%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM327+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 : n003.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 0.08s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM327+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
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 02:23:45 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.57 % Refutation found
% 0.08/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.57 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.57 fof(f1,axiom,(
% 0.08/0.57 rdn_translate(n0,rdn_pos(rdnn(n0))) ),
% 0.08/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.57 fof(f287,axiom,(
% 0.08/0.57 (! [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) ) )),
% 0.08/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.57 fof(f297,axiom,(
% 0.08/0.57 (! [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)) ) )),
% 0.08/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.57 fof(f302,axiom,(
% 0.08/0.57 rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)) ),
% 0.08/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.57 fof(f402,conjecture,(
% 0.08/0.57 (? [X] : sum(X,n0,X) )),
% 0.08/0.57 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.57 fof(f403,negated_conjecture,(
% 0.08/0.57 ~((? [X] : sum(X,n0,X) ))),
% 0.08/0.57 inference(negated_conjecture,[status(cth)],[f402])).
% 0.08/0.57 fof(f404,plain,(
% 0.08/0.57 rdn_translate(n0,rdn_pos(rdnn(n0)))),
% 0.08/0.57 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.57 fof(f716,plain,(
% 0.08/0.57 ![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))),
% 0.08/0.57 inference(pre_NNF_transformation,[status(thm)],[f287])).
% 0.08/0.57 fof(f717,plain,(
% 0.08/0.57 ![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))),
% 0.08/0.57 inference(miniscoping,[status(thm)],[f716])).
% 0.08/0.57 fof(f718,plain,(
% 0.08/0.57 ![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))),
% 0.08/0.57 inference(cnf_transformation,[status(thm)],[f717])).
% 0.08/0.57 fof(f747,plain,(
% 0.08/0.57 ![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)))),
% 0.08/0.57 inference(pre_NNF_transformation,[status(thm)],[f297])).
% 0.08/0.57 fof(f748,plain,(
% 0.08/0.57 ![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)))),
% 0.08/0.57 inference(miniscoping,[status(thm)],[f747])).
% 0.08/0.57 fof(f749,plain,(
% 0.08/0.57 ![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)))),
% 0.08/0.57 inference(cnf_transformation,[status(thm)],[f748])).
% 0.08/0.57 fof(f761,plain,(
% 0.08/0.57 rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0))),
% 0.08/0.57 inference(cnf_transformation,[status(thm)],[f302])).
% 0.08/0.57 fof(f861,plain,(
% 0.08/0.57 (![X]: ~sum(X,n0,X))),
% 0.08/0.57 inference(pre_NNF_transformation,[status(thm)],[f403])).
% 0.08/0.57 fof(f862,plain,(
% 0.08/0.57 ![X0]: (~sum(X0,n0,X0))),
% 0.08/0.57 inference(cnf_transformation,[status(thm)],[f861])).
% 0.08/0.57 fof(f901,plain,(
% 0.08/0.57 ![X0,X1]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n0),rdnn(n0))|rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n0)))),
% 0.08/0.57 inference(resolution,[status(thm)],[f749,f761])).
% 0.08/0.57 fof(f902,plain,(
% 0.08/0.57 rdn_add_with_carry(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0))),
% 0.08/0.57 inference(resolution,[status(thm)],[f901,f761])).
% 0.08/0.57 fof(f904,plain,(
% 0.08/0.57 ![X0,X1,X2]: (~rdn_translate(X0,rdn_pos(rdnn(n0)))|~rdn_translate(X1,rdn_pos(rdnn(n0)))|~rdn_translate(X2,rdn_pos(rdnn(n0)))|sum(X0,X1,X2))),
% 0.08/0.57 inference(resolution,[status(thm)],[f902,f718])).
% 0.08/0.57 fof(f906,plain,(
% 0.08/0.57 ![X0]: (~rdn_translate(X0,rdn_pos(rdnn(n0)))|sum(X0,n0,n0))),
% 0.08/0.57 inference(resolution,[status(thm)],[f904,f404])).
% 0.08/0.57 fof(f910,plain,(
% 0.08/0.57 sum(n0,n0,n0)),
% 0.08/0.57 inference(resolution,[status(thm)],[f906,f404])).
% 0.08/0.57 fof(f911,plain,(
% 0.08/0.57 $false),
% 0.08/0.57 inference(forward_subsumption_resolution,[status(thm)],[f910,f862])).
% 0.08/0.57 % SZS output end CNFRefutation for theBenchmark.p
% 0.55/0.57 % Elapsed time: 0.201387 seconds
% 0.55/0.57 % CPU time: 1.166424 seconds
% 0.55/0.57 % Total memory used: 126.163 MB
% 0.55/0.57 % Net memory used: 124.297 MB
%------------------------------------------------------------------------------