%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM311+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 : n005.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 10.48s 1.82s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM311+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
% 0.09/0.34 % Computer : n005.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 02:21:32 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 10.48/1.82 % Refutation found
% 10.48/1.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.48/1.82 % SZS output start CNFRefutation for theBenchmark
% 10.48/1.82 fof(f3,axiom,(
% 10.48/1.82 rdn_translate(n2,rdn_pos(rdnn(n2))) ),
% 10.48/1.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.48/1.82 fof(f4,axiom,(
% 10.48/1.82 rdn_translate(n3,rdn_pos(rdnn(n3))) ),
% 10.48/1.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.48/1.82 fof(f6,axiom,(
% 10.48/1.82 rdn_translate(n5,rdn_pos(rdnn(n5))) ),
% 10.48/1.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.48/1.82 fof(f287,axiom,(
% 10.48/1.82 (! [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) ) )),
% 10.48/1.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.48/1.82 fof(f293,axiom,(
% 10.48/1.82 (! [X,Y,Z1,Z2] :( ( sum(X,Y,Z1)& sum(X,Y,Z2) )=> Z1 = Z2 ) )),
% 10.48/1.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.48/1.82 fof(f297,axiom,(
% 10.48/1.82 (! [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)) ) )),
% 10.48/1.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.48/1.82 fof(f325,axiom,(
% 10.48/1.82 rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)) ),
% 10.48/1.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.48/1.82 fof(f352,axiom,(
% 10.48/1.82 rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)) ),
% 10.48/1.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.48/1.82 fof(f402,conjecture,(
% 10.48/1.82 (! [X] :( sum(n2,n3,X)=> X = n5 ) )),
% 10.48/1.82 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.48/1.82 fof(f403,negated_conjecture,(
% 10.48/1.82 ~((! [X] :( sum(n2,n3,X)=> X = n5 ) ))),
% 10.48/1.82 inference(negated_conjecture,[status(cth)],[f402])).
% 10.48/1.82 fof(f406,plain,(
% 10.48/1.82 rdn_translate(n2,rdn_pos(rdnn(n2)))),
% 10.48/1.82 inference(cnf_transformation,[status(thm)],[f3])).
% 10.48/1.82 fof(f407,plain,(
% 10.48/1.82 rdn_translate(n3,rdn_pos(rdnn(n3)))),
% 10.48/1.82 inference(cnf_transformation,[status(thm)],[f4])).
% 10.48/1.82 fof(f409,plain,(
% 10.48/1.82 rdn_translate(n5,rdn_pos(rdnn(n5)))),
% 10.48/1.82 inference(cnf_transformation,[status(thm)],[f6])).
% 10.48/1.82 fof(f716,plain,(
% 10.48/1.82 ![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))),
% 10.48/1.82 inference(pre_NNF_transformation,[status(thm)],[f287])).
% 10.48/1.82 fof(f717,plain,(
% 10.48/1.82 ![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))),
% 10.48/1.82 inference(miniscoping,[status(thm)],[f716])).
% 10.48/1.82 fof(f718,plain,(
% 10.48/1.82 ![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))),
% 10.48/1.82 inference(cnf_transformation,[status(thm)],[f717])).
% 10.48/1.82 fof(f734,plain,(
% 10.48/1.82 ![X,Y,Z1,Z2]: ((~sum(X,Y,Z1)|~sum(X,Y,Z2))|Z1=Z2)),
% 10.48/1.82 inference(pre_NNF_transformation,[status(thm)],[f293])).
% 10.48/1.82 fof(f735,plain,(
% 10.48/1.82 ![Z1,Z2]: ((![X,Y]: (~sum(X,Y,Z1)|~sum(X,Y,Z2)))|Z1=Z2)),
% 10.48/1.82 inference(miniscoping,[status(thm)],[f734])).
% 10.48/1.82 fof(f736,plain,(
% 10.48/1.82 ![X0,X1,X2,X3]: (~sum(X0,X1,X2)|~sum(X0,X1,X3)|X2=X3)),
% 10.48/1.82 inference(cnf_transformation,[status(thm)],[f735])).
% 10.48/1.82 fof(f747,plain,(
% 10.48/1.82 ![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)))),
% 10.48/1.82 inference(pre_NNF_transformation,[status(thm)],[f297])).
% 10.48/1.82 fof(f748,plain,(
% 10.48/1.82 ![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)))),
% 10.48/1.82 inference(miniscoping,[status(thm)],[f747])).
% 10.48/1.82 fof(f749,plain,(
% 10.48/1.82 ![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)))),
% 10.48/1.82 inference(cnf_transformation,[status(thm)],[f748])).
% 10.48/1.82 fof(f784,plain,(
% 10.48/1.82 rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0))),
% 10.48/1.82 inference(cnf_transformation,[status(thm)],[f325])).
% 11.17/1.86 fof(f811,plain,(
% 11.17/1.86 rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0))),
% 11.17/1.86 inference(cnf_transformation,[status(thm)],[f352])).
% 11.17/1.86 fof(f861,plain,(
% 11.17/1.86 (?[X]: (sum(n2,n3,X)&~X=n5))),
% 11.17/1.86 inference(pre_NNF_transformation,[status(thm)],[f403])).
% 11.17/1.86 fof(f862,plain,(
% 11.17/1.86 (sum(n2,n3,sK0_skl)&~sK0_skl=n5)),
% 11.17/1.86 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f861])).
% 11.17/1.86 fof(f863,plain,(
% 11.17/1.86 sum(n2,n3,sK0_skl)),
% 11.17/1.86 inference(cnf_transformation,[status(thm)],[f862])).
% 11.17/1.86 fof(f864,plain,(
% 11.17/1.86 ~sK0_skl=n5),
% 11.17/1.86 inference(cnf_transformation,[status(thm)],[f862])).
% 11.17/1.86 fof(f867,plain,(
% 11.17/1.86 ![X0]: (~sum(n2,n3,X0)|X0=sK0_skl)),
% 11.17/1.86 inference(resolution,[status(thm)],[f736,f863])).
% 11.17/1.86 fof(f2834,plain,(
% 11.17/1.86 ![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))),
% 11.17/1.86 inference(resolution,[status(thm)],[f749,f718])).
% 11.17/1.86 fof(f5922,plain,(
% 11.17/1.86 ![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))),
% 11.17/1.86 inference(resolution,[status(thm)],[f2834,f811])).
% 11.17/1.86 fof(f5930,plain,(
% 11.17/1.86 ![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))),
% 11.17/1.86 inference(resolution,[status(thm)],[f5922,f409])).
% 11.17/1.86 fof(f5965,plain,(
% 11.17/1.86 ![X0,X1]: (~rdn_translate(X0,rdn_pos(rdnn(n2)))|~rdn_translate(X1,rdn_pos(rdnn(n3)))|sum(X0,X1,n5))),
% 11.17/1.86 inference(resolution,[status(thm)],[f5930,f784])).
% 11.17/1.86 fof(f6132,plain,(
% 11.17/1.86 ![X0]: (~rdn_translate(X0,rdn_pos(rdnn(n2)))|sum(X0,n3,n5))),
% 11.17/1.86 inference(resolution,[status(thm)],[f5965,f407])).
% 11.17/1.86 fof(f6133,plain,(
% 11.17/1.86 sum(n2,n3,n5)),
% 11.17/1.86 inference(resolution,[status(thm)],[f6132,f406])).
% 11.17/1.86 fof(f6134,plain,(
% 11.17/1.86 n5=sK0_skl),
% 11.17/1.86 inference(resolution,[status(thm)],[f6133,f867])).
% 11.17/1.86 fof(f6138,plain,(
% 11.17/1.86 $false),
% 11.17/1.86 inference(forward_subsumption_resolution,[status(thm)],[f6134,f864])).
% 11.17/1.86 % SZS output end CNFRefutation for theBenchmark.p
% 11.17/1.89 % Elapsed time: 1.529344 seconds
% 11.17/1.89 % CPU time: 11.671601 seconds
% 11.17/1.89 % Total memory used: 236.786 MB
% 11.17/1.89 % Net memory used: 221.498 MB
%------------------------------------------------------------------------------