%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO172+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:25:56 PM UTC 2026
% Result : Theorem 0.13s 0.63s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO172+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n017.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sun Sep 20 12:51:26 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.57 % Drodi V4.1.1
% 0.13/0.63 % Refutation found
% 0.13/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.63 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.63 fof(f1,axiom,(
% 0.13/0.63 (! [X] : ~ distinct_points(X,X) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f3,axiom,(
% 0.13/0.63 (! [X] : ~ convergent_lines(X,X) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f4,axiom,(
% 0.13/0.63 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f9,axiom,(
% 0.13/0.63 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f10,axiom,(
% 0.13/0.63 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f11,axiom,(
% 0.13/0.63 (! [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) ) ) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f14,axiom,(
% 0.13/0.63 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f31,axiom,(
% 0.13/0.63 (! [X,Y] :( equal_points(X,Y)<=> ~ distinct_points(X,Y) ) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f34,axiom,(
% 0.13/0.63 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f36,conjecture,(
% 0.13/0.63 (! [X,Y,Z] :( ( convergent_lines(X,Y)& incident_point_and_line(Z,X)& incident_point_and_line(Z,Y) )=> equal_points(Z,intersection_point(X,Y)) ) )),
% 0.13/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.63 fof(f37,negated_conjecture,(
% 0.13/0.63 ~((! [X,Y,Z] :( ( convergent_lines(X,Y)& incident_point_and_line(Z,X)& incident_point_and_line(Z,Y) )=> equal_points(Z,intersection_point(X,Y)) ) ))),
% 0.13/0.63 inference(negated_conjecture,[status(cth)],[f36])).
% 0.13/0.63 fof(f38,plain,(
% 0.13/0.63 ![X0]: (~distinct_points(X0,X0))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.63 fof(f40,plain,(
% 0.13/0.63 ![X0]: (~convergent_lines(X0,X0))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.63 fof(f41,plain,(
% 0.13/0.63 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.13/0.63 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/0.63 fof(f42,plain,(
% 0.13/0.63 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.13/0.63 inference(miniscoping,[status(thm)],[f41])).
% 0.13/0.63 fof(f43,plain,(
% 0.13/0.63 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f42])).
% 0.13/0.63 fof(f54,plain,(
% 0.13/0.63 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.13/0.63 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.13/0.63 fof(f55,plain,(
% 0.13/0.63 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f54])).
% 0.13/0.63 fof(f56,plain,(
% 0.13/0.63 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.13/0.63 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.13/0.63 fof(f57,plain,(
% 0.13/0.63 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f56])).
% 0.13/0.63 fof(f58,plain,(
% 0.13/0.63 ![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)))),
% 0.13/0.63 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.13/0.63 fof(f59,plain,(
% 0.13/0.63 ![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))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f58])).
% 0.13/0.63 fof(f66,plain,(
% 0.13/0.63 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.13/0.63 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.13/0.63 fof(f67,plain,(
% 0.13/0.63 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.13/0.63 inference(miniscoping,[status(thm)],[f66])).
% 0.13/0.63 fof(f68,plain,(
% 0.13/0.63 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f67])).
% 0.13/0.63 fof(f107,plain,(
% 0.13/0.63 ![X,Y]: ((~equal_points(X,Y)|~distinct_points(X,Y))&(equal_points(X,Y)|distinct_points(X,Y)))),
% 0.13/0.63 inference(NNF_transformation,[status(thm)],[f31])).
% 0.13/0.63 fof(f108,plain,(
% 0.13/0.63 (![X,Y]: (~equal_points(X,Y)|~distinct_points(X,Y)))&(![X,Y]: (equal_points(X,Y)|distinct_points(X,Y)))),
% 0.13/0.63 inference(miniscoping,[status(thm)],[f107])).
% 0.13/0.63 fof(f110,plain,(
% 0.13/0.63 ![X0,X1]: (equal_points(X0,X1)|distinct_points(X0,X1))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f108])).
% 0.13/0.63 fof(f119,plain,(
% 0.13/0.63 ![X,Y]: ((~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y))&(incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 0.13/0.63 inference(NNF_transformation,[status(thm)],[f34])).
% 0.13/0.63 fof(f120,plain,(
% 0.13/0.63 (![X,Y]: (~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y)))&(![X,Y]: (incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 0.13/0.63 inference(miniscoping,[status(thm)],[f119])).
% 0.13/0.63 fof(f121,plain,(
% 0.13/0.63 ![X0,X1]: (~incident_point_and_line(X0,X1)|~apart_point_and_line(X0,X1))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f120])).
% 0.13/0.63 fof(f127,plain,(
% 0.13/0.63 (?[X,Y,Z]: (((convergent_lines(X,Y)&incident_point_and_line(Z,X))&incident_point_and_line(Z,Y))&~equal_points(Z,intersection_point(X,Y))))),
% 0.13/0.63 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.13/0.63 fof(f128,plain,(
% 0.13/0.63 (((convergent_lines(sK0_skl,sK1_skl)&incident_point_and_line(sK2_skl,sK0_skl))&incident_point_and_line(sK2_skl,sK1_skl))&~equal_points(sK2_skl,intersection_point(sK0_skl,sK1_skl)))),
% 0.13/0.63 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)],[f127])).
% 0.13/0.63 fof(f129,plain,(
% 0.13/0.63 convergent_lines(sK0_skl,sK1_skl)),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f128])).
% 0.13/0.63 fof(f130,plain,(
% 0.13/0.63 incident_point_and_line(sK2_skl,sK0_skl)),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f128])).
% 0.13/0.63 fof(f131,plain,(
% 0.13/0.63 incident_point_and_line(sK2_skl,sK1_skl)),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f128])).
% 0.13/0.63 fof(f132,plain,(
% 0.13/0.63 ~equal_points(sK2_skl,intersection_point(sK0_skl,sK1_skl))),
% 0.13/0.63 inference(cnf_transformation,[status(thm)],[f128])).
% 0.13/0.63 fof(f143,plain,(
% 0.13/0.63 distinct_points(sK2_skl,intersection_point(sK0_skl,sK1_skl))),
% 0.13/0.63 inference(resolution,[status(thm)],[f110,f132])).
% 0.13/0.63 fof(f148,plain,(
% 0.13/0.63 ![X0]: (distinct_points(sK2_skl,X0)|distinct_points(intersection_point(sK0_skl,sK1_skl),X0))),
% 0.13/0.63 inference(resolution,[status(thm)],[f43,f143])).
% 0.13/0.63 fof(f151,plain,(
% 0.13/0.63 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_points(intersection_point(sK0_skl,sK1_skl),X1)|distinct_points(X0,X1))),
% 0.13/0.63 inference(resolution,[status(thm)],[f148,f43])).
% 0.13/0.63 fof(f180,plain,(
% 0.13/0.63 distinct_points(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 0.13/0.63 inference(resolution,[status(thm)],[f151,f38])).
% 0.13/0.63 fof(f316,plain,(
% 0.13/0.63 ![X0]: (distinct_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.13/0.63 inference(resolution,[status(thm)],[f68,f129])).
% 0.13/0.63 fof(f329,plain,(
% 0.13/0.63 distinct_lines(sK1_skl,sK0_skl)),
% 0.13/0.63 inference(resolution,[status(thm)],[f316,f40])).
% 0.13/0.63 fof(f332,plain,(
% 0.13/0.63 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X1,sK1_skl)|apart_point_and_line(X1,sK0_skl))),
% 0.13/0.63 inference(resolution,[status(thm)],[f329,f59])).
% 0.13/0.63 fof(f968,plain,(
% 0.13/0.63 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(sK2_skl,sK1_skl)|apart_point_and_line(sK2_skl,sK0_skl)),
% 0.13/0.63 inference(resolution,[status(thm)],[f332,f180])).
% 0.13/0.63 fof(f978,definition,(
% 0.13/0.63 sQ40_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 0.13/0.63 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.13/0.63 fof(f979,plain,(
% 0.13/0.63 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ40_spl),
% 0.13/0.63 inference(component_clause,[status(thm)],[f978])).
% 0.13/0.63 fof(f981,definition,(
% 0.13/0.64 sQ41_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.13/0.64 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.13/0.64 fof(f982,plain,(
% 0.13/0.64 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ41_spl),
% 0.13/0.64 inference(component_clause,[status(thm)],[f981])).
% 0.13/0.64 fof(f984,definition,(
% 0.13/0.64 sQ42_spl <=> (apart_point_and_line(sK2_skl,sK1_skl))),
% 0.13/0.64 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.13/0.64 fof(f985,plain,(
% 0.13/0.64 apart_point_and_line(sK2_skl,sK1_skl)|~sQ42_spl),
% 0.13/0.64 inference(component_clause,[status(thm)],[f984])).
% 0.13/0.64 fof(f987,definition,(
% 0.13/0.64 sQ43_spl <=> (apart_point_and_line(sK2_skl,sK0_skl))),
% 0.13/0.64 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.13/0.64 fof(f988,plain,(
% 0.13/0.64 apart_point_and_line(sK2_skl,sK0_skl)|~sQ43_spl),
% 0.13/0.64 inference(component_clause,[status(thm)],[f987])).
% 0.13/0.64 fof(f990,plain,(
% 0.13/0.64 sQ40_spl|sQ41_spl|sQ42_spl|sQ43_spl),
% 0.13/0.64 inference(split_clause,[status(thm)],[f968,f978,f981,f984,f987])).
% 0.13/0.64 fof(f1050,plain,(
% 0.13/0.64 ~incident_point_and_line(sK2_skl,sK0_skl)|~sQ43_spl),
% 0.13/0.64 inference(resolution,[status(thm)],[f988,f121])).
% 0.13/0.64 fof(f1051,plain,(
% 0.13/0.64 $false|~sQ43_spl),
% 0.13/0.64 inference(forward_subsumption_resolution,[status(thm)],[f1050,f130])).
% 0.13/0.64 fof(f1052,plain,(
% 0.13/0.64 ~sQ43_spl),
% 0.13/0.64 inference(contradiction_clause,[status(thm)],[f1051])).
% 0.13/0.64 fof(f1055,plain,(
% 0.13/0.64 ~incident_point_and_line(sK2_skl,sK1_skl)|~sQ42_spl),
% 0.13/0.64 inference(resolution,[status(thm)],[f985,f121])).
% 0.13/0.64 fof(f1056,plain,(
% 0.13/0.64 $false|~sQ42_spl),
% 0.13/0.64 inference(forward_subsumption_resolution,[status(thm)],[f1055,f131])).
% 0.13/0.64 fof(f1057,plain,(
% 0.13/0.64 ~sQ42_spl),
% 0.13/0.64 inference(contradiction_clause,[status(thm)],[f1056])).
% 0.13/0.64 fof(f1058,plain,(
% 0.13/0.64 ~convergent_lines(sK0_skl,sK1_skl)|~sQ40_spl),
% 0.13/0.64 inference(resolution,[status(thm)],[f979,f57])).
% 0.13/0.64 fof(f1062,plain,(
% 0.13/0.64 $false|~sQ40_spl),
% 0.13/0.64 inference(forward_subsumption_resolution,[status(thm)],[f1058,f129])).
% 0.13/0.64 fof(f1063,plain,(
% 0.13/0.64 ~sQ40_spl),
% 0.13/0.64 inference(contradiction_clause,[status(thm)],[f1062])).
% 0.13/0.64 fof(f1064,plain,(
% 0.13/0.64 ~convergent_lines(sK0_skl,sK1_skl)|~sQ41_spl),
% 0.13/0.64 inference(resolution,[status(thm)],[f982,f55])).
% 0.13/0.64 fof(f1068,plain,(
% 0.13/0.64 $false|~sQ41_spl),
% 0.13/0.64 inference(forward_subsumption_resolution,[status(thm)],[f1064,f129])).
% 0.13/0.64 fof(f1069,plain,(
% 0.13/0.64 ~sQ41_spl),
% 0.13/0.64 inference(contradiction_clause,[status(thm)],[f1068])).
% 0.13/0.64 fof(f1070,plain,(
% 0.13/0.64 $false),
% 0.13/0.64 inference(sat_refutation,[status(thm)],[f990,f1052,f1057,f1063,f1069])).
% 0.13/0.64 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.65 % Elapsed time: 0.082657 seconds
% 0.13/0.65 % CPU time: 0.422279 seconds
% 0.13/0.65 % Total memory used: 22.075 MB
% 0.13/0.65 % Net memory used: 21.254 MB
%------------------------------------------------------------------------------