%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM329+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 : n012.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 5.69s 1.10s
% Output : CNFRefutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 36 ( 17 ~; 13 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 35 ( 1 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_entry_point_pos_pos,axiom,
! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :
( ( rdn_translate(Z,rdn_pos(RDN_Z))
& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_pos(RDN_X)) )
=> sum(X,Y,Z) ),
file('theBenchmark.p',sum_entry_point_pos_pos) ).
fof(add_digit_digit_digit,axiom,
! [C,D1,D2,RD,ID] :
( ( rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))
& rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ),
file('theBenchmark.p',add_digit_digit_digit) ).
fof(idempotent_element,conjecture,
? [X] : sum(X,X,X),
file('theBenchmark.p',idempotent_element) ).
fof(idempotent_element_neg,negated_conjecture,
~ ? [X] : sum(X,X,X),
inference(assume_negation,[status(cth)],[idempotent_element]) ).
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('theBenchmark.p',rdn0) ).
cnf(c_287,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(clausify,[status(thm)],[rdn0]) ).
cnf(c_321,plain,
( sum(A,C,F)
| ~ rdn_translate(F,rdn_pos(E))
| ~ rdn_add_with_carry(rdnn(n0),B,D,E)
| ~ rdn_translate(C,rdn_pos(D))
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(clausify,[status(thm)],[sum_entry_point_pos_pos]) ).
cnf(c_330,plain,
( rdn_add_with_carry(rdnn(D),rdnn(A),rdnn(B),rdnn(E))
| ~ rdn_digit_add(rdnn(C),rdnn(D),rdnn(E),rdnn(n0))
| ~ rdn_digit_add(rdnn(A),rdnn(B),rdnn(C),rdnn(n0)) ),
inference(clausify,[status(thm)],[add_digit_digit_digit]) ).
fof(rdn_digit_add_n0_n0_n0_n0,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('theBenchmark.p',rdn_digit_add_n0_n0_n0_n0) ).
cnf(c_335,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(clausify,[status(thm)],[rdn_digit_add_n0_n0_n0_n0]) ).
cnf(c_435,negated_conjecture,
~ sum(A,A,A),
inference(clausify,[status(thm)],[idempotent_element_neg]) ).
cnf(c_436,plain,
( sum(A,A,D)
| ~ rdn_translate(D,rdn_pos(C))
| ~ rdn_add_with_carry(rdnn(n0),B,B,C)
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(factor,[status(thm)],[c_321]) ).
cnf(c_444,plain,
( rdn_add_with_carry(rdnn(B),rdnn(A),rdnn(B),rdnn(A))
| ~ rdn_digit_add(rdnn(A),rdnn(B),rdnn(A),rdnn(n0)) ),
inference(factor,[status(thm)],[c_330]) ).
cnf(c_6593,plain,
( sum(A,A,A)
| ~ rdn_add_with_carry(rdnn(n0),B,B,B)
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(factor,[status(thm)],[c_436]) ).
cnf(c_458,negated_conjecture,
( ~ rdn_add_with_carry(rdnn(n0),B,B,B)
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(resolve,[status(thm)],[c_435,c_6593]) ).
cnf(c_498,plain,
~ rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(resolve,[status(thm)],[c_458,c_287]) ).
cnf(c_6594,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(resolve,[status(thm)],[c_444,c_335]) ).
cnf(c_6592,plain,
$false,
inference(resolve,[status(thm)],[c_498,c_6594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM329+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sat Sep 26 02:27:35 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 3703139 was started by sandbox2 on n012,
% 0.04/0.30 % Sat Sep 26 02:27:35 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.04/0.31
% 0.04/0.31 % From the command line: assign(max_seconds, 300).
% 0.04/0.31
% 0.04/0.31 % SInE: 148 to sos, 253 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 5.69/1.10
% 5.69/1.10 % given #500 (F,wt=5): 2885 -less(n0,nn38). [resolve(698,a,278,b)].
% 5.69/1.10
% 5.69/1.10 % SZS status Theorem for theBenchmark
% 5.69/1.10
% 5.69/1.10 % Proof 1 at 0.59 (+ 0.17) seconds.
% 5.69/1.10 % Length of proof is 13.
% 5.69/1.10 % Level of proof is 5.
% 5.69/1.10 % Maximum clause weight is 131.000.
% 5.69/1.10 % Given clauses 859.
% 5.69/1.10
% 5.69/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------