%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM321+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 01:42:32 PM UTC 2026
% Result : Theorem 11.31s 6.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM321+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n015.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Mon Sep 21 02:25:26 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.48 % Drodi V4.1.1
% 11.31/6.98 % Refutation found
% 11.31/6.98 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.31/6.98 % SZS output start CNFRefutation for theBenchmark
% 11.31/6.98 fof(f4,axiom,(
% 11.31/6.98 rdn_translate(n3,rdn_pos(rdnn(n3))) ),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f6,axiom,(
% 11.31/6.98 rdn_translate(n5,rdn_pos(rdnn(n5))) ),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f130,axiom,(
% 11.31/6.98 rdn_translate(nn2,rdn_neg(rdnn(n2))) ),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f268,axiom,(
% 11.31/6.98 rdn_positive_less(rdnn(n2),rdnn(n3)) ),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f269,axiom,(
% 11.31/6.98 rdn_positive_less(rdnn(n3),rdnn(n4)) ),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f270,axiom,(
% 11.31/6.98 rdn_positive_less(rdnn(n4),rdnn(n5)) ),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f275,axiom,(
% 11.31/6.98 (! [X,Y,Z] :( ( rdn_positive_less(rdnn(X),rdnn(Y))& rdn_positive_less(rdnn(Y),rdnn(Z)) )=> rdn_positive_less(rdnn(X),rdnn(Z)) ) )),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f290,axiom,(
% 11.31/6.98 (! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :( ( rdn_translate(X,rdn_pos(RDN_X))& rdn_translate(Y,rdn_neg(RDN_Y))& rdn_positive_less(RDN_Y,RDN_X)& rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)& rdn_translate(Z,rdn_pos(RDN_Z)) )=> sum(X,Y,Z) ) )),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f297,axiom,(
% 11.31/6.98 (! [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)) ) )),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f325,axiom,(
% 11.31/6.98 rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) ),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f352,axiom,(
% 11.31/6.98 rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) ),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f402,conjecture,(
% 11.31/6.98 (? [X] : sum(n5,nn2,X) )),
% 11.31/6.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 11.31/6.98 fof(f403,negated_conjecture,(
% 11.31/6.98 ~((? [X] : sum(n5,nn2,X) ))),
% 11.31/6.98 inference(negated_conjecture,[status(cth)],[f402])).
% 11.31/6.98 fof(f407,plain,(
% 11.31/6.98 rdn_translate(n3,rdn_pos(rdnn(n3)))),
% 11.31/6.98 inference(cnf_transformation,[status(thm)],[f4])).
% 11.31/6.98 fof(f409,plain,(
% 11.31/6.98 rdn_translate(n5,rdn_pos(rdnn(n5)))),
% 11.31/6.98 inference(cnf_transformation,[status(thm)],[f6])).
% 11.31/6.98 fof(f533,plain,(
% 11.31/6.98 rdn_translate(nn2,rdn_neg(rdnn(n2)))),
% 11.31/6.98 inference(cnf_transformation,[status(thm)],[f130])).
% 11.31/6.98 fof(f671,plain,(
% 11.31/6.98 rdn_positive_less(rdnn(n2),rdnn(n3))),
% 11.31/6.98 inference(cnf_transformation,[status(thm)],[f268])).
% 11.31/6.98 fof(f672,plain,(
% 11.31/6.98 rdn_positive_less(rdnn(n3),rdnn(n4))),
% 11.31/6.98 inference(cnf_transformation,[status(thm)],[f269])).
% 11.31/6.98 fof(f673,plain,(
% 11.31/6.98 rdn_positive_less(rdnn(n4),rdnn(n5))),
% 11.31/6.98 inference(cnf_transformation,[status(thm)],[f270])).
% 11.31/6.98 fof(f678,plain,(
% 11.31/6.98 ![X,Y,Z]: ((~rdn_positive_less(rdnn(X),rdnn(Y))|~rdn_positive_less(rdnn(Y),rdnn(Z)))|rdn_positive_less(rdnn(X),rdnn(Z)))),
% 11.31/6.98 inference(pre_NNF_transformation,[status(thm)],[f275])).
% 11.31/6.98 fof(f679,plain,(
% 11.31/6.98 ![X,Z]: ((![Y]: (~rdn_positive_less(rdnn(X),rdnn(Y))|~rdn_positive_less(rdnn(Y),rdnn(Z))))|rdn_positive_less(rdnn(X),rdnn(Z)))),
% 11.31/6.98 inference(miniscoping,[status(thm)],[f678])).
% 11.31/6.98 fof(f680,plain,(
% 11.31/6.98 ![X0,X1,X2]: (~rdn_positive_less(rdnn(X0),rdnn(X1))|~rdn_positive_less(rdnn(X1),rdnn(X2))|rdn_positive_less(rdnn(X0),rdnn(X2)))),
% 11.31/6.98 inference(cnf_transformation,[status(thm)],[f679])).
% 11.31/6.98 fof(f725,plain,(
% 11.31/6.98 ![X,Y,Z,RDN_X,RDN_Y,RDN_Z]: (((((~rdn_translate(X,rdn_pos(RDN_X))|~rdn_translate(Y,rdn_neg(RDN_Y)))|~rdn_positive_less(RDN_Y,RDN_X))|~rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X))|~rdn_translate(Z,rdn_pos(RDN_Z)))|sum(X,Y,Z))),
% 11.31/6.98 inference(pre_NNF_transformation,[status(thm)],[f290])).
% 11.31/6.98 fof(f726,plain,(
% 11.31/6.98 ![X,Y,Z]: ((![RDN_Z]: ((![RDN_X,RDN_Y]: (((~rdn_translate(X,rdn_pos(RDN_X))|~rdn_translate(Y,rdn_neg(RDN_Y)))|~rdn_positive_less(RDN_Y,RDN_X))|~rdn_add_with_carry(rdnn(n0),RDN_Y,RDN_Z,RDN_X)))|~rdn_translate(Z,rdn_pos(RDN_Z))))|sum(X,Y,Z))),
% 11.31/6.98 inference(miniscoping,[status(thm)],[f725])).
% 11.31/6.98 fof(f727,plain,(
% 11.31/6.98 ![X0,X1,X2,X3,X4,X5]: (~rdn_translate(X0,rdn_pos(X1))|~rdn_translate(X2,rdn_neg(X3))|~rdn_positive_less(X3,X1)|~rdn_add_with_carry(rdnn(n0),X3,X4,X1)|~rdn_translate(X5,rdn_pos(X4))|sum(X0,X2,X5))),
% 11.31/7.02 inference(cnf_transformation,[status(thm)],[f726])).
% 11.31/7.02 fof(f747,plain,(
% 11.31/7.02 ![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)))),
% 11.31/7.02 inference(pre_NNF_transformation,[status(thm)],[f297])).
% 11.31/7.02 fof(f748,plain,(
% 11.31/7.02 ![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)))),
% 11.31/7.02 inference(miniscoping,[status(thm)],[f747])).
% 11.31/7.02 fof(f749,plain,(
% 11.31/7.02 ![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)))),
% 11.31/7.02 inference(cnf_transformation,[status(thm)],[f748])).
% 11.31/7.02 fof(f784,plain,(
% 11.31/7.02 rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))),
% 11.31/7.02 inference(cnf_transformation,[status(thm)],[f325])).
% 11.31/7.02 fof(f811,plain,(
% 11.31/7.02 rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))),
% 11.31/7.02 inference(cnf_transformation,[status(thm)],[f352])).
% 11.31/7.02 fof(f861,plain,(
% 11.31/7.02 (![X]: ~sum(n5,nn2,X))),
% 11.31/7.02 inference(pre_NNF_transformation,[status(thm)],[f403])).
% 11.31/7.02 fof(f862,plain,(
% 11.31/7.02 ![X0]: (~sum(n5,nn2,X0))),
% 11.31/7.02 inference(cnf_transformation,[status(thm)],[f861])).
% 11.31/7.02 fof(f1860,plain,(
% 11.31/7.02 ![X0,X1]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))|rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n5)))),
% 11.31/7.02 inference(resolution,[status(thm)],[f749,f811])).
% 11.31/7.02 fof(f1953,plain,(
% 11.31/7.02 rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))),
% 11.31/7.02 inference(resolution,[status(thm)],[f784,f1860])).
% 11.31/7.02 fof(f1957,plain,(
% 11.31/7.02 ![X0,X1,X2]: (~rdn_translate(X0,rdn_pos(rdnn(n5)))|~rdn_translate(X1,rdn_neg(rdnn(n2)))|~rdn_positive_less(rdnn(n2),rdnn(n5))|~rdn_translate(X2,rdn_pos(rdnn(n3)))|sum(X0,X1,X2))),
% 11.31/7.02 inference(resolution,[status(thm)],[f1953,f727])).
% 11.31/7.02 fof(f3031,plain,(
% 11.31/7.02 ![X0,X1,X2,X3]: (~rdn_translate(X0,rdn_pos(rdnn(n5)))|~rdn_translate(X1,rdn_neg(rdnn(n2)))|~rdn_translate(X2,rdn_pos(rdnn(n3)))|sum(X0,X1,X2)|~rdn_positive_less(rdnn(n2),rdnn(X3))|~rdn_positive_less(rdnn(X3),rdnn(n5)))),
% 11.31/7.02 inference(resolution,[status(thm)],[f1957,f680])).
% 11.31/7.02 fof(f4045,plain,(
% 11.31/7.02 ![X0,X1,X2]: (~rdn_translate(X0,rdn_pos(rdnn(n5)))|~rdn_translate(X1,rdn_pos(rdnn(n3)))|sum(X0,nn2,X1)|~rdn_positive_less(rdnn(n2),rdnn(X2))|~rdn_positive_less(rdnn(X2),rdnn(n5)))),
% 11.31/7.02 inference(resolution,[status(thm)],[f3031,f533])).
% 11.31/7.02 fof(f4413,plain,(
% 11.31/7.02 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n3)))|sum(n5,nn2,X0)|~rdn_positive_less(rdnn(n2),rdnn(X1))|~rdn_positive_less(rdnn(X1),rdnn(n5)))),
% 11.31/7.02 inference(resolution,[status(thm)],[f4045,f409])).
% 11.31/7.02 fof(f4414,plain,(
% 11.31/7.02 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n3)))|~rdn_positive_less(rdnn(n2),rdnn(X1))|~rdn_positive_less(rdnn(X1),rdnn(n5)))),
% 11.31/7.02 inference(forward_subsumption_resolution,[status(thm)],[f4413,f862])).
% 11.31/7.02 fof(f4468,plain,(
% 11.31/7.02 ![X0]: (~rdn_positive_less(rdnn(n2),rdnn(X0))|~rdn_positive_less(rdnn(X0),rdnn(n5)))),
% 11.31/7.02 inference(resolution,[status(thm)],[f4414,f407])).
% 11.31/7.02 fof(f4469,plain,(
% 11.31/7.02 ~rdn_positive_less(rdnn(n3),rdnn(n5))),
% 11.31/7.02 inference(resolution,[status(thm)],[f4468,f671])).
% 11.31/7.02 fof(f4471,plain,(
% 11.31/7.02 ![X0]: (~rdn_positive_less(rdnn(n3),rdnn(X0))|~rdn_positive_less(rdnn(X0),rdnn(n5)))),
% 11.31/7.02 inference(resolution,[status(thm)],[f4469,f680])).
% 11.31/7.02 fof(f4497,plain,(
% 11.31/7.02 ~rdn_positive_less(rdnn(n4),rdnn(n5))),
% 11.31/7.02 inference(resolution,[status(thm)],[f4471,f672])).
% 11.31/7.02 fof(f4499,plain,(
% 11.31/7.02 $false),
% 11.31/7.02 inference(forward_subsumption_resolution,[status(thm)],[f4497,f673])).
% 11.31/7.02 % SZS output end CNFRefutation for theBenchmark.p
% 1.75/7.04 % Elapsed time: 1.568599 seconds
% 1.75/7.04 % CPU time: 12.087389 seconds
% 1.75/7.04 % Total memory used: 240.645 MB
% 1.75/7.04 % Net memory used: 227.620 MB
%------------------------------------------------------------------------------