%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO203+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 : n013.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 0.10s 0.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO203+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
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 13:23:36 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.55 % Refutation found
% 0.10/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.55 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.55 fof(f1,axiom,(
% 0.10/0.55 (! [X] : ~ distinct_points(X,X) )),
% 0.10/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.55 fof(f4,axiom,(
% 0.10/0.55 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.10/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.55 fof(f7,axiom,(
% 0.10/0.55 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 0.10/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.55 fof(f8,axiom,(
% 0.10/0.55 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( ( apart_point_and_line(Z,X)| apart_point_and_line(Z,Y) )=> distinct_points(Z,intersection_point(X,Y)) ) ) )),
% 0.10/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.55 fof(f9,axiom,(
% 0.10/0.55 (! [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) ) ) )),
% 0.10/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.55 fof(f13,conjecture,(
% 0.10/0.55 (! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(X,Z)& distinct_points(intersection_point(X,Y),intersection_point(X,Z)) )=> ~ distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ) )),
% 0.10/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.55 fof(f14,negated_conjecture,(
% 0.10/0.55 ~((! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(X,Z)& distinct_points(intersection_point(X,Y),intersection_point(X,Z)) )=> ~ distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ) ))),
% 0.10/0.55 inference(negated_conjecture,[status(cth)],[f13])).
% 0.10/0.55 fof(f15,plain,(
% 0.10/0.55 ![X0]: (~distinct_points(X0,X0))),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.55 fof(f18,plain,(
% 0.10/0.55 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.10/0.55 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.10/0.55 fof(f19,plain,(
% 0.10/0.55 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.10/0.55 inference(miniscoping,[status(thm)],[f18])).
% 0.10/0.55 fof(f20,plain,(
% 0.10/0.55 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f19])).
% 0.10/0.55 fof(f27,plain,(
% 0.10/0.55 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 0.10/0.55 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.10/0.55 fof(f28,plain,(
% 0.10/0.55 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 0.10/0.55 inference(miniscoping,[status(thm)],[f27])).
% 0.10/0.55 fof(f29,plain,(
% 0.10/0.55 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f28])).
% 0.10/0.55 fof(f30,plain,(
% 0.10/0.55 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f28])).
% 0.10/0.55 fof(f31,plain,(
% 0.10/0.55 ![X,Y,Z]: (~convergent_lines(X,Y)|((~apart_point_and_line(Z,X)&~apart_point_and_line(Z,Y))|distinct_points(Z,intersection_point(X,Y))))),
% 0.10/0.55 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.10/0.55 fof(f32,plain,(
% 0.10/0.55 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: ((~apart_point_and_line(Z,X)&~apart_point_and_line(Z,Y))|distinct_points(Z,intersection_point(X,Y)))))),
% 0.10/0.55 inference(miniscoping,[status(thm)],[f31])).
% 0.10/0.55 fof(f33,plain,(
% 0.10/0.55 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f32])).
% 0.10/0.55 fof(f35,plain,(
% 0.10/0.55 ![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)))),
% 0.10/0.55 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.10/0.55 fof(f36,plain,(
% 0.10/0.55 ![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))),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f35])).
% 0.10/0.55 fof(f45,plain,(
% 0.10/0.55 (?[X,Y,Z]: (((convergent_lines(X,Y)&convergent_lines(X,Z))&distinct_points(intersection_point(X,Y),intersection_point(X,Z)))&distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X)))),
% 0.10/0.55 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.10/0.55 fof(f46,plain,(
% 0.10/0.55 (((convergent_lines(sK0_skl,sK1_skl)&convergent_lines(sK0_skl,sK2_skl))&distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))&distinct_lines(line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)),sK0_skl))),
% 0.10/0.55 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])).
% 0.10/0.55 fof(f47,plain,(
% 0.10/0.55 convergent_lines(sK0_skl,sK1_skl)),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f46])).
% 0.10/0.55 fof(f48,plain,(
% 0.10/0.55 convergent_lines(sK0_skl,sK2_skl)),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f46])).
% 0.10/0.55 fof(f49,plain,(
% 0.10/0.55 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f46])).
% 0.10/0.55 fof(f50,plain,(
% 0.10/0.55 distinct_lines(line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)),sK0_skl)),
% 0.10/0.55 inference(cnf_transformation,[status(thm)],[f46])).
% 0.10/0.55 fof(f51,plain,(
% 0.10/0.55 ![X0]: (~apart_point_and_line(X0,sK0_skl)|distinct_points(X0,intersection_point(sK0_skl,sK2_skl)))),
% 0.10/0.55 inference(resolution,[status(thm)],[f33,f48])).
% 0.10/0.55 fof(f52,plain,(
% 0.10/0.55 ![X0]: (~apart_point_and_line(X0,sK0_skl)|distinct_points(X0,intersection_point(sK0_skl,sK1_skl)))),
% 0.10/0.55 inference(resolution,[status(thm)],[f33,f47])).
% 0.10/0.55 fof(f57,plain,(
% 0.10/0.55 ![X0]: (distinct_points(intersection_point(sK0_skl,sK1_skl),X0)|distinct_points(intersection_point(sK0_skl,sK2_skl),X0))),
% 0.10/0.55 inference(resolution,[status(thm)],[f20,f49])).
% 0.10/0.55 fof(f58,plain,(
% 0.10/0.55 ![X0,X1]: (distinct_points(intersection_point(sK0_skl,sK1_skl),X0)|distinct_points(intersection_point(sK0_skl,sK2_skl),X1)|distinct_points(X0,X1))),
% 0.10/0.55 inference(resolution,[status(thm)],[f57,f20])).
% 0.10/0.55 fof(f64,plain,(
% 0.10/0.55 ![X0,X1]: (distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))|distinct_points(intersection_point(sK0_skl,sK2_skl),X0)|distinct_points(X1,X0))),
% 0.10/0.55 inference(resolution,[status(thm)],[f58,f20])).
% 0.10/0.55 fof(f77,definition,(
% 0.10/0.55 sQ2_spl <=> (distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))),
% 0.10/0.55 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.10/0.55 fof(f80,definition,(
% 0.10/0.55 ![X0,X1]: (sQ3_spl <=> (distinct_points(intersection_point(sK0_skl,sK2_skl),X0)|distinct_points(X1,X0)))),
% 0.10/0.55 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.55 fof(f81,plain,(
% 0.10/0.55 ![X0,X1]: (distinct_points(intersection_point(sK0_skl,sK2_skl),X0)|distinct_points(X1,X0)|~sQ3_spl)),
% 0.10/0.55 inference(component_clause,[status(thm)],[f80])).
% 0.10/0.55 fof(f83,plain,(
% 0.10/0.55 sQ2_spl|sQ3_spl),
% 0.10/0.55 inference(split_clause,[status(thm)],[f64,f77,f80])).
% 0.10/0.55 fof(f150,plain,(
% 0.10/0.55 $false|~sQ3_spl),
% 0.10/0.55 inference(resolution,[status(thm)],[f81,f15])).
% 0.10/0.55 fof(f154,plain,(
% 0.10/0.55 ~sQ3_spl),
% 0.10/0.55 inference(contradiction_clause,[status(thm)],[f150])).
% 0.10/0.55 fof(f222,plain,(
% 0.10/0.55 ![X0,X1]: (~distinct_lines(X0,X1)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1))),
% 0.10/0.55 inference(resolution,[status(thm)],[f36,f49])).
% 0.10/0.55 fof(f265,plain,(
% 0.10/0.55 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)),
% 0.10/0.55 inference(resolution,[status(thm)],[f222,f50])).
% 0.10/0.55 fof(f286,definition,(
% 0.10/0.55 sQ16_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))))),
% 0.10/0.55 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.10/0.55 fof(f287,plain,(
% 0.10/0.55 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))|~sQ16_spl),
% 0.10/0.55 inference(component_clause,[status(thm)],[f286])).
% 0.10/0.55 fof(f289,definition,(
% 0.10/0.55 sQ17_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.10/0.55 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.10/0.55 fof(f290,plain,(
% 0.10/0.55 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ17_spl),
% 0.10/0.55 inference(component_clause,[status(thm)],[f289])).
% 0.10/0.55 fof(f292,definition,(
% 0.10/0.55 sQ18_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))))),
% 0.10/0.55 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.10/0.55 fof(f293,plain,(
% 0.10/0.55 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))|~sQ18_spl),
% 0.10/0.55 inference(component_clause,[status(thm)],[f292])).
% 0.10/0.55 fof(f295,definition,(
% 0.10/0.55 sQ19_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl))),
% 0.10/0.55 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.10/0.55 fof(f296,plain,(
% 0.10/0.55 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|~sQ19_spl),
% 0.10/0.55 inference(component_clause,[status(thm)],[f295])).
% 0.10/0.55 fof(f298,plain,(
% 0.10/0.55 sQ16_spl|sQ17_spl|sQ18_spl|sQ19_spl),
% 0.10/0.55 inference(split_clause,[status(thm)],[f265,f286,f289,f292,f295])).
% 0.10/0.55 fof(f1336,plain,(
% 0.10/0.55 ~distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))|distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl))|~sQ18_spl),
% 0.10/0.55 inference(resolution,[status(thm)],[f293,f30])).
% 0.10/0.55 fof(f1349,definition,(
% 0.10/0.55 sQ129_spl <=> (distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl)))),
% 0.10/0.55 introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition])).
% 0.10/0.55 fof(f1350,plain,(
% 0.10/0.55 distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl))|~sQ129_spl),
% 0.10/0.55 inference(component_clause,[status(thm)],[f1349])).
% 0.10/0.55 fof(f1352,plain,(
% 0.10/0.55 ~sQ2_spl|sQ129_spl|~sQ18_spl),
% 0.10/0.55 inference(split_clause,[status(thm)],[f1336,f77,f1349,f292])).
% 0.10/0.55 fof(f1399,plain,(
% 0.10/0.55 $false|~sQ129_spl),
% 0.10/0.55 inference(forward_subsumption_resolution,[status(thm)],[f1350,f15])).
% 0.10/0.55 fof(f1400,plain,(
% 0.10/0.55 ~sQ129_spl),
% 0.10/0.55 inference(contradiction_clause,[status(thm)],[f1399])).
% 0.10/0.55 fof(f1421,plain,(
% 0.10/0.55 distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl))|~sQ19_spl),
% 0.10/0.55 inference(resolution,[status(thm)],[f296,f51])).
% 0.10/0.55 fof(f1433,plain,(
% 0.10/0.55 sQ129_spl|~sQ19_spl),
% 0.10/0.55 inference(split_clause,[status(thm)],[f1421,f1349,f295])).
% 0.10/0.55 fof(f1468,plain,(
% 0.10/0.55 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ17_spl),
% 0.10/0.55 inference(resolution,[status(thm)],[f290,f52])).
% 0.10/0.55 fof(f1481,plain,(
% 0.10/0.55 $false|~sQ17_spl),
% 0.10/0.55 inference(forward_subsumption_resolution,[status(thm)],[f1468,f15])).
% 0.10/0.55 fof(f1482,plain,(
% 0.10/0.55 ~sQ17_spl),
% 0.10/0.55 inference(contradiction_clause,[status(thm)],[f1481])).
% 0.10/0.55 fof(f1484,plain,(
% 0.10/0.55 ~distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))|distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ16_spl),
% 0.10/0.55 inference(resolution,[status(thm)],[f287,f29])).
% 0.10/0.55 fof(f1497,definition,(
% 0.10/0.55 sQ149_spl <=> (distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl)))),
% 0.10/0.55 introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition])).
% 0.10/0.55 fof(f1498,plain,(
% 0.10/0.55 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ149_spl),
% 0.10/0.55 inference(component_clause,[status(thm)],[f1497])).
% 0.10/0.55 fof(f1500,plain,(
% 0.10/0.55 ~sQ2_spl|sQ149_spl|~sQ16_spl),
% 0.10/0.55 inference(split_clause,[status(thm)],[f1484,f77,f1497,f286])).
% 0.10/0.55 fof(f1525,plain,(
% 0.10/0.55 $false|~sQ149_spl),
% 0.10/0.55 inference(forward_subsumption_resolution,[status(thm)],[f1498,f15])).
% 0.10/0.55 fof(f1526,plain,(
% 0.10/0.55 ~sQ149_spl),
% 0.10/0.55 inference(contradiction_clause,[status(thm)],[f1525])).
% 0.10/0.55 fof(f1527,plain,(
% 0.10/0.55 $false),
% 0.10/0.55 inference(sat_refutation,[status(thm)],[f83,f154,f298,f1352,f1400,f1433,f1482,f1500,f1526])).
% 0.10/0.55 % SZS output end CNFRefutation for theBenchmark.p
% 0.23/0.57 % Elapsed time: 0.174665 seconds
% 0.23/0.57 % CPU time: 1.074506 seconds
% 0.23/0.57 % Total memory used: 31.428 MB
% 0.23/0.57 % Net memory used: 28.527 MB
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