%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:26:00 PM UTC 2026
% Result : Theorem 0.11s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO186+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 13:15:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.57 % Refutation found
% 0.11/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.57 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.57 fof(f3,axiom,(
% 0.11/0.57 (! [X] : ~ convergent_lines(X,X) )),
% 0.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.57 fof(f9,axiom,(
% 0.11/0.57 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.57 fof(f10,axiom,(
% 0.11/0.57 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.57 fof(f11,axiom,(
% 0.11/0.57 (! [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) ) ) )),
% 0.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.57 fof(f14,axiom,(
% 0.11/0.57 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.57 fof(f31,axiom,(
% 0.11/0.57 (! [X,Y] :( equal_points(X,Y)<=> ~ distinct_points(X,Y) ) )),
% 0.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.57 fof(f34,axiom,(
% 0.11/0.57 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 0.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.57 fof(f36,conjecture,(
% 0.11/0.57 (! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& incident_point_and_line(X,U)& incident_point_and_line(X,V) )=> equal_points(X,intersection_point(U,V)) ) )),
% 0.11/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.57 fof(f37,negated_conjecture,(
% 0.11/0.57 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& incident_point_and_line(X,U)& incident_point_and_line(X,V) )=> equal_points(X,intersection_point(U,V)) ) ))),
% 0.11/0.57 inference(negated_conjecture,[status(cth)],[f36])).
% 0.11/0.57 fof(f40,plain,(
% 0.11/0.57 ![X0]: (~convergent_lines(X0,X0))),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f3])).
% 0.11/0.57 fof(f54,plain,(
% 0.11/0.57 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.11/0.57 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.11/0.57 fof(f55,plain,(
% 0.11/0.57 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f54])).
% 0.11/0.57 fof(f56,plain,(
% 0.11/0.57 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.11/0.57 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.11/0.57 fof(f57,plain,(
% 0.11/0.57 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f56])).
% 0.11/0.57 fof(f58,plain,(
% 0.11/0.57 ![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)))),
% 0.11/0.57 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.11/0.57 fof(f59,plain,(
% 0.11/0.57 ![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))),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f58])).
% 0.11/0.57 fof(f66,plain,(
% 0.11/0.57 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.11/0.57 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.11/0.57 fof(f67,plain,(
% 0.11/0.57 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.11/0.57 inference(miniscoping,[status(thm)],[f66])).
% 0.11/0.57 fof(f68,plain,(
% 0.11/0.57 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f67])).
% 0.11/0.57 fof(f107,plain,(
% 0.11/0.57 ![X,Y]: ((~equal_points(X,Y)|~distinct_points(X,Y))&(equal_points(X,Y)|distinct_points(X,Y)))),
% 0.11/0.57 inference(NNF_transformation,[status(thm)],[f31])).
% 0.11/0.57 fof(f108,plain,(
% 0.11/0.57 (![X,Y]: (~equal_points(X,Y)|~distinct_points(X,Y)))&(![X,Y]: (equal_points(X,Y)|distinct_points(X,Y)))),
% 0.11/0.57 inference(miniscoping,[status(thm)],[f107])).
% 0.11/0.57 fof(f110,plain,(
% 0.11/0.57 ![X0,X1]: (equal_points(X0,X1)|distinct_points(X0,X1))),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f108])).
% 0.11/0.57 fof(f119,plain,(
% 0.11/0.57 ![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)))),
% 0.11/0.57 inference(NNF_transformation,[status(thm)],[f34])).
% 0.11/0.57 fof(f120,plain,(
% 0.11/0.57 (![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)))),
% 0.11/0.57 inference(miniscoping,[status(thm)],[f119])).
% 0.11/0.57 fof(f121,plain,(
% 0.11/0.57 ![X0,X1]: (~incident_point_and_line(X0,X1)|~apart_point_and_line(X0,X1))),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f120])).
% 0.11/0.57 fof(f127,plain,(
% 0.11/0.57 (?[X,Y,U,V]: ((((distinct_points(X,Y)&convergent_lines(U,V))&incident_point_and_line(X,U))&incident_point_and_line(X,V))&~equal_points(X,intersection_point(U,V))))),
% 0.11/0.57 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.11/0.57 fof(f128,plain,(
% 0.11/0.57 ?[X,U,V]: (((((?[Y]: distinct_points(X,Y))&convergent_lines(U,V))&incident_point_and_line(X,U))&incident_point_and_line(X,V))&~equal_points(X,intersection_point(U,V)))),
% 0.11/0.57 inference(miniscoping,[status(thm)],[f127])).
% 0.11/0.57 fof(f129,plain,(
% 0.11/0.57 ((((distinct_points(sK0_skl,sK3_skl)&convergent_lines(sK1_skl,sK2_skl))&incident_point_and_line(sK0_skl,sK1_skl))&incident_point_and_line(sK0_skl,sK2_skl))&~equal_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)))),
% 0.11/0.57 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(U,sK1_skl),skolemize(V,sK2_skl),skolemize(Y,sK3_skl)],[f128])).
% 0.11/0.57 fof(f131,plain,(
% 0.11/0.57 convergent_lines(sK1_skl,sK2_skl)),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f129])).
% 0.11/0.57 fof(f132,plain,(
% 0.11/0.57 incident_point_and_line(sK0_skl,sK1_skl)),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f129])).
% 0.11/0.57 fof(f133,plain,(
% 0.11/0.57 incident_point_and_line(sK0_skl,sK2_skl)),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f129])).
% 0.11/0.57 fof(f134,plain,(
% 0.11/0.57 ~equal_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))),
% 0.11/0.57 inference(cnf_transformation,[status(thm)],[f129])).
% 0.11/0.57 fof(f150,plain,(
% 0.11/0.57 distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))),
% 0.11/0.57 inference(resolution,[status(thm)],[f134,f110])).
% 0.11/0.57 fof(f190,plain,(
% 0.11/0.57 ![X0]: (distinct_lines(sK2_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.11/0.57 inference(resolution,[status(thm)],[f68,f131])).
% 0.11/0.57 fof(f198,plain,(
% 0.11/0.57 distinct_lines(sK2_skl,sK1_skl)),
% 0.11/0.57 inference(resolution,[status(thm)],[f190,f40])).
% 0.11/0.57 fof(f199,plain,(
% 0.11/0.57 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X1,sK2_skl)|apart_point_and_line(X1,sK1_skl))),
% 0.11/0.57 inference(resolution,[status(thm)],[f198,f59])).
% 0.11/0.57 fof(f798,plain,(
% 0.11/0.57 apart_point_and_line(sK0_skl,sK2_skl)|apart_point_and_line(sK0_skl,sK1_skl)|apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl)|apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl)),
% 0.11/0.57 inference(resolution,[status(thm)],[f199,f150])).
% 0.11/0.57 fof(f812,definition,(
% 0.11/0.57 sQ39_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl))),
% 0.11/0.57 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.11/0.57 fof(f813,plain,(
% 0.11/0.57 apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl)|~sQ39_spl),
% 0.11/0.57 inference(component_clause,[status(thm)],[f812])).
% 0.11/0.57 fof(f815,definition,(
% 0.11/0.57 sQ40_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl))),
% 0.11/0.57 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.11/0.57 fof(f816,plain,(
% 0.11/0.57 apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl)|~sQ40_spl),
% 0.11/0.57 inference(component_clause,[status(thm)],[f815])).
% 0.11/0.57 fof(f828,definition,(
% 0.11/0.57 sQ44_spl <=> (apart_point_and_line(sK0_skl,sK2_skl))),
% 0.11/0.57 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.11/0.57 fof(f829,plain,(
% 0.11/0.57 apart_point_and_line(sK0_skl,sK2_skl)|~sQ44_spl),
% 0.11/0.57 inference(component_clause,[status(thm)],[f828])).
% 0.11/0.57 fof(f831,definition,(
% 0.11/0.57 sQ45_spl <=> (apart_point_and_line(sK0_skl,sK1_skl))),
% 0.11/0.57 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.11/0.57 fof(f832,plain,(
% 0.11/0.57 apart_point_and_line(sK0_skl,sK1_skl)|~sQ45_spl),
% 0.11/0.57 inference(component_clause,[status(thm)],[f831])).
% 0.11/0.57 fof(f846,plain,(
% 0.11/0.57 sQ44_spl|sQ45_spl|sQ39_spl|sQ40_spl),
% 0.11/0.57 inference(split_clause,[status(thm)],[f798,f828,f831,f812,f815])).
% 0.11/0.57 fof(f877,plain,(
% 0.11/0.57 ~incident_point_and_line(sK0_skl,sK1_skl)|~sQ45_spl),
% 0.11/0.57 inference(resolution,[status(thm)],[f832,f121])).
% 0.11/0.57 fof(f878,plain,(
% 0.11/0.57 $false|~sQ45_spl),
% 0.11/0.57 inference(forward_subsumption_resolution,[status(thm)],[f877,f132])).
% 0.11/0.57 fof(f879,plain,(
% 0.11/0.57 ~sQ45_spl),
% 0.11/0.57 inference(contradiction_clause,[status(thm)],[f878])).
% 0.11/0.57 fof(f882,plain,(
% 0.11/0.57 ~incident_point_and_line(sK0_skl,sK2_skl)|~sQ44_spl),
% 0.11/0.57 inference(resolution,[status(thm)],[f829,f121])).
% 0.11/0.57 fof(f883,plain,(
% 0.11/0.57 $false|~sQ44_spl),
% 0.11/0.57 inference(forward_subsumption_resolution,[status(thm)],[f882,f133])).
% 0.11/0.57 fof(f884,plain,(
% 0.11/0.57 ~sQ44_spl),
% 0.11/0.57 inference(contradiction_clause,[status(thm)],[f883])).
% 0.11/0.57 fof(f889,plain,(
% 0.11/0.57 ~convergent_lines(sK1_skl,sK2_skl)|~sQ39_spl),
% 0.11/0.57 inference(resolution,[status(thm)],[f813,f57])).
% 0.11/0.57 fof(f893,plain,(
% 0.11/0.57 $false|~sQ39_spl),
% 0.11/0.57 inference(forward_subsumption_resolution,[status(thm)],[f889,f131])).
% 0.11/0.57 fof(f894,plain,(
% 0.11/0.57 ~sQ39_spl),
% 0.11/0.57 inference(contradiction_clause,[status(thm)],[f893])).
% 0.11/0.57 fof(f1094,plain,(
% 0.11/0.57 ~convergent_lines(sK1_skl,sK2_skl)|~sQ40_spl),
% 0.11/0.57 inference(resolution,[status(thm)],[f816,f55])).
% 0.11/0.57 fof(f1098,plain,(
% 0.11/0.57 $false|~sQ40_spl),
% 0.11/0.57 inference(forward_subsumption_resolution,[status(thm)],[f1094,f131])).
% 0.11/0.57 fof(f1099,plain,(
% 0.11/0.57 ~sQ40_spl),
% 0.11/0.57 inference(contradiction_clause,[status(thm)],[f1098])).
% 0.11/0.57 fof(f1100,plain,(
% 0.11/0.57 $false),
% 0.11/0.57 inference(sat_refutation,[status(thm)],[f846,f879,f884,f894,f1099])).
% 0.11/0.57 % SZS output end CNFRefutation for theBenchmark.p
% 0.22/0.59 % Elapsed time: 0.199542 seconds
% 0.22/0.59 % CPU time: 1.383683 seconds
% 0.22/0.59 % Total memory used: 31.241 MB
% 0.22/0.59 % Net memory used: 28.657 MB
%------------------------------------------------------------------------------