%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO175+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 : n010.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 6.91s 1.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO175+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n010.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 13:02:24 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 6.91/1.40 % Refutation found
% 6.91/1.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.91/1.40 % SZS output start CNFRefutation for theBenchmark
% 6.91/1.40 fof(f1,axiom,(
% 6.91/1.40 (! [X] : ~ distinct_points(X,X) )),
% 6.91/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.91/1.40 fof(f3,axiom,(
% 6.91/1.40 (! [X] : ~ convergent_lines(X,X) )),
% 6.91/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.91/1.40 fof(f4,axiom,(
% 6.91/1.40 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 6.91/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.91/1.40 fof(f9,axiom,(
% 6.91/1.40 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 6.91/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.91/1.40 fof(f10,axiom,(
% 6.91/1.40 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 6.91/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.91/1.40 fof(f11,axiom,(
% 6.91/1.40 (! [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) ) ) )),
% 6.91/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.91/1.40 fof(f14,axiom,(
% 6.91/1.40 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 6.91/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.91/1.40 fof(f36,conjecture,(
% 6.91/1.40 (! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& distinct_points(X,intersection_point(U,V)) )=> ( apart_point_and_line(X,U)| apart_point_and_line(X,V) ) ) )),
% 6.91/1.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 6.91/1.40 fof(f37,negated_conjecture,(
% 6.91/1.40 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& distinct_points(X,intersection_point(U,V)) )=> ( apart_point_and_line(X,U)| apart_point_and_line(X,V) ) ) ))),
% 6.91/1.40 inference(negated_conjecture,[status(cth)],[f36])).
% 6.91/1.40 fof(f38,plain,(
% 6.91/1.40 ![X0]: (~distinct_points(X0,X0))),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f1])).
% 6.91/1.40 fof(f40,plain,(
% 6.91/1.40 ![X0]: (~convergent_lines(X0,X0))),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f3])).
% 6.91/1.40 fof(f41,plain,(
% 6.91/1.40 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 6.91/1.40 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 6.91/1.40 fof(f42,plain,(
% 6.91/1.40 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 6.91/1.40 inference(miniscoping,[status(thm)],[f41])).
% 6.91/1.40 fof(f43,plain,(
% 6.91/1.40 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f42])).
% 6.91/1.40 fof(f54,plain,(
% 6.91/1.40 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 6.91/1.40 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 6.91/1.40 fof(f55,plain,(
% 6.91/1.40 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f54])).
% 6.91/1.40 fof(f56,plain,(
% 6.91/1.40 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 6.91/1.40 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 6.91/1.40 fof(f57,plain,(
% 6.91/1.40 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f56])).
% 6.91/1.40 fof(f58,plain,(
% 6.91/1.40 ![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)))),
% 6.91/1.40 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 6.91/1.40 fof(f59,plain,(
% 6.91/1.40 ![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))),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f58])).
% 6.91/1.40 fof(f66,plain,(
% 6.91/1.40 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 6.91/1.40 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 6.91/1.40 fof(f67,plain,(
% 6.91/1.40 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 6.91/1.40 inference(miniscoping,[status(thm)],[f66])).
% 6.91/1.40 fof(f68,plain,(
% 6.91/1.40 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f67])).
% 6.91/1.40 fof(f127,plain,(
% 6.91/1.40 (?[X,Y,U,V]: (((distinct_points(X,Y)&convergent_lines(U,V))&distinct_points(X,intersection_point(U,V)))&(~apart_point_and_line(X,U)&~apart_point_and_line(X,V))))),
% 6.91/1.40 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 6.91/1.40 fof(f128,plain,(
% 6.91/1.40 ?[X,U,V]: ((((?[Y]: distinct_points(X,Y))&convergent_lines(U,V))&distinct_points(X,intersection_point(U,V)))&(~apart_point_and_line(X,U)&~apart_point_and_line(X,V)))),
% 6.91/1.40 inference(miniscoping,[status(thm)],[f127])).
% 6.91/1.40 fof(f129,plain,(
% 6.91/1.40 (((distinct_points(sK0_skl,sK3_skl)&convergent_lines(sK1_skl,sK2_skl))&distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)))&(~apart_point_and_line(sK0_skl,sK1_skl)&~apart_point_and_line(sK0_skl,sK2_skl)))),
% 6.91/1.40 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])).
% 6.91/1.40 fof(f131,plain,(
% 6.91/1.40 convergent_lines(sK1_skl,sK2_skl)),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f129])).
% 6.91/1.40 fof(f132,plain,(
% 6.91/1.40 distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f129])).
% 6.91/1.40 fof(f133,plain,(
% 6.91/1.40 ~apart_point_and_line(sK0_skl,sK1_skl)),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f129])).
% 6.91/1.40 fof(f134,plain,(
% 6.91/1.40 ~apart_point_and_line(sK0_skl,sK2_skl)),
% 6.91/1.40 inference(cnf_transformation,[status(thm)],[f129])).
% 6.91/1.40 fof(f145,plain,(
% 6.91/1.40 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(intersection_point(sK1_skl,sK2_skl),X0))),
% 6.91/1.40 inference(resolution,[status(thm)],[f43,f132])).
% 6.91/1.40 fof(f154,plain,(
% 6.91/1.40 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(intersection_point(sK1_skl,sK2_skl),X1)|distinct_points(X0,X1))),
% 6.91/1.40 inference(resolution,[status(thm)],[f145,f43])).
% 6.91/1.40 fof(f215,plain,(
% 6.91/1.40 distinct_points(intersection_point(sK1_skl,sK2_skl),sK0_skl)),
% 6.91/1.40 inference(resolution,[status(thm)],[f154,f38])).
% 6.91/1.40 fof(f248,plain,(
% 6.91/1.40 ![X0]: (distinct_lines(sK2_skl,X0)|convergent_lines(sK1_skl,X0))),
% 6.91/1.40 inference(resolution,[status(thm)],[f68,f131])).
% 6.91/1.40 fof(f290,plain,(
% 6.91/1.40 distinct_lines(sK2_skl,sK1_skl)),
% 6.91/1.40 inference(resolution,[status(thm)],[f248,f40])).
% 6.91/1.40 fof(f291,plain,(
% 6.91/1.40 ![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))),
% 6.91/1.40 inference(resolution,[status(thm)],[f290,f59])).
% 6.91/1.40 fof(f1739,plain,(
% 6.91/1.40 apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl)|apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl)|apart_point_and_line(sK0_skl,sK2_skl)|apart_point_and_line(sK0_skl,sK1_skl)),
% 6.91/1.40 inference(resolution,[status(thm)],[f291,f215])).
% 6.91/1.40 fof(f1791,definition,(
% 6.91/1.40 sQ70_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl))),
% 6.91/1.40 introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 6.91/1.40 fof(f1792,plain,(
% 6.91/1.40 apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl)|~sQ70_spl),
% 6.91/1.40 inference(component_clause,[status(thm)],[f1791])).
% 6.91/1.40 fof(f1794,definition,(
% 6.91/1.40 sQ71_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl))),
% 6.91/1.40 introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition])).
% 6.91/1.40 fof(f1795,plain,(
% 6.91/1.40 apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl)|~sQ71_spl),
% 6.91/1.40 inference(component_clause,[status(thm)],[f1794])).
% 6.91/1.40 fof(f1797,definition,(
% 6.91/1.40 sQ72_spl <=> (apart_point_and_line(sK0_skl,sK2_skl))),
% 6.91/1.40 introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 6.91/1.40 fof(f1798,plain,(
% 6.91/1.40 apart_point_and_line(sK0_skl,sK2_skl)|~sQ72_spl),
% 6.91/1.40 inference(component_clause,[status(thm)],[f1797])).
% 6.91/1.40 fof(f1800,definition,(
% 6.91/1.40 sQ73_spl <=> (apart_point_and_line(sK0_skl,sK1_skl))),
% 6.91/1.40 introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition])).
% 6.91/1.40 fof(f1801,plain,(
% 6.91/1.40 apart_point_and_line(sK0_skl,sK1_skl)|~sQ73_spl),
% 6.91/1.40 inference(component_clause,[status(thm)],[f1800])).
% 6.91/1.40 fof(f1803,plain,(
% 6.91/1.40 sQ70_spl|sQ71_spl|sQ72_spl|sQ73_spl),
% 6.91/1.40 inference(split_clause,[status(thm)],[f1739,f1791,f1794,f1797,f1800])).
% 6.91/1.40 fof(f1909,plain,(
% 6.91/1.40 $false|~sQ73_spl),
% 6.91/1.41 inference(forward_subsumption_resolution,[status(thm)],[f1801,f133])).
% 6.91/1.41 fof(f1910,plain,(
% 6.91/1.41 ~sQ73_spl),
% 6.91/1.41 inference(contradiction_clause,[status(thm)],[f1909])).
% 6.91/1.41 fof(f1911,plain,(
% 6.91/1.41 $false|~sQ72_spl),
% 6.91/1.41 inference(forward_subsumption_resolution,[status(thm)],[f1798,f134])).
% 6.91/1.41 fof(f1912,plain,(
% 6.91/1.41 ~sQ72_spl),
% 6.91/1.41 inference(contradiction_clause,[status(thm)],[f1911])).
% 6.91/1.41 fof(f1965,plain,(
% 6.91/1.41 ~convergent_lines(sK1_skl,sK2_skl)|~sQ70_spl),
% 6.91/1.41 inference(resolution,[status(thm)],[f1792,f57])).
% 6.91/1.41 fof(f1968,plain,(
% 6.91/1.41 $false|~sQ70_spl),
% 6.91/1.41 inference(forward_subsumption_resolution,[status(thm)],[f1965,f131])).
% 6.91/1.41 fof(f1969,plain,(
% 6.91/1.41 ~sQ70_spl),
% 6.91/1.41 inference(contradiction_clause,[status(thm)],[f1968])).
% 6.91/1.41 fof(f2012,plain,(
% 6.91/1.41 ~convergent_lines(sK1_skl,sK2_skl)|~sQ71_spl),
% 6.91/1.41 inference(resolution,[status(thm)],[f1795,f55])).
% 6.91/1.41 fof(f2015,plain,(
% 6.91/1.41 $false|~sQ71_spl),
% 6.91/1.41 inference(forward_subsumption_resolution,[status(thm)],[f2012,f131])).
% 6.91/1.41 fof(f2016,plain,(
% 6.91/1.41 ~sQ71_spl),
% 6.91/1.41 inference(contradiction_clause,[status(thm)],[f2015])).
% 6.91/1.41 fof(f2017,plain,(
% 6.91/1.41 $false),
% 6.91/1.41 inference(sat_refutation,[status(thm)],[f1803,f1910,f1912,f1969,f2016])).
% 6.91/1.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.61/1.44 % Elapsed time: 0.980266 seconds
% 0.61/1.44 % CPU time: 7.366654 seconds
% 0.61/1.44 % Total memory used: 54.895 MB
% 0.61/1.44 % Net memory used: 46.710 MB
%------------------------------------------------------------------------------