%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM326+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 : 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 08:16:27 AM UTC 2026
% Result : Theorem 0.08s 0.48s
% Output : CNFRefutation 0.08s
% 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 : 11 ( 6 ~; 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 : 11 ( 2 sgn 3 !; 2 ?)
% 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_what_nn5_n0,conjecture,
? [X] : sum(X,nn5,n0),
file('theBenchmark.p',sum_what_nn5_n0) ).
fof(sum_what_nn5_n0_neg,negated_conjecture,
~ ? [X] : sum(X,nn5,n0),
inference(assume_negation,[status(cth)],[sum_what_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(A,nn5,n0),
inference(clausify,[status(thm)],[sum_what_nn5_n0_neg]) ).
cnf(c_1037,plain,
( sum(A,nn5,n0)
| ~ rdn_translate(A,rdn_pos(rdnn(n5))) ),
inference(resolve,[status(thm)],[c_325,c_296]) ).
cnf(c_1035,negated_conjecture,
~ rdn_translate(A,rdn_pos(rdnn(n5))),
inference(resolve,[status(thm)],[c_435,c_1037]) ).
cnf(c_1036,plain,
$false,
inference(resolve,[status(thm)],[c_1035,c_291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM326+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % 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 02:28:19 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 411061 was started by sandbox on n020,
% 0.08/0.36 % Sat Sep 26 02:28:19 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SInE: 149 to sos, 252 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.08/0.48
% 0.08/0.48 % SZS status Theorem for theBenchmark
% 0.08/0.48
% 0.08/0.48 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.08/0.48 % Length of proof is 8.
% 0.08/0.48 % Level of proof is 3.
% 0.08/0.48 % Maximum clause weight is 120.000.
% 0.08/0.48 % Given clauses 167.
% 0.08/0.48
% 0.08/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------