%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM310+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 : Thu Sep 24 01:42:31 PM UTC 2026
% Result : Theorem 4.65s 1.07s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM310+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 02:24:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 4.65/1.07 % Refutation found
% 4.65/1.07 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.65/1.07 % SZS output start CNFRefutation for theBenchmark
% 4.65/1.07 fof(f4,axiom,(
% 4.65/1.07 rdn_translate(n3,rdn_pos(rdnn(n3))) ),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f7,axiom,(
% 4.65/1.07 rdn_translate(n6,rdn_pos(rdnn(n6))) ),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f131,axiom,(
% 4.65/1.07 rdn_translate(nn3,rdn_neg(rdnn(n3))) ),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f268,axiom,(
% 4.65/1.07 rdn_positive_less(rdnn(n2),rdnn(n3)) ),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f283,axiom,(
% 4.65/1.07 (! [X,Y,RDN_X,RDN_Y] :( ( rdn_translate(X,rdn_neg(RDN_X))& rdn_translate(Y,rdn_neg(RDN_Y))& rdn_positive_less(RDN_Y,RDN_X) )=> less(X,Y) ) )),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f284,axiom,(
% 4.65/1.07 (! [X,Y] :( less(X,Y)<=> ( ~ less(Y,X)& Y != X ) ) )),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f287,axiom,(
% 4.65/1.07 (! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :( ( rdn_translate(X,rdn_pos(RDN_X))& rdn_translate(Y,rdn_pos(RDN_Y))& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)& rdn_translate(Z,rdn_pos(RDN_Z)) )=> sum(X,Y,Z) ) )),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f294,axiom,(
% 4.65/1.07 (! [X1,X2,Y,Z] :( ( sum(X1,Y,Z)& sum(X2,Y,Z) )=> X1 = X2 ) )),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f297,axiom,(
% 4.65/1.07 (! [C,D1,D2,RD,ID] :( ( rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))& rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0)) )=> rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)) ) )),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f335,axiom,(
% 4.65/1.07 rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)) ),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f362,axiom,(
% 4.65/1.07 rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)) ),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f402,conjecture,(
% 4.65/1.07 ~ sum(n2,n3,n6) ),
% 4.65/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.65/1.07 fof(f403,negated_conjecture,(
% 4.65/1.07 ~(~ sum(n2,n3,n6) )),
% 4.65/1.07 inference(negated_conjecture,[status(cth)],[f402])).
% 4.65/1.07 fof(f407,plain,(
% 4.65/1.07 rdn_translate(n3,rdn_pos(rdnn(n3)))),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f4])).
% 4.65/1.07 fof(f410,plain,(
% 4.65/1.07 rdn_translate(n6,rdn_pos(rdnn(n6)))),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f7])).
% 4.65/1.07 fof(f534,plain,(
% 4.65/1.07 rdn_translate(nn3,rdn_neg(rdnn(n3)))),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f131])).
% 4.65/1.07 fof(f671,plain,(
% 4.65/1.07 rdn_positive_less(rdnn(n2),rdnn(n3))),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f268])).
% 4.65/1.07 fof(f700,plain,(
% 4.65/1.07 ![X,Y,RDN_X,RDN_Y]: (((~rdn_translate(X,rdn_neg(RDN_X))|~rdn_translate(Y,rdn_neg(RDN_Y)))|~rdn_positive_less(RDN_Y,RDN_X))|less(X,Y))),
% 4.65/1.07 inference(pre_NNF_transformation,[status(thm)],[f283])).
% 4.65/1.07 fof(f701,plain,(
% 4.65/1.07 ![X,Y]: ((![RDN_X,RDN_Y]: ((~rdn_translate(X,rdn_neg(RDN_X))|~rdn_translate(Y,rdn_neg(RDN_Y)))|~rdn_positive_less(RDN_Y,RDN_X)))|less(X,Y))),
% 4.65/1.07 inference(miniscoping,[status(thm)],[f700])).
% 4.65/1.07 fof(f702,plain,(
% 4.65/1.07 ![X0,X1,X2,X3]: (~rdn_translate(X0,rdn_neg(X1))|~rdn_translate(X2,rdn_neg(X3))|~rdn_positive_less(X3,X1)|less(X0,X2))),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f701])).
% 4.65/1.07 fof(f703,plain,(
% 4.65/1.07 ![X,Y]: ((~less(X,Y)|(~less(Y,X)&~Y=X))&(less(X,Y)|(less(Y,X)|Y=X)))),
% 4.65/1.07 inference(NNF_transformation,[status(thm)],[f284])).
% 4.65/1.07 fof(f704,plain,(
% 4.65/1.07 (![X,Y]: (~less(X,Y)|(~less(Y,X)&~Y=X)))&(![X,Y]: (less(X,Y)|(less(Y,X)|Y=X)))),
% 4.65/1.07 inference(miniscoping,[status(thm)],[f703])).
% 4.65/1.07 fof(f706,plain,(
% 4.65/1.07 ![X0,X1]: (~less(X0,X1)|~X1=X0)),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f704])).
% 4.65/1.07 fof(f716,plain,(
% 4.65/1.07 ![X,Y,Z,RDN_X,RDN_Y,RDN_Z]: ((((~rdn_translate(X,rdn_pos(RDN_X))|~rdn_translate(Y,rdn_pos(RDN_Y)))|~rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z))|~rdn_translate(Z,rdn_pos(RDN_Z)))|sum(X,Y,Z))),
% 4.65/1.07 inference(pre_NNF_transformation,[status(thm)],[f287])).
% 4.65/1.07 fof(f717,plain,(
% 4.65/1.07 ![X,Y,Z]: ((![RDN_Z]: ((![RDN_X,RDN_Y]: ((~rdn_translate(X,rdn_pos(RDN_X))|~rdn_translate(Y,rdn_pos(RDN_Y)))|~rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)))|~rdn_translate(Z,rdn_pos(RDN_Z))))|sum(X,Y,Z))),
% 4.65/1.07 inference(miniscoping,[status(thm)],[f716])).
% 4.65/1.07 fof(f718,plain,(
% 4.65/1.07 ![X0,X1,X2,X3,X4,X5]: (~rdn_translate(X0,rdn_pos(X1))|~rdn_translate(X2,rdn_pos(X3))|~rdn_add_with_carry(rdnn(n0),X1,X3,X4)|~rdn_translate(X5,rdn_pos(X4))|sum(X0,X2,X5))),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f717])).
% 4.65/1.07 fof(f737,plain,(
% 4.65/1.07 ![X1,X2,Y,Z]: ((~sum(X1,Y,Z)|~sum(X2,Y,Z))|X1=X2)),
% 4.65/1.07 inference(pre_NNF_transformation,[status(thm)],[f294])).
% 4.65/1.07 fof(f738,plain,(
% 4.65/1.07 ![X1,X2]: ((![Y,Z]: (~sum(X1,Y,Z)|~sum(X2,Y,Z)))|X1=X2)),
% 4.65/1.07 inference(miniscoping,[status(thm)],[f737])).
% 4.65/1.07 fof(f739,plain,(
% 4.65/1.07 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X3,X1,X2)|X0=X3)),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f738])).
% 4.65/1.07 fof(f747,plain,(
% 4.65/1.07 ![C,D1,D2,RD,ID]: ((~rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))|~rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0)))|rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)))),
% 4.65/1.07 inference(pre_NNF_transformation,[status(thm)],[f297])).
% 4.65/1.07 fof(f748,plain,(
% 4.65/1.07 ![C,D1,D2,RD]: ((![ID]: (~rdn_digit_add(rdnn(D1),rdnn(D2),rdnn(ID),rdnn(n0))|~rdn_digit_add(rdnn(ID),rdnn(C),rdnn(RD),rdnn(n0))))|rdn_add_with_carry(rdnn(C),rdnn(D1),rdnn(D2),rdnn(RD)))),
% 4.65/1.07 inference(miniscoping,[status(thm)],[f747])).
% 4.65/1.07 fof(f749,plain,(
% 4.65/1.07 ![X0,X1,X2,X3,X4]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))|~rdn_digit_add(rdnn(X2),rdnn(X3),rdnn(X4),rdnn(n0))|rdn_add_with_carry(rdnn(X3),rdnn(X0),rdnn(X1),rdnn(X4)))),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f748])).
% 4.65/1.07 fof(f794,plain,(
% 4.65/1.07 rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0))),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f335])).
% 4.65/1.07 fof(f821,plain,(
% 4.65/1.07 rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0))),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f362])).
% 4.65/1.07 fof(f861,plain,(
% 4.65/1.07 sum(n2,n3,n6)),
% 4.65/1.07 inference(cnf_transformation,[status(thm)],[f403])).
% 4.65/1.07 fof(f862,plain,(
% 4.65/1.07 ![X0]: (~less(X0,X0))),
% 4.65/1.07 inference(destructive_equality_resolution,[status(thm)],[f706])).
% 4.65/1.07 fof(f866,plain,(
% 4.65/1.07 ![X0]: (~sum(X0,n3,n6)|X0=n2)),
% 4.65/1.07 inference(resolution,[status(thm)],[f739,f861])).
% 4.65/1.07 fof(f2882,plain,(
% 4.65/1.07 ![X0,X1,X2]: (~rdn_translate(X0,rdn_neg(X1))|~rdn_translate(X0,rdn_neg(X2))|~rdn_positive_less(X2,X1))),
% 4.65/1.07 inference(resolution,[status(thm)],[f702,f862])).
% 4.65/1.07 fof(f3064,plain,(
% 4.65/1.07 ![X0,X1,X2,X3,X4,X5,X6]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(X2),rdnn(n0))|~rdn_digit_add(rdnn(X2),rdnn(n0),rdnn(X3),rdnn(n0))|~rdn_translate(X4,rdn_pos(rdnn(X0)))|~rdn_translate(X5,rdn_pos(rdnn(X1)))|~rdn_translate(X6,rdn_pos(rdnn(X3)))|sum(X4,X5,X6))),
% 4.65/1.07 inference(resolution,[status(thm)],[f749,f718])).
% 4.65/1.07 fof(f3753,plain,(
% 4.65/1.07 ![X0]: (~rdn_translate(X0,rdn_neg(rdnn(n3)))|~rdn_translate(X0,rdn_neg(rdnn(n2))))),
% 4.65/1.07 inference(resolution,[status(thm)],[f2882,f671])).
% 4.65/1.07 fof(f5584,plain,(
% 4.65/1.07 ![X0,X1,X2,X3,X4]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n6),rdnn(n0))|~rdn_translate(X2,rdn_pos(rdnn(X0)))|~rdn_translate(X3,rdn_pos(rdnn(X1)))|~rdn_translate(X4,rdn_pos(rdnn(n6)))|sum(X2,X3,X4))),
% 4.65/1.07 inference(resolution,[status(thm)],[f3064,f821])).
% 4.65/1.07 fof(f5628,plain,(
% 4.65/1.07 ![X0,X1,X2,X3]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n6),rdnn(n0))|~rdn_translate(X2,rdn_pos(rdnn(X0)))|~rdn_translate(X3,rdn_pos(rdnn(X1)))|sum(X2,X3,n6))),
% 4.65/1.07 inference(resolution,[status(thm)],[f5584,f410])).
% 4.65/1.07 fof(f5788,plain,(
% 4.65/1.07 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n3)))|~rdn_translate(X1,rdn_pos(rdnn(n3)))|sum(X0,X1,n6))),
% 4.65/1.07 inference(resolution,[status(thm)],[f5628,f794])).
% 4.65/1.07 fof(f6128,plain,(
% 4.65/1.07 ![X0]: (~rdn_translate(X0,rdn_pos(rdnn(n3)))|sum(X0,n3,n6))),
% 4.65/1.07 inference(resolution,[status(thm)],[f5788,f407])).
% 4.65/1.07 fof(f6441,plain,(
% 4.65/1.07 sum(n3,n3,n6)),
% 4.65/1.07 inference(resolution,[status(thm)],[f6128,f407])).
% 4.65/1.07 fof(f6442,plain,(
% 4.65/1.07 n3=n2),
% 4.65/1.07 inference(resolution,[status(thm)],[f6441,f866])).
% 4.65/1.07 fof(f6447,plain,(
% 4.65/1.07 ![X0]: (~rdn_translate(X0,rdn_neg(rdnn(n3)))|~rdn_translate(X0,rdn_neg(rdnn(n3))))),
% 4.65/1.07 inference(backward_demodulation,[status(thm)],[f6442,f3753])).
% 4.65/1.07 fof(f6633,plain,(
% 4.65/1.07 ![X0]: (~rdn_translate(X0,rdn_neg(rdnn(n3))))),
% 4.65/1.07 inference(duplicate_literals_removal,[status(thm)],[f6447])).
% 4.65/1.07 fof(f6634,plain,(
% 4.65/1.07 $false),
% 4.65/1.07 inference(backward_subsumption_resolution,[status(thm)],[f534,f6633])).
% 4.65/1.07 % SZS output end CNFRefutation for theBenchmark.p
% 0.43/1.12 % Elapsed time: 0.745710 seconds
% 0.43/1.12 % CPU time: 5.423301 seconds
% 0.43/1.12 % Total memory used: 179.063 MB
% 0.43/1.12 % Net memory used: 172.448 MB
%------------------------------------------------------------------------------