%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM330+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 : n007.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 10.25s 6.75s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM330+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
% 0.12/5.38 % Computer : n007.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Mon Sep 21 02:20:26 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.16/5.40 % Drodi V4.1.1
% 10.25/6.75 % Refutation found
% 10.25/6.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.25/6.75 % SZS output start CNFRefutation for theBenchmark
% 10.25/6.75 fof(f5,axiom,(
% 10.25/6.75 rdn_translate(n4,rdn_pos(rdnn(n4))) ),
% 10.25/6.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.25/6.75 fof(f9,axiom,(
% 10.25/6.75 rdn_translate(n8,rdn_pos(rdnn(n8))) ),
% 10.25/6.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.25/6.75 fof(f287,axiom,(
% 10.25/6.75 (! [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) ) )),
% 10.25/6.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.25/6.75 fof(f297,axiom,(
% 10.25/6.75 (! [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)) ) )),
% 10.25/6.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.25/6.75 fof(f346,axiom,(
% 10.25/6.75 rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)) ),
% 10.25/6.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.25/6.75 fof(f382,axiom,(
% 10.25/6.75 rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)) ),
% 10.25/6.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.25/6.75 fof(f402,conjecture,(
% 10.25/6.75 (? [X,Y] :( sum(X,Y,n8)& X = n4& Y = n4 ) )),
% 10.25/6.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.25/6.75 fof(f403,negated_conjecture,(
% 10.25/6.75 ~((? [X,Y] :( sum(X,Y,n8)& X = n4& Y = n4 ) ))),
% 10.25/6.75 inference(negated_conjecture,[status(cth)],[f402])).
% 10.25/6.75 fof(f408,plain,(
% 10.25/6.75 rdn_translate(n4,rdn_pos(rdnn(n4)))),
% 10.25/6.75 inference(cnf_transformation,[status(thm)],[f5])).
% 10.25/6.75 fof(f412,plain,(
% 10.25/6.75 rdn_translate(n8,rdn_pos(rdnn(n8)))),
% 10.25/6.75 inference(cnf_transformation,[status(thm)],[f9])).
% 10.25/6.75 fof(f716,plain,(
% 10.25/6.75 ![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))),
% 10.25/6.75 inference(pre_NNF_transformation,[status(thm)],[f287])).
% 10.25/6.75 fof(f717,plain,(
% 10.25/6.75 ![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))),
% 10.25/6.75 inference(miniscoping,[status(thm)],[f716])).
% 10.25/6.75 fof(f718,plain,(
% 10.25/6.75 ![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))),
% 10.25/6.75 inference(cnf_transformation,[status(thm)],[f717])).
% 10.25/6.75 fof(f747,plain,(
% 10.25/6.75 ![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)))),
% 10.25/6.75 inference(pre_NNF_transformation,[status(thm)],[f297])).
% 10.25/6.75 fof(f748,plain,(
% 10.25/6.75 ![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)))),
% 10.25/6.75 inference(miniscoping,[status(thm)],[f747])).
% 10.25/6.75 fof(f749,plain,(
% 10.25/6.75 ![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)))),
% 10.25/6.75 inference(cnf_transformation,[status(thm)],[f748])).
% 10.25/6.75 fof(f805,plain,(
% 10.25/6.75 rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0))),
% 10.25/6.75 inference(cnf_transformation,[status(thm)],[f346])).
% 10.25/6.75 fof(f841,plain,(
% 10.25/6.75 rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0))),
% 10.25/6.75 inference(cnf_transformation,[status(thm)],[f382])).
% 10.25/6.75 fof(f861,plain,(
% 10.25/6.75 (![X,Y]: ((~sum(X,Y,n8)|~X=n4)|~Y=n4))),
% 10.25/6.75 inference(pre_NNF_transformation,[status(thm)],[f403])).
% 10.25/6.75 fof(f862,plain,(
% 10.25/6.75 ![Y]: ((![X]: (~sum(X,Y,n8)|~X=n4))|~Y=n4)),
% 10.25/6.75 inference(miniscoping,[status(thm)],[f861])).
% 10.25/6.75 fof(f863,plain,(
% 10.25/6.75 ![X0,X1]: (~sum(X0,X1,n8)|~X0=n4|~X1=n4)),
% 10.25/6.75 inference(cnf_transformation,[status(thm)],[f862])).
% 10.25/6.75 fof(f866,plain,(
% 10.25/6.75 ![X0]: (~sum(X0,n4,n8)|~X0=n4)),
% 10.25/6.75 inference(equality_resolution,[status(thm)],[f863])).
% 10.25/6.75 fof(f1861,plain,(
% 10.25/6.75 ![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))),
% 10.25/6.78 inference(resolution,[status(thm)],[f749,f718])).
% 10.25/6.78 fof(f2516,plain,(
% 10.25/6.78 ![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))),
% 10.25/6.78 inference(resolution,[status(thm)],[f1861,f841])).
% 10.25/6.78 fof(f2533,plain,(
% 10.25/6.78 ![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))),
% 10.25/6.78 inference(resolution,[status(thm)],[f2516,f412])).
% 10.25/6.78 fof(f3152,plain,(
% 10.25/6.78 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n4)))|~rdn_translate(X1,rdn_pos(rdnn(n4)))|sum(X0,X1,n8))),
% 10.25/6.78 inference(resolution,[status(thm)],[f2533,f805])).
% 10.25/6.78 fof(f3335,plain,(
% 10.25/6.78 ![X0]: (~rdn_translate(X0,rdn_pos(rdnn(n4)))|sum(X0,n4,n8))),
% 10.25/6.78 inference(resolution,[status(thm)],[f3152,f408])).
% 10.25/6.78 fof(f4098,plain,(
% 10.25/6.78 sum(n4,n4,n8)),
% 10.25/6.78 inference(resolution,[status(thm)],[f3335,f408])).
% 10.25/6.78 fof(f4100,plain,(
% 10.25/6.78 ~n4=n4),
% 10.25/6.78 inference(resolution,[status(thm)],[f4098,f866])).
% 10.25/6.78 fof(f4104,plain,(
% 10.25/6.78 $false),
% 10.25/6.78 inference(trivial_equality_resolution,[status(thm)],[f4100])).
% 10.25/6.78 % SZS output end CNFRefutation for theBenchmark.p
% 10.25/6.79 % Elapsed time: 1.395231 seconds
% 10.25/6.79 % CPU time: 10.762242 seconds
% 10.25/6.79 % Total memory used: 269.177 MB
% 10.25/6.79 % Net memory used: 250.732 MB
%------------------------------------------------------------------------------