%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM315+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 31.11s 4.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM315+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 02:21:48 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 31.11/4.43 % Refutation found
% 31.11/4.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 31.11/4.43 % SZS output start CNFRefutation for theBenchmark
% 31.11/4.43 fof(f130,axiom,(
% 31.11/4.43 rdn_translate(nn2,rdn_neg(rdnn(n2))) ),
% 31.11/4.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.11/4.43 fof(f133,axiom,(
% 31.11/4.43 rdn_translate(nn5,rdn_neg(rdnn(n5))) ),
% 31.11/4.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.11/4.43 fof(f135,axiom,(
% 31.11/4.43 rdn_translate(nn7,rdn_neg(rdnn(n7))) ),
% 31.11/4.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.11/4.43 fof(f288,axiom,(
% 31.11/4.43 (! [X,Y,Z,RDN_X,RDN_Y,RDN_Z] :( ( rdn_translate(X,rdn_neg(RDN_X))& rdn_translate(Y,rdn_neg(RDN_Y))& rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)& rdn_translate(Z,rdn_neg(RDN_Z)) )=> sum(X,Y,Z) ) )),
% 31.11/4.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.11/4.43 fof(f297,axiom,(
% 31.11/4.43 (! [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)) ) )),
% 31.11/4.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.11/4.43 fof(f327,axiom,(
% 31.11/4.43 rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0)) ),
% 31.11/4.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.11/4.43 fof(f372,axiom,(
% 31.11/4.43 rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)) ),
% 31.11/4.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.11/4.43 fof(f402,conjecture,(
% 31.11/4.43 sum(nn2,nn5,nn7) ),
% 31.11/4.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 31.11/4.43 fof(f403,negated_conjecture,(
% 31.11/4.43 ~(sum(nn2,nn5,nn7) )),
% 31.11/4.43 inference(negated_conjecture,[status(cth)],[f402])).
% 31.11/4.43 fof(f533,plain,(
% 31.11/4.43 rdn_translate(nn2,rdn_neg(rdnn(n2)))),
% 31.11/4.43 inference(cnf_transformation,[status(thm)],[f130])).
% 31.11/4.43 fof(f536,plain,(
% 31.11/4.43 rdn_translate(nn5,rdn_neg(rdnn(n5)))),
% 31.11/4.43 inference(cnf_transformation,[status(thm)],[f133])).
% 31.11/4.43 fof(f538,plain,(
% 31.11/4.43 rdn_translate(nn7,rdn_neg(rdnn(n7)))),
% 31.11/4.43 inference(cnf_transformation,[status(thm)],[f135])).
% 31.11/4.43 fof(f719,plain,(
% 31.11/4.43 ![X,Y,Z,RDN_X,RDN_Y,RDN_Z]: ((((~rdn_translate(X,rdn_neg(RDN_X))|~rdn_translate(Y,rdn_neg(RDN_Y)))|~rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z))|~rdn_translate(Z,rdn_neg(RDN_Z)))|sum(X,Y,Z))),
% 31.11/4.43 inference(pre_NNF_transformation,[status(thm)],[f288])).
% 31.11/4.43 fof(f720,plain,(
% 31.11/4.43 ![X,Y,Z]: ((![RDN_Z]: ((![RDN_X,RDN_Y]: ((~rdn_translate(X,rdn_neg(RDN_X))|~rdn_translate(Y,rdn_neg(RDN_Y)))|~rdn_add_with_carry(rdnn(n0),RDN_X,RDN_Y,RDN_Z)))|~rdn_translate(Z,rdn_neg(RDN_Z))))|sum(X,Y,Z))),
% 31.11/4.43 inference(miniscoping,[status(thm)],[f719])).
% 31.11/4.43 fof(f721,plain,(
% 31.11/4.43 ![X0,X1,X2,X3,X4,X5]: (~rdn_translate(X0,rdn_neg(X1))|~rdn_translate(X2,rdn_neg(X3))|~rdn_add_with_carry(rdnn(n0),X1,X3,X4)|~rdn_translate(X5,rdn_neg(X4))|sum(X0,X2,X5))),
% 31.11/4.43 inference(cnf_transformation,[status(thm)],[f720])).
% 31.11/4.43 fof(f747,plain,(
% 31.11/4.43 ![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)))),
% 31.11/4.43 inference(pre_NNF_transformation,[status(thm)],[f297])).
% 31.11/4.43 fof(f748,plain,(
% 31.11/4.43 ![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)))),
% 31.11/4.43 inference(miniscoping,[status(thm)],[f747])).
% 31.11/4.43 fof(f749,plain,(
% 31.11/4.43 ![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)))),
% 31.11/4.43 inference(cnf_transformation,[status(thm)],[f748])).
% 31.11/4.43 fof(f786,plain,(
% 31.11/4.43 rdn_digit_add(rdnn(n2),rdnn(n5),rdnn(n7),rdnn(n0))),
% 31.11/4.43 inference(cnf_transformation,[status(thm)],[f327])).
% 31.11/4.43 fof(f831,plain,(
% 31.11/4.43 rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0))),
% 31.11/4.43 inference(cnf_transformation,[status(thm)],[f372])).
% 31.11/4.43 fof(f861,plain,(
% 31.11/4.43 ~sum(nn2,nn5,nn7)),
% 31.11/4.43 inference(cnf_transformation,[status(thm)],[f403])).
% 31.11/4.43 fof(f5111,plain,(
% 31.11/4.43 ![X0,X1]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n7),rdnn(n0))|rdn_add_with_carry(rdnn(n0),rdnn(X0),rdnn(X1),rdnn(n7)))),
% 31.11/4.43 inference(resolution,[status(thm)],[f831,f749])).
% 31.11/4.43 fof(f9238,plain,(
% 31.11/4.43 ![X0,X1,X2,X3,X4]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n7),rdnn(n0))|~rdn_translate(X2,rdn_neg(rdnn(X0)))|~rdn_translate(X3,rdn_neg(rdnn(X1)))|~rdn_translate(X4,rdn_neg(rdnn(n7)))|sum(X2,X3,X4))),
% 31.11/4.50 inference(resolution,[status(thm)],[f5111,f721])).
% 31.11/4.50 fof(f12218,plain,(
% 31.11/4.50 ![X0,X1,X2,X3]: (~rdn_digit_add(rdnn(X0),rdnn(X1),rdnn(n7),rdnn(n0))|~rdn_translate(X2,rdn_neg(rdnn(X0)))|~rdn_translate(X3,rdn_neg(rdnn(X1)))|sum(X2,X3,nn7))),
% 31.11/4.50 inference(resolution,[status(thm)],[f9238,f538])).
% 31.11/4.50 fof(f12263,plain,(
% 31.11/4.50 ![X0,X1]: (~rdn_translate(X0,rdn_neg(rdnn(n2)))|~rdn_translate(X1,rdn_neg(rdnn(n5)))|sum(X0,X1,nn7))),
% 31.11/4.50 inference(resolution,[status(thm)],[f12218,f786])).
% 31.11/4.50 fof(f12486,plain,(
% 31.11/4.50 ![X0]: (~rdn_translate(X0,rdn_neg(rdnn(n5)))|sum(nn2,X0,nn7))),
% 31.11/4.50 inference(resolution,[status(thm)],[f12263,f533])).
% 31.11/4.50 fof(f12487,plain,(
% 31.11/4.50 sum(nn2,nn5,nn7)),
% 31.11/4.50 inference(resolution,[status(thm)],[f12486,f536])).
% 31.11/4.50 fof(f12488,plain,(
% 31.11/4.50 $false),
% 31.11/4.50 inference(forward_subsumption_resolution,[status(thm)],[f12487,f861])).
% 31.11/4.50 % SZS output end CNFRefutation for theBenchmark.p
% 3.01/4.53 % Elapsed time: 4.087509 seconds
% 3.01/4.53 % CPU time: 31.835690 seconds
% 3.01/4.53 % Total memory used: 417.120 MB
% 3.01/4.53 % Net memory used: 392.499 MB
%------------------------------------------------------------------------------