%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM344+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 : n012.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 01:42:34 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM344+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:22:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.40 fof(f1,axiom,(
% 0.12/0.40 rdn_translate(n0,rdn_pos(rdnn(n0))) ),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f2,axiom,(
% 0.12/0.40 rdn_translate(n1,rdn_pos(rdnn(n1))) ),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f129,axiom,(
% 0.12/0.40 rdn_translate(nn1,rdn_neg(rdnn(n1))) ),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f282,axiom,(
% 0.12/0.40 (! [X,Y,RDN_X,RDN_Y] :( ( rdn_translate(X,rdn_neg(RDN_X))& rdn_translate(Y,rdn_pos(RDN_Y)) )=> less(X,Y) ) )),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f291,axiom,(
% 0.12/0.40 (! [POS_X,NEG_X,RDN_X] :( ( rdn_translate(POS_X,rdn_pos(RDN_X))& rdn_translate(NEG_X,rdn_neg(RDN_X)) )=> sum(POS_X,NEG_X,n0) ) )),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f292,axiom,(
% 0.12/0.40 (! [X,Y,Z,RDN_X,RDN_Y] :( ( rdn_translate(X,rdn_neg(RDN_X))& rdn_translate(Y,rdn_pos(RDN_Y))& sum(Y,X,Z) )=> sum(X,Y,Z) ) )),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f402,conjecture,(
% 0.12/0.40 (? [X,Y] :( sum(X,n1,Y)& less(X,Y) ) )),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f403,negated_conjecture,(
% 0.12/0.40 ~((? [X,Y] :( sum(X,n1,Y)& less(X,Y) ) ))),
% 0.12/0.40 inference(negated_conjecture,[status(cth)],[f402])).
% 0.12/0.40 fof(f404,plain,(
% 0.12/0.40 rdn_translate(n0,rdn_pos(rdnn(n0)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.40 fof(f405,plain,(
% 0.12/0.40 rdn_translate(n1,rdn_pos(rdnn(n1)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.40 fof(f532,plain,(
% 0.12/0.40 rdn_translate(nn1,rdn_neg(rdnn(n1)))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f129])).
% 0.12/0.40 fof(f697,plain,(
% 0.12/0.40 ![X,Y,RDN_X,RDN_Y]: ((~rdn_translate(X,rdn_neg(RDN_X))|~rdn_translate(Y,rdn_pos(RDN_Y)))|less(X,Y))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f282])).
% 0.12/0.40 fof(f698,plain,(
% 0.12/0.40 ![X,Y]: (((![RDN_X]: ~rdn_translate(X,rdn_neg(RDN_X)))|(![RDN_Y]: ~rdn_translate(Y,rdn_pos(RDN_Y))))|less(X,Y))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f697])).
% 0.12/0.40 fof(f699,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~rdn_translate(X0,rdn_neg(X1))|~rdn_translate(X2,rdn_pos(X3))|less(X0,X2))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f698])).
% 0.12/0.40 fof(f728,plain,(
% 0.12/0.40 ![POS_X,NEG_X,RDN_X]: ((~rdn_translate(POS_X,rdn_pos(RDN_X))|~rdn_translate(NEG_X,rdn_neg(RDN_X)))|sum(POS_X,NEG_X,n0))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f291])).
% 0.12/0.40 fof(f729,plain,(
% 0.12/0.40 ![POS_X,NEG_X]: ((![RDN_X]: (~rdn_translate(POS_X,rdn_pos(RDN_X))|~rdn_translate(NEG_X,rdn_neg(RDN_X))))|sum(POS_X,NEG_X,n0))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f728])).
% 0.12/0.40 fof(f730,plain,(
% 0.12/0.40 ![X0,X1,X2]: (~rdn_translate(X0,rdn_pos(X1))|~rdn_translate(X2,rdn_neg(X1))|sum(X0,X2,n0))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f729])).
% 0.12/0.40 fof(f731,plain,(
% 0.12/0.40 ![X,Y,Z,RDN_X,RDN_Y]: (((~rdn_translate(X,rdn_neg(RDN_X))|~rdn_translate(Y,rdn_pos(RDN_Y)))|~sum(Y,X,Z))|sum(X,Y,Z))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f292])).
% 0.12/0.40 fof(f732,plain,(
% 0.12/0.40 ![X,Y,Z]: ((((![RDN_X]: ~rdn_translate(X,rdn_neg(RDN_X)))|(![RDN_Y]: ~rdn_translate(Y,rdn_pos(RDN_Y))))|~sum(Y,X,Z))|sum(X,Y,Z))),
% 0.12/0.40 inference(miniscoping,[status(thm)],[f731])).
% 0.12/0.40 fof(f733,plain,(
% 0.12/0.40 ![X0,X1,X2,X3,X4]: (~rdn_translate(X0,rdn_neg(X1))|~rdn_translate(X2,rdn_pos(X3))|~sum(X2,X0,X4)|sum(X0,X2,X4))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f732])).
% 0.12/0.40 fof(f861,plain,(
% 0.12/0.40 (![X,Y]: (~sum(X,n1,Y)|~less(X,Y)))),
% 0.12/0.40 inference(pre_NNF_transformation,[status(thm)],[f403])).
% 0.12/0.40 fof(f862,plain,(
% 0.12/0.40 ![X0,X1]: (~sum(X0,n1,X1)|~less(X0,X1))),
% 0.12/0.40 inference(cnf_transformation,[status(thm)],[f861])).
% 0.12/0.40 fof(f883,plain,(
% 0.12/0.40 ![X0,X1]: (~rdn_translate(X0,rdn_neg(X1))|less(X0,n0))),
% 0.12/0.40 inference(resolution,[status(thm)],[f404,f699])).
% 0.12/0.40 fof(f925,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~rdn_translate(X0,rdn_neg(X1))|~rdn_translate(n1,rdn_pos(X2))|~sum(n1,X0,X3)|~less(X0,X3))),
% 0.12/0.40 inference(resolution,[status(thm)],[f733,f862])).
% 0.12/0.40 fof(f968,plain,(
% 0.12/0.40 ![X0,X1,X2,X3]: (~rdn_translate(X0,rdn_neg(X1))|~rdn_translate(n1,rdn_pos(X2))|~less(X0,n0)|~rdn_translate(n1,rdn_pos(X3))|~rdn_translate(X0,rdn_neg(X3)))),
% 0.12/0.40 inference(resolution,[status(thm)],[f925,f730])).
% 0.12/0.40 fof(f1340,plain,(
% 0.12/0.40 ![X0]: (~rdn_translate(n1,rdn_pos(X0))|~less(nn1,n0)|~rdn_translate(n1,rdn_pos(rdnn(n1))))),
% 0.12/0.40 inference(resolution,[status(thm)],[f968,f532])).
% 0.12/0.40 fof(f1349,plain,(
% 0.12/0.40 ![X0]: (~rdn_translate(n1,rdn_pos(X0))|~less(nn1,n0))),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f1340,f405])).
% 0.12/0.40 fof(f1597,plain,(
% 0.12/0.40 ~less(nn1,n0)),
% 0.12/0.40 inference(resolution,[status(thm)],[f1349,f405])).
% 0.12/0.40 fof(f1672,plain,(
% 0.12/0.40 less(nn1,n0)),
% 0.12/0.40 inference(resolution,[status(thm)],[f883,f532])).
% 0.12/0.40 fof(f1673,plain,(
% 0.12/0.40 $false),
% 0.12/0.40 inference(forward_subsumption_resolution,[status(thm)],[f1672,f1597])).
% 0.12/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.42 % Elapsed time: 0.068175 seconds
% 0.12/0.42 % CPU time: 0.265680 seconds
% 0.12/0.42 % Total memory used: 101.696 MB
% 0.12/0.42 % Net memory used: 101.518 MB
%------------------------------------------------------------------------------