%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU167+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:21:52 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU167+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 05:54:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.41 fof(f53,lemma,(
% 0.11/0.41 (! [A,B,C] :( subset(A,B)=> ( subset(cartesian_product2(A,C),cartesian_product2(B,C))& subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f54,conjecture,(
% 0.11/0.41 (! [A,B,C,D] :( ( subset(A,B)& subset(C,D) )=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f55,negated_conjecture,(
% 0.11/0.41 ~((! [A,B,C,D] :( ( subset(A,B)& subset(C,D) )=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ) ))),
% 0.11/0.41 inference(negated_conjecture,[status(cth)],[f54])).
% 0.11/0.41 fof(f60,lemma,(
% 0.11/0.41 (! [A,B,C] :( ( subset(A,B)& subset(B,C) )=> subset(A,C) ) )),
% 0.11/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.41 fof(f261,plain,(
% 0.11/0.41 ![A,B,C]: (~subset(A,B)|(subset(cartesian_product2(A,C),cartesian_product2(B,C))&subset(cartesian_product2(C,A),cartesian_product2(C,B))))),
% 0.11/0.41 inference(pre_NNF_transformation,[status(thm)],[f53])).
% 0.11/0.41 fof(f262,plain,(
% 0.11/0.41 ![A,B]: (~subset(A,B)|((![C]: subset(cartesian_product2(A,C),cartesian_product2(B,C)))&(![C]: subset(cartesian_product2(C,A),cartesian_product2(C,B)))))),
% 0.11/0.41 inference(miniscoping,[status(thm)],[f261])).
% 0.11/0.41 fof(f263,plain,(
% 0.11/0.41 ![X0,X1,X2]: (~subset(X0,X1)|subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f262])).
% 0.11/0.41 fof(f264,plain,(
% 0.11/0.41 ![X0,X1,X2]: (~subset(X0,X1)|subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1)))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f262])).
% 0.11/0.41 fof(f265,plain,(
% 0.11/0.41 (?[A,B,C,D]: ((subset(A,B)&subset(C,D))&~subset(cartesian_product2(A,C),cartesian_product2(B,D))))),
% 0.11/0.41 inference(pre_NNF_transformation,[status(thm)],[f55])).
% 0.11/0.41 fof(f266,plain,(
% 0.11/0.41 ((subset(sK18_skl,sK19_skl)&subset(sK20_skl,sK21_skl))&~subset(cartesian_product2(sK18_skl,sK20_skl),cartesian_product2(sK19_skl,sK21_skl)))),
% 0.11/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl,sK21_skl]),skolemize(A,sK18_skl),skolemize(B,sK19_skl),skolemize(C,sK20_skl),skolemize(D,sK21_skl)],[f265])).
% 0.11/0.41 fof(f267,plain,(
% 0.11/0.41 subset(sK18_skl,sK19_skl)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f266])).
% 0.11/0.41 fof(f268,plain,(
% 0.11/0.41 subset(sK20_skl,sK21_skl)),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f266])).
% 0.11/0.41 fof(f269,plain,(
% 0.11/0.41 ~subset(cartesian_product2(sK18_skl,sK20_skl),cartesian_product2(sK19_skl,sK21_skl))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f266])).
% 0.11/0.41 fof(f276,plain,(
% 0.11/0.41 ![A,B,C]: ((~subset(A,B)|~subset(B,C))|subset(A,C))),
% 0.11/0.41 inference(pre_NNF_transformation,[status(thm)],[f60])).
% 0.11/0.41 fof(f277,plain,(
% 0.11/0.41 ![A,C]: ((![B]: (~subset(A,B)|~subset(B,C)))|subset(A,C))),
% 0.11/0.41 inference(miniscoping,[status(thm)],[f276])).
% 0.11/0.41 fof(f278,plain,(
% 0.11/0.41 ![X0,X1,X2]: (~subset(X0,X1)|~subset(X1,X2)|subset(X0,X2))),
% 0.11/0.41 inference(cnf_transformation,[status(thm)],[f277])).
% 0.11/0.41 fof(f420,plain,(
% 0.11/0.41 ![X0,X1,X2,X3]: (~subset(X0,X1)|~subset(X2,cartesian_product2(X0,X3))|subset(X2,cartesian_product2(X1,X3)))),
% 0.11/0.41 inference(resolution,[status(thm)],[f263,f278])).
% 0.11/0.41 fof(f424,plain,(
% 0.11/0.41 ![X0]: (~subset(X0,sK19_skl)|~subset(cartesian_product2(sK18_skl,sK20_skl),cartesian_product2(X0,sK21_skl)))),
% 0.11/0.41 inference(resolution,[status(thm)],[f420,f269])).
% 0.11/0.41 fof(f444,plain,(
% 0.11/0.41 ~subset(sK18_skl,sK19_skl)|~subset(sK20_skl,sK21_skl)),
% 0.11/0.41 inference(resolution,[status(thm)],[f424,f264])).
% 0.11/0.41 fof(f447,plain,(
% 0.11/0.41 ~subset(sK20_skl,sK21_skl)),
% 0.11/0.41 inference(forward_subsumption_resolution,[status(thm)],[f444,f267])).
% 0.11/0.41 fof(f448,plain,(
% 0.11/0.41 $false),
% 0.11/0.41 inference(backward_subsumption_resolution,[status(thm)],[f268,f447])).
% 0.11/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.44 % Elapsed time: 0.057831 seconds
% 0.11/0.44 % CPU time: 0.160911 seconds
% 0.11/0.44 % Total memory used: 107.654 MB
% 0.11/0.44 % Net memory used: 107.479 MB
%------------------------------------------------------------------------------