%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO178+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:25:57 PM UTC 2026
% Result : Theorem 0.11s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO178+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n016.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 13:06:38 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Drodi V4.1.1
% 0.11/0.36 % Refutation found
% 0.11/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.36 fof(f7,axiom,(
% 0.11/0.36 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 0.11/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f13,conjecture,(
% 0.11/0.36 (! [X,Y,Z] :( ( distinct_points(X,Y)& apart_point_and_line(Z,line_connecting(X,Y)) )=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) )),
% 0.11/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.36 fof(f14,negated_conjecture,(
% 0.11/0.36 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& apart_point_and_line(Z,line_connecting(X,Y)) )=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ))),
% 0.11/0.36 inference(negated_conjecture,[status(cth)],[f13])).
% 0.11/0.36 fof(f27,plain,(
% 0.11/0.36 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.11/0.36 fof(f28,plain,(
% 0.11/0.36 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 0.11/0.36 inference(miniscoping,[status(thm)],[f27])).
% 0.11/0.36 fof(f29,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 0.11/0.36 inference(cnf_transformation,[status(thm)],[f28])).
% 0.11/0.36 fof(f30,plain,(
% 0.11/0.36 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 0.11/0.36 inference(cnf_transformation,[status(thm)],[f28])).
% 0.11/0.36 fof(f45,plain,(
% 0.11/0.36 (?[X,Y,Z]: ((distinct_points(X,Y)&apart_point_and_line(Z,line_connecting(X,Y)))&(~distinct_points(Z,X)|~distinct_points(Z,Y))))),
% 0.11/0.36 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.11/0.36 fof(f46,plain,(
% 0.11/0.36 ((distinct_points(sK0_skl,sK1_skl)&apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)))&(~distinct_points(sK2_skl,sK0_skl)|~distinct_points(sK2_skl,sK1_skl)))),
% 0.11/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f45])).
% 0.11/0.36 fof(f47,plain,(
% 0.11/0.36 distinct_points(sK0_skl,sK1_skl)),
% 0.11/0.36 inference(cnf_transformation,[status(thm)],[f46])).
% 0.11/0.36 fof(f48,plain,(
% 0.11/0.36 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.11/0.36 inference(cnf_transformation,[status(thm)],[f46])).
% 0.11/0.36 fof(f49,plain,(
% 0.11/0.36 ~distinct_points(sK2_skl,sK0_skl)|~distinct_points(sK2_skl,sK1_skl)),
% 0.11/0.36 inference(cnf_transformation,[status(thm)],[f46])).
% 0.11/0.36 fof(f50,definition,(
% 0.11/0.36 sQ0_spl <=> (distinct_points(sK2_skl,sK0_skl))),
% 0.11/0.36 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.11/0.36 fof(f53,definition,(
% 0.11/0.36 sQ1_spl <=> (distinct_points(sK2_skl,sK1_skl))),
% 0.11/0.36 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.11/0.36 fof(f56,plain,(
% 0.11/0.36 ~sQ0_spl|~sQ1_spl),
% 0.11/0.36 inference(split_clause,[status(thm)],[f49,f50,f53])).
% 0.11/0.36 fof(f57,plain,(
% 0.11/0.36 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK2_skl,sK0_skl)),
% 0.11/0.36 inference(resolution,[status(thm)],[f29,f48])).
% 0.11/0.36 fof(f58,definition,(
% 0.11/0.36 sQ2_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.11/0.36 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.11/0.36 fof(f60,plain,(
% 0.11/0.36 ~distinct_points(sK0_skl,sK1_skl)|sQ2_spl),
% 0.11/0.36 inference(component_clause,[status(thm)],[f58])).
% 0.11/0.36 fof(f61,plain,(
% 0.11/0.36 ~sQ2_spl|sQ0_spl),
% 0.11/0.36 inference(split_clause,[status(thm)],[f57,f58,f50])).
% 0.11/0.36 fof(f62,plain,(
% 0.11/0.36 $false|sQ2_spl),
% 0.11/0.36 inference(forward_subsumption_resolution,[status(thm)],[f60,f47])).
% 0.11/0.36 fof(f63,plain,(
% 0.11/0.36 sQ2_spl),
% 0.11/0.36 inference(contradiction_clause,[status(thm)],[f62])).
% 0.11/0.36 fof(f64,plain,(
% 0.11/0.36 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK2_skl,sK1_skl)),
% 0.11/0.36 inference(resolution,[status(thm)],[f30,f48])).
% 0.11/0.36 fof(f65,plain,(
% 0.11/0.36 ~sQ2_spl|sQ1_spl),
% 0.11/0.36 inference(split_clause,[status(thm)],[f64,f58,f53])).
% 0.11/0.36 fof(f66,plain,(
% 0.11/0.36 $false),
% 0.11/0.36 inference(sat_refutation,[status(thm)],[f56,f61,f63,f65])).
% 0.11/0.36 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.37 % Elapsed time: 0.030054 seconds
% 0.11/0.37 % CPU time: 0.091723 seconds
% 0.11/0.37 % Total memory used: 13.834 MB
% 0.11/0.37 % Net memory used: 13.520 MB
%------------------------------------------------------------------------------