%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM324+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 122.68s 15.95s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM324+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
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:25:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 122.68/15.95 % Refutation found
% 122.68/15.95 % SZS status Theorem for theBenchmark: Theorem is valid
% 122.68/15.95 % SZS output start CNFRefutation for theBenchmark
% 122.68/15.95 fof(f3,axiom,(
% 122.68/15.95 rdn_translate(n2,rdn_pos(rdnn(n2))) ),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f131,axiom,(
% 122.68/15.95 rdn_translate(nn3,rdn_neg(rdnn(n3))) ),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f133,axiom,(
% 122.68/15.95 rdn_translate(nn5,rdn_neg(rdnn(n5))) ),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f268,axiom,(
% 122.68/15.95 rdn_positive_less(rdnn(n2),rdnn(n3)) ),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f269,axiom,(
% 122.68/15.95 rdn_positive_less(rdnn(n3),rdnn(n4)) ),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f270,axiom,(
% 122.68/15.95 rdn_positive_less(rdnn(n4),rdnn(n5)) ),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f275,axiom,(
% 122.68/15.95 (! [X,Y,Z] :( ( rdn_positive_less(rdnn(X),rdnn(Y))& rdn_positive_less(rdnn(Y),rdnn(Z)) )=> rdn_positive_less(rdnn(X),rdnn(Z)) ) )),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f289,axiom,(
% 122.68/15.95 (! [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_X,RDN_Y)& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)& rdn_translate(Z,rdn_neg(RDN_Z)) )=> sum(X,Y,Z) ) )),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f297,axiom,(
% 122.68/15.95 (! [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)) ) )),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f325,axiom,(
% 122.68/15.95 rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) ),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f352,axiom,(
% 122.68/15.95 rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) ),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f402,conjecture,(
% 122.68/15.95 (? [X] : sum(X,nn5,nn3) )),
% 122.68/15.95 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 122.68/15.95 fof(f403,negated_conjecture,(
% 122.68/15.95 ~((? [X] : sum(X,nn5,nn3) ))),
% 122.68/15.95 inference(negated_conjecture,[status(cth)],[f402])).
% 122.68/15.95 fof(f406,plain,(
% 122.68/15.95 rdn_translate(n2,rdn_pos(rdnn(n2)))),
% 122.68/15.95 inference(cnf_transformation,[status(thm)],[f3])).
% 122.68/15.95 fof(f534,plain,(
% 122.68/15.95 rdn_translate(nn3,rdn_neg(rdnn(n3)))),
% 122.68/15.95 inference(cnf_transformation,[status(thm)],[f131])).
% 122.68/15.95 fof(f536,plain,(
% 122.68/15.95 rdn_translate(nn5,rdn_neg(rdnn(n5)))),
% 122.68/15.95 inference(cnf_transformation,[status(thm)],[f133])).
% 122.68/15.95 fof(f671,plain,(
% 122.68/15.95 rdn_positive_less(rdnn(n2),rdnn(n3))),
% 122.68/15.95 inference(cnf_transformation,[status(thm)],[f268])).
% 122.68/15.95 fof(f672,plain,(
% 122.68/15.95 rdn_positive_less(rdnn(n3),rdnn(n4))),
% 122.68/15.95 inference(cnf_transformation,[status(thm)],[f269])).
% 122.68/15.95 fof(f673,plain,(
% 122.68/15.95 rdn_positive_less(rdnn(n4),rdnn(n5))),
% 122.68/15.95 inference(cnf_transformation,[status(thm)],[f270])).
% 122.68/15.95 fof(f678,plain,(
% 122.68/15.95 ![X,Y,Z]: ((~rdn_positive_less(rdnn(X),rdnn(Y))|~rdn_positive_less(rdnn(Y),rdnn(Z)))|rdn_positive_less(rdnn(X),rdnn(Z)))),
% 122.68/15.95 inference(pre_NNF_transformation,[status(thm)],[f275])).
% 122.68/15.95 fof(f679,plain,(
% 122.68/15.95 ![X,Z]: ((![Y]: (~rdn_positive_less(rdnn(X),rdnn(Y))|~rdn_positive_less(rdnn(Y),rdnn(Z))))|rdn_positive_less(rdnn(X),rdnn(Z)))),
% 122.68/15.95 inference(miniscoping,[status(thm)],[f678])).
% 122.68/15.95 fof(f680,plain,(
% 122.68/15.95 ![X0,X1,X2]: (~rdn_positive_less(rdnn(X0),rdnn(X1))|~rdn_positive_less(rdnn(X1),rdnn(X2))|rdn_positive_less(rdnn(X0),rdnn(X2)))),
% 122.68/15.95 inference(cnf_transformation,[status(thm)],[f679])).
% 122.68/15.95 fof(f722,plain,(
% 122.68/15.95 ![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_X,RDN_Y))|~rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y))|~rdn_translate(Z,rdn_neg(RDN_Z)))|sum(X,Y,Z))),
% 122.68/15.95 inference(pre_NNF_transformation,[status(thm)],[f289])).
% 122.68/15.95 fof(f723,plain,(
% 122.68/15.95 ![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_X,RDN_Y))|~rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Z,RDN_Y)))|~rdn_translate(Z,rdn_neg(RDN_Z))))|sum(X,Y,Z))),
% 122.68/15.95 inference(miniscoping,[status(thm)],[f722])).
% 122.68/15.95 fof(f724,plain,(
% 122.68/15.95 ![X0,X1,X2,X3,X4,X5]: (~rdn_translate(X0,rdn_pos(X1))|~rdn_translate(X2,rdn_neg(X3))|~rdn_positive_less(X1,X3)|~rdn_add_with_carry(rdnn(n0),X1,X4,X3)|~rdn_translate(X5,rdn_neg(X4))|sum(X0,X2,X5))),
% 100.64/16.09 inference(cnf_transformation,[status(thm)],[f723])).
% 100.64/16.09 fof(f747,plain,(
% 100.64/16.09 ![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)))),
% 100.64/16.09 inference(pre_NNF_transformation,[status(thm)],[f297])).
% 100.64/16.09 fof(f748,plain,(
% 100.64/16.09 ![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)))),
% 100.64/16.09 inference(miniscoping,[status(thm)],[f747])).
% 100.64/16.09 fof(f749,plain,(
% 100.64/16.09 ![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)))),
% 100.64/16.09 inference(cnf_transformation,[status(thm)],[f748])).
% 100.64/16.09 fof(f784,plain,(
% 100.64/16.09 rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))),
% 100.64/16.09 inference(cnf_transformation,[status(thm)],[f325])).
% 100.64/16.09 fof(f811,plain,(
% 100.64/16.09 rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))),
% 100.64/16.09 inference(cnf_transformation,[status(thm)],[f352])).
% 100.64/16.09 fof(f861,plain,(
% 100.64/16.09 (![X]: ~sum(X,nn5,nn3))),
% 100.64/16.09 inference(pre_NNF_transformation,[status(thm)],[f403])).
% 100.64/16.09 fof(f862,plain,(
% 100.64/16.09 ![X0]: (~sum(X0,nn5,nn3))),
% 100.64/16.09 inference(cnf_transformation,[status(thm)],[f861])).
% 100.64/16.09 fof(f2169,plain,(
% 100.64/16.09 ![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)))),
% 100.64/16.09 inference(resolution,[status(thm)],[f811,f749])).
% 100.64/16.09 fof(f2948,plain,(
% 100.64/16.09 rdn_add_with_carry(rdnn(n0),rdnn(n2),rdnn(n3),rdnn(n5))),
% 100.64/16.09 inference(resolution,[status(thm)],[f2169,f784])).
% 100.64/16.09 fof(f3960,plain,(
% 100.64/16.09 ![X0,X1,X2]: (~rdn_translate(X0,rdn_pos(rdnn(n2)))|~rdn_translate(X1,rdn_neg(rdnn(n5)))|~rdn_positive_less(rdnn(n2),rdnn(n5))|~rdn_translate(X2,rdn_neg(rdnn(n3)))|sum(X0,X1,X2))),
% 100.64/16.09 inference(resolution,[status(thm)],[f2948,f724])).
% 100.64/16.09 fof(f7723,plain,(
% 100.64/16.09 ![X0,X1,X2,X3]: (~rdn_translate(X0,rdn_pos(rdnn(n2)))|~rdn_translate(X1,rdn_neg(rdnn(n5)))|~rdn_translate(X2,rdn_neg(rdnn(n3)))|sum(X0,X1,X2)|~rdn_positive_less(rdnn(n2),rdnn(X3))|~rdn_positive_less(rdnn(X3),rdnn(n5)))),
% 100.64/16.09 inference(resolution,[status(thm)],[f3960,f680])).
% 100.64/16.09 fof(f11687,plain,(
% 100.64/16.09 ![X0,X1,X2]: (~rdn_translate(X0,rdn_pos(rdnn(n2)))|~rdn_translate(X1,rdn_neg(rdnn(n3)))|sum(X0,nn5,X1)|~rdn_positive_less(rdnn(n2),rdnn(X2))|~rdn_positive_less(rdnn(X2),rdnn(n5)))),
% 100.64/16.09 inference(resolution,[status(thm)],[f7723,f536])).
% 100.64/16.09 fof(f11692,plain,(
% 100.64/16.09 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n2)))|sum(X0,nn5,nn3)|~rdn_positive_less(rdnn(n2),rdnn(X1))|~rdn_positive_less(rdnn(X1),rdnn(n5)))),
% 100.64/16.09 inference(resolution,[status(thm)],[f11687,f534])).
% 100.64/16.09 fof(f11693,plain,(
% 100.64/16.09 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n2)))|~rdn_positive_less(rdnn(n2),rdnn(X1))|~rdn_positive_less(rdnn(X1),rdnn(n5)))),
% 100.64/16.09 inference(forward_subsumption_resolution,[status(thm)],[f11692,f862])).
% 100.64/16.09 fof(f11694,plain,(
% 100.64/16.09 ![X0]: (~rdn_positive_less(rdnn(n2),rdnn(X0))|~rdn_positive_less(rdnn(X0),rdnn(n5)))),
% 100.64/16.09 inference(resolution,[status(thm)],[f11693,f406])).
% 100.64/16.09 fof(f11697,plain,(
% 100.64/16.09 ~rdn_positive_less(rdnn(n3),rdnn(n5))),
% 100.64/16.09 inference(resolution,[status(thm)],[f11694,f671])).
% 100.64/16.09 fof(f11701,plain,(
% 100.64/16.09 ![X0]: (~rdn_positive_less(rdnn(n3),rdnn(X0))|~rdn_positive_less(rdnn(X0),rdnn(n5)))),
% 100.64/16.09 inference(resolution,[status(thm)],[f11697,f680])).
% 100.64/16.09 fof(f11711,plain,(
% 100.64/16.09 ~rdn_positive_less(rdnn(n4),rdnn(n5))),
% 100.64/16.09 inference(resolution,[status(thm)],[f11701,f672])).
% 100.64/16.09 fof(f11713,plain,(
% 100.64/16.09 $false),
% 100.64/16.09 inference(forward_subsumption_resolution,[status(thm)],[f11711,f673])).
% 100.64/16.09 % SZS output end CNFRefutation for theBenchmark.p
% 23.52/16.17 % Elapsed time: 15.784182 seconds
% 23.52/16.17 % CPU time: 124.152528 seconds
% 23.52/16.17 % Total memory used: 775.031 MB
% 23.52/16.17 % Net memory used: 733.273 MB
%------------------------------------------------------------------------------