%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM318+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 : n001.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 08:16:26 AM UTC 2026
% Result : Theorem 2.34s 0.76s
% Output : CNFRefutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 3 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-1 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_entry_point_posx_negx,axiom,
! [POS_X,NEG_X,RDN_X] :
( ( rdn_translate(NEG_X,rdn_neg(RDN_X))
& rdn_translate(POS_X,rdn_pos(RDN_X)) )
=> sum(POS_X,NEG_X,n0) ),
file('theBenchmark.p',sum_entry_point_posx_negx) ).
fof(sum_n5_nn5_n0,conjecture,
sum(n5,nn5,n0),
file('theBenchmark.p',sum_n5_nn5_n0) ).
fof(sum_n5_nn5_n0_neg,negated_conjecture,
~ sum(n5,nn5,n0),
inference(assume_negation,[status(cth)],[sum_n5_nn5_n0]) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('theBenchmark.p',rdn5) ).
cnf(c_291,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(clausify,[status(thm)],[rdn5]) ).
fof(rdnn5,axiom,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
file('theBenchmark.p',rdnn5) ).
cnf(c_296,plain,
rdn_translate(nn5,rdn_neg(rdnn(n5))),
inference(clausify,[status(thm)],[rdnn5]) ).
cnf(c_325,plain,
( sum(A,C,n0)
| ~ rdn_translate(C,rdn_neg(B))
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(clausify,[status(thm)],[sum_entry_point_posx_negx]) ).
cnf(c_435,negated_conjecture,
~ sum(n5,nn5,n0),
inference(clausify,[status(thm)],[sum_n5_nn5_n0_neg]) ).
cnf(c_1019,plain,
( sum(n5,A,n0)
| ~ rdn_translate(A,rdn_neg(rdnn(n5))) ),
inference(resolve,[status(thm)],[c_325,c_291]) ).
cnf(c_4000,plain,
sum(n5,nn5,n0),
inference(resolve,[status(thm)],[c_1019,c_296]) ).
cnf(c_3999,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_435,c_4000]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM318+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.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 02:32:12 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 715231 was started by sandbox2 on n001,
% 0.08/0.36 % Sat Sep 26 02:32:12 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SInE: 149 to sos, 252 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 2.34/0.76
% 2.34/0.76 % given #500 (W,wt=8): 948 -less(n0,nn38). [resolve(575,a,277,b)].
% 2.34/0.76
% 2.34/0.76 % given #1000 (T,wt=8): 1920 less_or_equal(nn72,n1). [resolve(1622,a,281,b)].
% 2.34/0.76
% 2.34/0.76 % given #1500 (F,wt=8): 3490 -less(n2,nn93). [resolve(2243,a,277,b)].
% 2.34/0.76
% 2.34/0.76 % SZS status Theorem for theBenchmark
% 2.34/0.76
% 2.34/0.76 % Proof 1 at 0.24 (+ 0.07) seconds.
% 2.34/0.76 % Length of proof is 8.
% 2.34/0.76 % Level of proof is 3.
% 2.34/0.76 % Maximum clause weight is 24.000.
% 2.34/0.76 % Given clauses 1558.
% 2.34/0.76
% 2.34/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------