%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM313+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 01:42:31 PM UTC 2026
% Result : Theorem 15.76s 2.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM313+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.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 02:16:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 15.76/2.45 % Refutation found
% 15.76/2.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 15.76/2.45 % SZS output start CNFRefutation for theBenchmark
% 15.76/2.45 fof(f3,axiom,(
% 15.76/2.45 rdn_translate(n2,rdn_pos(rdnn(n2))) ),
% 15.76/2.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.76/2.45 fof(f4,axiom,(
% 15.76/2.45 rdn_translate(n3,rdn_pos(rdnn(n3))) ),
% 15.76/2.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.76/2.45 fof(f6,axiom,(
% 15.76/2.45 rdn_translate(n5,rdn_pos(rdnn(n5))) ),
% 15.76/2.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.76/2.45 fof(f287,axiom,(
% 15.76/2.45 (! [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) ) )),
% 15.76/2.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.76/2.45 fof(f295,axiom,(
% 15.76/2.45 (! [X,Y1,Y2,Z] :( ( sum(X,Y1,Z)& sum(X,Y2,Z) )=> Y1 = Y2 ) )),
% 15.76/2.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.76/2.45 fof(f297,axiom,(
% 15.76/2.45 (! [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)) ) )),
% 15.76/2.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.76/2.45 fof(f325,axiom,(
% 15.76/2.45 rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) ),
% 15.76/2.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.76/2.45 fof(f352,axiom,(
% 15.76/2.45 rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) ),
% 15.76/2.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.76/2.45 fof(f402,conjecture,(
% 15.76/2.45 (! [X] :( sum(n2,X,n5)=> X = n3 ) )),
% 15.76/2.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 15.76/2.45 fof(f403,negated_conjecture,(
% 15.76/2.45 ~((! [X] :( sum(n2,X,n5)=> X = n3 ) ))),
% 15.76/2.45 inference(negated_conjecture,[status(cth)],[f402])).
% 15.76/2.45 fof(f406,plain,(
% 15.76/2.45 rdn_translate(n2,rdn_pos(rdnn(n2)))),
% 15.76/2.45 inference(cnf_transformation,[status(thm)],[f3])).
% 15.76/2.45 fof(f407,plain,(
% 15.76/2.45 rdn_translate(n3,rdn_pos(rdnn(n3)))),
% 15.76/2.45 inference(cnf_transformation,[status(thm)],[f4])).
% 15.76/2.45 fof(f409,plain,(
% 15.76/2.45 rdn_translate(n5,rdn_pos(rdnn(n5)))),
% 15.76/2.45 inference(cnf_transformation,[status(thm)],[f6])).
% 15.76/2.45 fof(f716,plain,(
% 15.76/2.45 ![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))),
% 15.76/2.45 inference(pre_NNF_transformation,[status(thm)],[f287])).
% 15.76/2.45 fof(f717,plain,(
% 15.76/2.45 ![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))),
% 15.76/2.45 inference(miniscoping,[status(thm)],[f716])).
% 15.76/2.45 fof(f718,plain,(
% 15.76/2.45 ![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))),
% 15.76/2.45 inference(cnf_transformation,[status(thm)],[f717])).
% 15.76/2.45 fof(f740,plain,(
% 15.76/2.45 ![X,Y1,Y2,Z]: ((~sum(X,Y1,Z)|~sum(X,Y2,Z))|Y1=Y2)),
% 15.76/2.45 inference(pre_NNF_transformation,[status(thm)],[f295])).
% 15.76/2.45 fof(f741,plain,(
% 15.76/2.45 ![Y1,Y2]: ((![X,Z]: (~sum(X,Y1,Z)|~sum(X,Y2,Z)))|Y1=Y2)),
% 15.76/2.45 inference(miniscoping,[status(thm)],[f740])).
% 15.76/2.45 fof(f742,plain,(
% 15.76/2.45 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X3,X2)|X1=X3)),
% 15.76/2.45 inference(cnf_transformation,[status(thm)],[f741])).
% 15.76/2.45 fof(f747,plain,(
% 15.76/2.45 ![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)))),
% 15.76/2.45 inference(pre_NNF_transformation,[status(thm)],[f297])).
% 15.76/2.45 fof(f748,plain,(
% 15.76/2.45 ![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)))),
% 15.76/2.45 inference(miniscoping,[status(thm)],[f747])).
% 15.76/2.45 fof(f749,plain,(
% 15.76/2.45 ![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)))),
% 15.76/2.45 inference(cnf_transformation,[status(thm)],[f748])).
% 15.76/2.45 fof(f784,plain,(
% 15.76/2.45 rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))),
% 15.76/2.45 inference(cnf_transformation,[status(thm)],[f325])).
% 15.76/2.50 fof(f811,plain,(
% 15.76/2.50 rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))),
% 15.76/2.50 inference(cnf_transformation,[status(thm)],[f352])).
% 15.76/2.50 fof(f861,plain,(
% 15.76/2.50 (?[X]: (sum(n2,X,n5)&~X=n3))),
% 15.76/2.50 inference(pre_NNF_transformation,[status(thm)],[f403])).
% 15.76/2.50 fof(f862,plain,(
% 15.76/2.50 (sum(n2,sK0_skl,n5)&~sK0_skl=n3)),
% 15.76/2.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f861])).
% 15.76/2.50 fof(f863,plain,(
% 15.76/2.50 sum(n2,sK0_skl,n5)),
% 15.76/2.50 inference(cnf_transformation,[status(thm)],[f862])).
% 15.76/2.50 fof(f864,plain,(
% 15.76/2.50 ~sK0_skl=n3),
% 15.76/2.50 inference(cnf_transformation,[status(thm)],[f862])).
% 15.76/2.50 fof(f871,plain,(
% 15.76/2.50 ![X0]: (~sum(n2,X0,n5)|X0=sK0_skl)),
% 15.76/2.50 inference(resolution,[status(thm)],[f742,f863])).
% 15.76/2.50 fof(f1744,plain,(
% 15.76/2.50 ![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))),
% 15.76/2.50 inference(resolution,[status(thm)],[f749,f718])).
% 15.76/2.50 fof(f2310,plain,(
% 15.76/2.50 ![X0,X1,X2,X3,X4]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))|~rdn_translate(X2,rdn_pos(rdnn(X0)))|~rdn_translate(X3,rdn_pos(rdnn(X1)))|~rdn_translate(X4,rdn_pos(rdnn(n5)))|sum(X2,X3,X4))),
% 15.76/2.50 inference(resolution,[status(thm)],[f1744,f811])).
% 15.76/2.50 fof(f2322,plain,(
% 15.76/2.50 ![X0,X1,X2,X3]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n5),rdnn(n0))|~rdn_translate(X2,rdn_pos(rdnn(X0)))|~rdn_translate(X3,rdn_pos(rdnn(X1)))|sum(X2,X3,n5))),
% 15.76/2.50 inference(resolution,[status(thm)],[f2310,f409])).
% 15.76/2.50 fof(f3264,plain,(
% 15.76/2.50 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n2)))|~rdn_translate(X1,rdn_pos(rdnn(n3)))|sum(X0,X1,n5))),
% 15.76/2.50 inference(resolution,[status(thm)],[f2322,f784])).
% 15.76/2.50 fof(f3493,plain,(
% 15.76/2.50 ![X0]: (~rdn_translate(X0,rdn_pos(rdnn(n2)))|sum(X0,n3,n5))),
% 15.76/2.50 inference(resolution,[status(thm)],[f3264,f407])).
% 15.76/2.50 fof(f4348,plain,(
% 15.76/2.50 sum(n2,n3,n5)),
% 15.76/2.50 inference(resolution,[status(thm)],[f3493,f406])).
% 15.76/2.50 fof(f4354,plain,(
% 15.76/2.50 n3=sK0_skl),
% 15.76/2.50 inference(resolution,[status(thm)],[f4348,f871])).
% 15.76/2.50 fof(f4358,plain,(
% 15.76/2.50 $false),
% 15.76/2.50 inference(forward_subsumption_resolution,[status(thm)],[f4354,f864])).
% 15.76/2.50 % SZS output end CNFRefutation for theBenchmark.p
% 4.33/2.52 % Elapsed time: 2.141507 seconds
% 4.33/2.52 % CPU time: 16.462263 seconds
% 4.33/2.52 % Total memory used: 268.318 MB
% 4.33/2.52 % Net memory used: 249.598 MB
%------------------------------------------------------------------------------