%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO200+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 : n020.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 12:26:04 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO200+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 13:20:17 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.39 fof(f1,axiom,(
% 0.08/0.39 (! [X] : ~ distinct_points(X,X) )),
% 0.08/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f4,axiom,(
% 0.08/0.39 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.08/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f7,axiom,(
% 0.08/0.39 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 0.08/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f9,axiom,(
% 0.08/0.39 (! [X,Y,U,V] :( ( distinct_points(X,Y)& distinct_lines(U,V) )=> ( apart_point_and_line(X,U)| apart_point_and_line(X,V)| apart_point_and_line(Y,U)| apart_point_and_line(Y,V) ) ) )),
% 0.08/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f13,conjecture,(
% 0.08/0.39 (! [X,Y] :( distinct_points(X,Y)=> ~ distinct_lines(line_connecting(X,Y),line_connecting(Y,X)) ) )),
% 0.08/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.39 fof(f14,negated_conjecture,(
% 0.08/0.39 ~((! [X,Y] :( distinct_points(X,Y)=> ~ distinct_lines(line_connecting(X,Y),line_connecting(Y,X)) ) ))),
% 0.08/0.39 inference(negated_conjecture,[status(cth)],[f13])).
% 0.08/0.39 fof(f15,plain,(
% 0.08/0.39 ![X0]: (~distinct_points(X0,X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.39 fof(f18,plain,(
% 0.08/0.39 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.08/0.39 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.08/0.39 fof(f19,plain,(
% 0.08/0.39 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.08/0.39 inference(miniscoping,[status(thm)],[f18])).
% 0.08/0.39 fof(f20,plain,(
% 0.08/0.39 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.08/0.39 fof(f27,plain,(
% 0.08/0.39 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 0.08/0.39 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.08/0.39 fof(f28,plain,(
% 0.08/0.39 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 0.08/0.39 inference(miniscoping,[status(thm)],[f27])).
% 0.08/0.39 fof(f29,plain,(
% 0.08/0.39 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f28])).
% 0.08/0.39 fof(f30,plain,(
% 0.08/0.39 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f28])).
% 0.08/0.39 fof(f35,plain,(
% 0.08/0.39 ![X,Y,U,V]: ((~distinct_points(X,Y)|~distinct_lines(U,V))|(((apart_point_and_line(X,U)|apart_point_and_line(X,V))|apart_point_and_line(Y,U))|apart_point_and_line(Y,V)))),
% 0.08/0.39 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.08/0.39 fof(f36,plain,(
% 0.08/0.39 ![X0,X1,X2,X3]: (~distinct_points(X0,X1)|~distinct_lines(X2,X3)|apart_point_and_line(X0,X2)|apart_point_and_line(X0,X3)|apart_point_and_line(X1,X2)|apart_point_and_line(X1,X3))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f35])).
% 0.08/0.39 fof(f45,plain,(
% 0.08/0.39 (?[X,Y]: (distinct_points(X,Y)&distinct_lines(line_connecting(X,Y),line_connecting(Y,X))))),
% 0.08/0.39 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.08/0.39 fof(f46,plain,(
% 0.08/0.39 (distinct_points(sK0_skl,sK1_skl)&distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl)))),
% 0.08/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f45])).
% 0.08/0.39 fof(f47,plain,(
% 0.08/0.39 distinct_points(sK0_skl,sK1_skl)),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f46])).
% 0.08/0.39 fof(f48,plain,(
% 0.08/0.39 distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl))),
% 0.08/0.39 inference(cnf_transformation,[status(thm)],[f46])).
% 0.08/0.39 fof(f49,plain,(
% 0.08/0.39 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.08/0.39 inference(resolution,[status(thm)],[f20,f47])).
% 0.08/0.39 fof(f50,plain,(
% 0.08/0.39 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.08/0.39 inference(resolution,[status(thm)],[f49,f20])).
% 0.08/0.39 fof(f55,plain,(
% 0.08/0.39 distinct_points(sK1_skl,sK0_skl)),
% 0.08/0.39 inference(resolution,[status(thm)],[f50,f15])).
% 0.08/0.39 fof(f63,definition,(
% 0.08/0.39 sQ0_spl <=> (distinct_points(sK1_skl,sK0_skl))),
% 0.08/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/0.39 fof(f65,plain,(
% 0.08/0.39 ~distinct_points(sK1_skl,sK0_skl)|sQ0_spl),
% 0.08/0.39 inference(component_clause,[status(thm)],[f63])).
% 0.08/0.39 fof(f70,definition,(
% 0.08/0.39 sQ2_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.08/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.08/0.39 fof(f72,plain,(
% 0.08/0.39 ~distinct_points(sK0_skl,sK1_skl)|sQ2_spl),
% 0.08/0.39 inference(component_clause,[status(thm)],[f70])).
% 0.08/0.39 fof(f109,plain,(
% 0.08/0.39 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X0,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,line_connecting(sK1_skl,sK0_skl)))),
% 0.08/0.39 inference(resolution,[status(thm)],[f36,f48])).
% 0.08/0.39 fof(f132,plain,(
% 0.08/0.39 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))),
% 0.08/0.39 inference(resolution,[status(thm)],[f109,f55])).
% 0.08/0.39 fof(f164,definition,(
% 0.08/0.39 sQ6_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.08/0.39 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.08/0.39 fof(f165,plain,(
% 0.08/0.39 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ6_spl),
% 0.08/0.39 inference(component_clause,[status(thm)],[f164])).
% 0.08/0.39 fof(f167,definition,(
% 0.08/0.39 sQ7_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.08/0.39 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.08/0.39 fof(f168,plain,(
% 0.08/0.39 apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|~sQ7_spl),
% 0.08/0.39 inference(component_clause,[status(thm)],[f167])).
% 0.08/0.39 fof(f170,definition,(
% 0.08/0.39 sQ8_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.08/0.39 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.08/0.39 fof(f171,plain,(
% 0.08/0.39 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ8_spl),
% 0.08/0.39 inference(component_clause,[status(thm)],[f170])).
% 0.08/0.39 fof(f173,definition,(
% 0.08/0.39 sQ9_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.08/0.39 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.08/0.39 fof(f174,plain,(
% 0.08/0.39 apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))|~sQ9_spl),
% 0.08/0.39 inference(component_clause,[status(thm)],[f173])).
% 0.08/0.39 fof(f176,plain,(
% 0.08/0.39 sQ6_spl|sQ7_spl|sQ8_spl|sQ9_spl),
% 0.08/0.39 inference(split_clause,[status(thm)],[f132,f164,f167,f170,f173])).
% 0.08/0.39 fof(f241,plain,(
% 0.08/0.39 ~distinct_points(sK1_skl,sK0_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ9_spl),
% 0.08/0.39 inference(resolution,[status(thm)],[f174,f30])).
% 0.08/0.39 fof(f247,definition,(
% 0.08/0.39 sQ21_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 0.08/0.39 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.08/0.39 fof(f248,plain,(
% 0.08/0.39 distinct_points(sK0_skl,sK0_skl)|~sQ21_spl),
% 0.08/0.39 inference(component_clause,[status(thm)],[f247])).
% 0.08/0.39 fof(f250,plain,(
% 0.08/0.39 ~sQ0_spl|sQ21_spl|~sQ9_spl),
% 0.08/0.39 inference(split_clause,[status(thm)],[f241,f63,f247,f173])).
% 0.08/0.39 fof(f253,plain,(
% 0.08/0.39 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ8_spl),
% 0.08/0.39 inference(resolution,[status(thm)],[f171,f29])).
% 0.08/0.39 fof(f259,plain,(
% 0.08/0.39 ~sQ2_spl|sQ21_spl|~sQ8_spl),
% 0.08/0.39 inference(split_clause,[status(thm)],[f253,f70,f247,f170])).
% 0.08/0.39 fof(f261,plain,(
% 0.08/0.39 $false|sQ2_spl),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f72,f47])).
% 0.08/0.39 fof(f262,plain,(
% 0.08/0.39 sQ2_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f261])).
% 0.08/0.39 fof(f264,plain,(
% 0.08/0.39 $false|sQ0_spl),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f65,f55])).
% 0.08/0.39 fof(f265,plain,(
% 0.08/0.39 sQ0_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f264])).
% 0.08/0.39 fof(f266,plain,(
% 0.08/0.39 $false|~sQ21_spl),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f248,f15])).
% 0.08/0.39 fof(f267,plain,(
% 0.08/0.39 ~sQ21_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f266])).
% 0.08/0.39 fof(f268,plain,(
% 0.08/0.39 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ6_spl),
% 0.08/0.39 inference(resolution,[status(thm)],[f165,f30])).
% 0.08/0.39 fof(f274,definition,(
% 0.08/0.39 sQ22_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 0.08/0.39 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.08/0.39 fof(f275,plain,(
% 0.08/0.39 distinct_points(sK1_skl,sK1_skl)|~sQ22_spl),
% 0.08/0.39 inference(component_clause,[status(thm)],[f274])).
% 0.08/0.39 fof(f277,plain,(
% 0.08/0.39 ~sQ2_spl|sQ22_spl|~sQ6_spl),
% 0.08/0.39 inference(split_clause,[status(thm)],[f268,f70,f274,f164])).
% 0.08/0.39 fof(f280,plain,(
% 0.08/0.39 ~distinct_points(sK1_skl,sK0_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ7_spl),
% 0.08/0.39 inference(resolution,[status(thm)],[f168,f29])).
% 0.08/0.39 fof(f286,plain,(
% 0.08/0.39 ~sQ0_spl|sQ22_spl|~sQ7_spl),
% 0.08/0.39 inference(split_clause,[status(thm)],[f280,f63,f274,f167])).
% 0.08/0.39 fof(f287,plain,(
% 0.08/0.39 $false|~sQ22_spl),
% 0.08/0.39 inference(forward_subsumption_resolution,[status(thm)],[f275,f15])).
% 0.08/0.39 fof(f288,plain,(
% 0.08/0.39 ~sQ22_spl),
% 0.08/0.39 inference(contradiction_clause,[status(thm)],[f287])).
% 0.08/0.39 fof(f289,plain,(
% 0.08/0.39 $false),
% 0.08/0.39 inference(sat_refutation,[status(thm)],[f176,f250,f259,f262,f265,f267,f277,f286,f288])).
% 0.08/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.41 % Elapsed time: 0.046852 seconds
% 0.08/0.41 % CPU time: 0.134495 seconds
% 0.08/0.41 % Total memory used: 17.642 MB
% 0.08/0.41 % Net memory used: 17.193 MB
%------------------------------------------------------------------------------