%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM342+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 : n002.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 01:42:33 PM UTC 2026
% Result : Theorem 257.59s 43.05s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM342+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
% 0.10/10.38 % Computer : n002.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Mon Sep 21 02:25:57 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.14/10.40 % Drodi V4.1.1
% 257.59/43.05 % Refutation found
% 257.59/43.05 % SZS status Theorem for theBenchmark: Theorem is valid
% 257.59/43.05 % SZS output start CNFRefutation for theBenchmark
% 257.59/43.05 fof(f1,axiom,(
% 257.59/43.05 rdn_translate(n0,rdn_pos(rdnn(n0))) ),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f5,axiom,(
% 257.59/43.05 rdn_translate(n4,rdn_pos(rdnn(n4))) ),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f9,axiom,(
% 257.59/43.05 rdn_translate(n8,rdn_pos(rdnn(n8))) ),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f287,axiom,(
% 257.59/43.05 (! [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) ) )),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f296,axiom,(
% 257.59/43.05 (! [X,Y,Z] :( sum(Y,Z,X)<=> difference(X,Y,Z) ) )),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f297,axiom,(
% 257.59/43.05 (! [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)) ) )),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f342,axiom,(
% 257.59/43.05 rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)) ),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f346,axiom,(
% 257.59/43.05 rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)) ),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f382,axiom,(
% 257.59/43.05 rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)) ),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f402,conjecture,(
% 257.59/43.05 (? [X,Y] :( sum(X,Y,n8)& difference(X,Y,n0) ) )),
% 257.59/43.05 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 257.59/43.05 fof(f403,negated_conjecture,(
% 257.59/43.05 ~((? [X,Y] :( sum(X,Y,n8)& difference(X,Y,n0) ) ))),
% 257.59/43.05 inference(negated_conjecture,[status(cth)],[f402])).
% 257.59/43.05 fof(f404,plain,(
% 257.59/43.05 rdn_translate(n0,rdn_pos(rdnn(n0)))),
% 257.59/43.05 inference(cnf_transformation,[status(thm)],[f1])).
% 257.59/43.05 fof(f408,plain,(
% 257.59/43.05 rdn_translate(n4,rdn_pos(rdnn(n4)))),
% 257.59/43.05 inference(cnf_transformation,[status(thm)],[f5])).
% 257.59/43.05 fof(f412,plain,(
% 257.59/43.05 rdn_translate(n8,rdn_pos(rdnn(n8)))),
% 257.59/43.05 inference(cnf_transformation,[status(thm)],[f9])).
% 257.59/43.05 fof(f716,plain,(
% 257.59/43.05 ![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))),
% 257.59/43.05 inference(pre_NNF_transformation,[status(thm)],[f287])).
% 257.59/43.05 fof(f717,plain,(
% 257.59/43.05 ![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))),
% 257.59/43.05 inference(miniscoping,[status(thm)],[f716])).
% 257.59/43.05 fof(f718,plain,(
% 257.59/43.05 ![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))),
% 257.59/43.05 inference(cnf_transformation,[status(thm)],[f717])).
% 257.59/43.05 fof(f743,plain,(
% 257.59/43.05 ![X,Y,Z]: ((~sum(Y,Z,X)|difference(X,Y,Z))&(sum(Y,Z,X)|~difference(X,Y,Z)))),
% 257.59/43.05 inference(NNF_transformation,[status(thm)],[f296])).
% 257.59/43.05 fof(f744,plain,(
% 257.59/43.05 (![X,Y,Z]: (~sum(Y,Z,X)|difference(X,Y,Z)))&(![X,Y,Z]: (sum(Y,Z,X)|~difference(X,Y,Z)))),
% 257.59/43.05 inference(miniscoping,[status(thm)],[f743])).
% 257.59/43.05 fof(f745,plain,(
% 257.59/43.05 ![X0,X1,X2]: (~sum(X0,X1,X2)|difference(X2,X0,X1))),
% 257.59/43.05 inference(cnf_transformation,[status(thm)],[f744])).
% 257.59/43.05 fof(f747,plain,(
% 257.59/43.05 ![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)))),
% 257.59/43.05 inference(pre_NNF_transformation,[status(thm)],[f297])).
% 257.59/43.05 fof(f748,plain,(
% 257.59/43.05 ![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)))),
% 257.59/43.05 inference(miniscoping,[status(thm)],[f747])).
% 257.59/43.05 fof(f749,plain,(
% 257.59/43.05 ![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)))),
% 196.10/43.31 inference(cnf_transformation,[status(thm)],[f748])).
% 196.10/43.31 fof(f801,plain,(
% 196.10/43.31 rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0))),
% 196.10/43.31 inference(cnf_transformation,[status(thm)],[f342])).
% 196.10/43.31 fof(f805,plain,(
% 196.10/43.31 rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0))),
% 196.10/43.31 inference(cnf_transformation,[status(thm)],[f346])).
% 196.10/43.31 fof(f841,plain,(
% 196.10/43.31 rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0))),
% 196.10/43.31 inference(cnf_transformation,[status(thm)],[f382])).
% 196.10/43.31 fof(f861,plain,(
% 196.10/43.31 (![X,Y]: (~sum(X,Y,n8)|~difference(X,Y,n0)))),
% 196.10/43.31 inference(pre_NNF_transformation,[status(thm)],[f403])).
% 196.10/43.31 fof(f862,plain,(
% 196.10/43.31 ![X0,X1]: (~sum(X0,X1,n8)|~difference(X0,X1,n0))),
% 196.10/43.31 inference(cnf_transformation,[status(thm)],[f861])).
% 196.10/43.31 fof(f1824,plain,(
% 196.10/43.31 ![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))),
% 196.10/43.31 inference(resolution,[status(thm)],[f749,f718])).
% 196.10/43.31 fof(f2420,plain,(
% 196.10/43.31 ![X0,X1,X2,X3,X4]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n8),rdnn(n0))|~rdn_translate(X2,rdn_pos(rdnn(X0)))|~rdn_translate(X3,rdn_pos(rdnn(X1)))|~rdn_translate(X4,rdn_pos(rdnn(n8)))|sum(X2,X3,X4))),
% 196.10/43.31 inference(resolution,[status(thm)],[f1824,f841])).
% 196.10/43.31 fof(f2424,plain,(
% 196.10/43.31 ![X0,X1,X2,X3,X4]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n4),rdnn(n0))|~rdn_translate(X2,rdn_pos(rdnn(X0)))|~rdn_translate(X3,rdn_pos(rdnn(X1)))|~rdn_translate(X4,rdn_pos(rdnn(n4)))|sum(X2,X3,X4))),
% 196.10/43.31 inference(resolution,[status(thm)],[f1824,f801])).
% 196.10/43.31 fof(f2434,plain,(
% 196.10/43.31 ![X0,X1,X2,X3]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n8),rdnn(n0))|~rdn_translate(X2,rdn_pos(rdnn(X0)))|~rdn_translate(X3,rdn_pos(rdnn(X1)))|sum(X2,X3,n8))),
% 196.10/43.31 inference(resolution,[status(thm)],[f2420,f412])).
% 196.10/43.31 fof(f3082,plain,(
% 196.10/43.31 ![X0,X1,X2,X3]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n4),rdnn(n0))|~rdn_translate(X2,rdn_pos(rdnn(X0)))|~rdn_translate(X3,rdn_pos(rdnn(X1)))|sum(X2,X3,n4))),
% 196.10/43.31 inference(resolution,[status(thm)],[f2424,f408])).
% 196.10/43.31 fof(f3741,plain,(
% 196.10/43.31 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n4)))|~rdn_translate(X1,rdn_pos(rdnn(n4)))|sum(X0,X1,n8))),
% 196.10/43.31 inference(resolution,[status(thm)],[f2434,f805])).
% 196.10/43.31 fof(f3931,plain,(
% 196.10/43.31 ![X0]: (~rdn_translate(X0,rdn_pos(rdnn(n4)))|sum(X0,n4,n8))),
% 196.10/43.31 inference(resolution,[status(thm)],[f3741,f408])).
% 196.10/43.31 fof(f4686,plain,(
% 196.10/43.31 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n4)))|~rdn_translate(X1,rdn_pos(rdnn(n0)))|sum(X0,X1,n4))),
% 196.10/43.31 inference(resolution,[status(thm)],[f3082,f801])).
% 196.10/43.31 fof(f4773,plain,(
% 196.10/43.31 sum(n4,n4,n8)),
% 196.10/43.31 inference(resolution,[status(thm)],[f3931,f408])).
% 196.10/43.31 fof(f9676,plain,(
% 196.10/43.31 ![X0]: (~rdn_translate(X0,rdn_pos(rdnn(n0)))|sum(n4,X0,n4))),
% 196.10/43.31 inference(resolution,[status(thm)],[f4686,f408])).
% 196.10/43.31 fof(f16625,plain,(
% 196.10/43.31 sum(n4,n0,n4)),
% 196.10/43.31 inference(resolution,[status(thm)],[f9676,f404])).
% 196.10/43.31 fof(f17093,plain,(
% 196.10/43.31 difference(n4,n4,n0)),
% 196.10/43.31 inference(resolution,[status(thm)],[f16625,f745])).
% 196.10/43.31 fof(f17230,plain,(
% 196.10/43.31 ~sum(n4,n4,n8)),
% 196.10/43.31 inference(resolution,[status(thm)],[f17093,f862])).
% 196.10/43.31 fof(f17232,plain,(
% 196.10/43.31 $false),
% 196.10/43.31 inference(forward_subsumption_resolution,[status(thm)],[f17230,f4773])).
% 196.10/43.31 % SZS output end CNFRefutation for theBenchmark.p
% 62.83/43.41 % Elapsed time: 33.010922 seconds
% 62.83/43.41 % CPU time: 259.844087 seconds
% 62.83/43.41 % Total memory used: 1.198 GB
% 62.83/43.41 % Net memory used: 1.152 GB
%------------------------------------------------------------------------------