%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM330+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 : n006.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 229.24s 31.19s
% Output : CNFRefutation 229.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 56 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 57 ( 27 ~; 20 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn 11 !; 4 ?)
% 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(sum_n4_n4_n8,conjecture,
? [X,Y] :
( Y = n4
& X = n4
& sum(X,Y,n8) ),
file('theBenchmark.p',sum_n4_n4_n8) ).
fof(sum_n4_n4_n8_neg,negated_conjecture,
~ ? [X,Y] :
( Y = n4
& X = n4
& sum(X,Y,n8) ),
inference(assume_negation,[status(cth)],[sum_n4_n4_n8]) ).
fof(rdn4,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('theBenchmark.p',rdn4) ).
cnf(c_291,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(clausify,[status(thm)],[rdn4]) ).
fof(rdn8,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('theBenchmark.p',rdn8) ).
cnf(c_295,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(clausify,[status(thm)],[rdn8]) ).
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_n4_n4_n8_n0,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('theBenchmark.p',rdn_digit_add_n4_n4_n8_n0) ).
cnf(c_379,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(clausify,[status(thm)],[rdn_digit_add_n4_n4_n8_n0]) ).
fof(rdn_digit_add_n8_n0_n8_n0,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('theBenchmark.p',rdn_digit_add_n8_n0_n8_n0) ).
cnf(c_415,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(clausify,[status(thm)],[rdn_digit_add_n8_n0_n8_n0]) ).
cnf(c_435,negated_conjecture,
( B != n4
| A != n4
| ~ sum(A,B,n8) ),
inference(clausify,[status(thm)],[sum_n4_n4_n8_neg]) ).
cnf(c_19863,negated_conjecture,
( B != n4
| n4 != A
| ~ sum(A,B,n8) ),
inference(copy,[status(thm)],[c_435]) ).
cnf(c_436,negated_conjecture,
( n4 != B
| n4 != A
| ~ sum(A,B,n8) ),
inference(copy,[status(thm)],[c_19863]) ).
cnf(c_459,plain,
( n4 != A
| ~ sum(A,A,n8) ),
inference(factor,[status(thm)],[c_436]) ).
cnf(c_488,plain,
~ sum(n4,n4,n8),
inference(xxres,[status(thm)],[c_459]) ).
cnf(c_1242,plain,
( sum(A,C,n8)
| ~ rdn_add_with_carry(rdnn(n0),B,D,rdnn(n8))
| ~ rdn_translate(C,rdn_pos(D))
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(resolve,[status(thm)],[c_321,c_295]) ).
cnf(c_1272,plain,
( sum(A,A,n8)
| ~ rdn_add_with_carry(rdnn(n0),B,B,rdnn(n8))
| ~ rdn_translate(A,rdn_pos(B)) ),
inference(factor,[status(thm)],[c_1242]) ).
cnf(c_2205,plain,
( rdn_add_with_carry(rdnn(A),rdnn(n4),rdnn(n4),rdnn(B))
| ~ rdn_digit_add(rdnn(n8),rdnn(A),rdnn(B),rdnn(n0)) ),
inference(resolve,[status(thm)],[c_379,c_330]) ).
cnf(c_19864,plain,
( sum(n4,n4,n8)
| ~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)) ),
inference(resolve,[status(thm)],[c_1272,c_291]) ).
cnf(c_9877,plain,
~ rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)),
inference(resolve,[status(thm)],[c_488,c_19864]) ).
cnf(c_19865,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)),
inference(resolve,[status(thm)],[c_2205,c_415]) ).
cnf(c_19862,plain,
$false,
inference(resolve,[status(thm)],[c_9877,c_19865]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM330+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n006.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 02:27:32 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 181430 was started by sandbox2 on n006,
% 0.17/0.44 % Sat Sep 26 02:27:32 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SInE: 148 to sos, 253 to usable, of 401 axioms (tolerance 2.00, depth 0 fixpoint).
% 229.24/31.19
% 229.24/31.19 % given #500 (F,wt=8): 1056 nn26 != n0. [resolve(593,a,279,a),flip(a)].
% 229.24/31.19
% 229.24/31.19 % given #1000 (W,wt=8): 1887 less_or_equal(nn110,n1). [resolve(1700,a,282,b)].
% 229.24/31.19
% 229.24/31.19 % given #1500 (F,wt=8): 2564 nn119 != n2. [resolve(2387,a,279,a),flip(a)].
% 229.24/31.19
% 229.24/31.19 % given #2000 (T,wt=8): 3269 less(n0,n90). [resolve(487,a,109,a),unit_del(a,1663)].
% 229.24/31.19
% 229.24/31.19 % given #2500 (F,wt=8): 5450 -less(n16,n0). [resolve(3343,a,278,b)].
% 229.24/31.19
% 229.24/31.19 % given #3000 (T,wt=8): 4270 less(nn108,n4). [resolve(708,a,254,a)].
% 229.24/31.19
% 229.24/31.19 % given #3500 (F,wt=8): 7322 n16 != n2. [resolve(3814,a,279,a)].
% 229.24/31.19
% 229.24/31.19 % given #4000 (T,wt=8): 5161 less(nn37,n6). [resolve(762,a,183,a)].
% 229.24/31.19
% 229.24/31.19 % given #4500 (A,wt=22): 1371 -rdn_translate(A,rdn_pos(B)) | -sum(A,nn111,C) | sum(nn111,A,C). [resolve(326,a,257,a)].
% 229.24/31.19
% 229.24/31.19 % given #5000 (T,wt=8): 6157 less(n8,n71). [resolve(818,a,90,a),unit_del(a,1669)].
% 229.24/31.19
% 229.24/31.19 % given #5500 (W,wt=8): 6597 less(n9,n32). [resolve(845,a,51,a),unit_del(a,1677)].
% 229.24/31.19
% 229.24/31.19 % given #6000 (F,wt=8): 9889 -less(n5,nn118). [resolve(4671,a,278,b)].
% 229.24/31.19
% 229.24/31.19 % given #6500 (W,wt=8): 9391 less_or_equal(n4,n75). [resolve(4564,a,282,b)].
% 229.24/31.19
% 229.24/31.19 % given #7000 (F,wt=8): 10988 n32 != n5. [resolve(5016,a,279,a)].
% 229.24/31.19
% 229.24/31.19 % given #7500 (T,wt=8): 12004 less_or_equal(n6,n66). [resolve(5389,a,282,b)].
% 229.24/31.19
% 229.24/31.19 % given #8000 (F,wt=8): 12543 -less(n7,nn98). [resolve(5507,a,278,b)].
% 229.24/31.19
% 229.24/31.19 % SZS status Theorem for theBenchmark
% 229.24/31.19
% 229.24/31.19 % Proof 1 at 4.90 (+ 0.87) seconds.
% 229.24/31.19 % Length of proof is 18.
% 229.24/31.19 % Level of proof is 6.
% 229.24/31.19 % Maximum clause weight is 137.000.
% 229.24/31.19 % Given clauses 8174.
% 229.24/31.19
% 229.24/31.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------