 0 def)
% Number of atoms : 26 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 4 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 11 sgn 6 !; 2 ?)
% 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(something_not_n12,conjecture,
? [X] : X != n12,
file('theBenchmark.p',something_not_n12) ).
fof(something_not_n12_neg,negated_conjecture,
~ ? [X] : X != n12,
inference(assume_negation,[status(cth)],[something_not_n12]) ).
fof(rdnn128,axiom,
rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))),
file('theBenchmark.p',rdnn128) ).
cnf(c_273,plain,
rdn_translate(nn128,rdn_neg(rdn(rdnn(n8),rdn(rdnn(n2),rdnn(n1))))),
inference(clausify,[status(thm)],[rdnn128]) ).
cnf(c_299,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_302,plain,
( B != A
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_property]) ).
fof(rdn1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('theBenchmark.p',rdn1) ).
cnf(c_325,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(clausify,[status(thm)],[rdn1]) ).
cnf(c_435,negated_conjecture,
A = n12,
inference(clausify,[status(thm)],[something_not_n12_neg]) ).
cnf(c_436,negated_conjecture,
n12 = A,
inference(copy,[status(thm)],[c_435]) ).
cnf(c_440,plain,
( less(A,n1)
| ~ rdn_translate(A,rdn_neg(B)) ),
inference(resolve,[status(thm)],[c_325,c_299]) ).
cnf(c_2300,plain,
rdn_translate(nn128,rdn_neg(n12)),
inference(paramod,[status(thm)],[c_436,c_273]) ).
cnf(c_2402,plain,
A = B,
inference(paramod,[status(thm)],[c_436,c_436]) ).
cnf(c_2456,plain,
~ less(A,B),
inference(resolve,[status(thm)],[c_2402,c_302]) ).
cnf(c_2486,plain,
~ rdn_translate(A,rdn_neg(B)),
inference(resolve,[status(thm)],[c_2456,c_440]) ).
cnf(c_2487,plain,
$false,
inference(resolve,[status(thm)],[c_2486,c_2300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM304+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 02:27:35 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3503257 was started by sandbox on n018,
% 0.19/0.45 % Sat Sep 26 02:27:35 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.48
% 0.19/0.48 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % SInE: 111 to sos, 290 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.26/0.62
% 0.26/0.62 % SZS status Theorem for theBenchmark
% 0.26/0.62
% 0.26/0.62 % Proof 1 at 0.09 (+ 0.05) seconds.
% 0.26/0.62 % Length of proof is 15.
% 0.26/0.62 % Level of proof is 6.
% 0.26/0.62 % Maximum clause weight is 120.000.
% 0.26/0.62 % Given clauses 3.
% 0.26/0.62
% 0.26/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------