%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO194+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 : n014.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 12:26:02 PM UTC 2026
% Result : Theorem 0.09s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO194+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
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 13:17:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.51 % Refutation found
% 0.09/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.51 fof(f1,axiom,(
% 0.09/0.51 (! [X] : ~ distinct_points(X,X) )),
% 0.09/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f8,axiom,(
% 0.09/0.51 (! [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)) ) ) )),
% 0.09/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f9,axiom,(
% 0.09/0.51 (! [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) ) ) )),
% 0.09/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f12,axiom,(
% 0.09/0.51 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 0.09/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f13,conjecture,(
% 0.09/0.51 (! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(Z,Y)& convergent_lines(X,Z) )=> ( apart_point_and_line(intersection_point(X,Y),Z)=> apart_point_and_line(intersection_point(X,Z),Y) ) ) )),
% 0.09/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f14,negated_conjecture,(
% 0.09/0.51 ~((! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(Z,Y)& convergent_lines(X,Z) )=> ( apart_point_and_line(intersection_point(X,Y),Z)=> apart_point_and_line(intersection_point(X,Z),Y) ) ) ))),
% 0.09/0.51 inference(negated_conjecture,[status(cth)],[f13])).
% 0.09/0.51 fof(f15,plain,(
% 0.09/0.51 ![X0]: (~distinct_points(X0,X0))),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.51 fof(f31,plain,(
% 0.09/0.51 ![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))))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.09/0.51 fof(f32,plain,(
% 0.09/0.51 ![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)))))),
% 0.09/0.51 inference(miniscoping,[status(thm)],[f31])).
% 0.09/0.51 fof(f33,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f32])).
% 0.09/0.51 fof(f34,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f32])).
% 0.09/0.51 fof(f35,plain,(
% 0.09/0.51 ![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)))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.09/0.51 fof(f36,plain,(
% 0.09/0.51 ![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))),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f35])).
% 0.09/0.51 fof(f43,plain,(
% 0.09/0.51 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.09/0.51 fof(f44,plain,(
% 0.09/0.51 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f43])).
% 0.09/0.51 fof(f45,plain,(
% 0.09/0.51 (?[X,Y,Z]: (((convergent_lines(X,Y)&convergent_lines(Z,Y))&convergent_lines(X,Z))&(apart_point_and_line(intersection_point(X,Y),Z)&~apart_point_and_line(intersection_point(X,Z),Y))))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.09/0.51 fof(f46,plain,(
% 0.09/0.51 (((convergent_lines(sK0_skl,sK1_skl)&convergent_lines(sK2_skl,sK1_skl))&convergent_lines(sK0_skl,sK2_skl))&(apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)&~apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)))),
% 0.09/0.51 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])).
% 0.09/0.51 fof(f47,plain,(
% 0.09/0.51 convergent_lines(sK0_skl,sK1_skl)),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f46])).
% 0.09/0.51 fof(f49,plain,(
% 0.09/0.51 convergent_lines(sK0_skl,sK2_skl)),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f46])).
% 0.09/0.51 fof(f50,plain,(
% 0.09/0.51 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f46])).
% 0.09/0.51 fof(f51,plain,(
% 0.09/0.51 ~apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f46])).
% 0.09/0.51 fof(f56,plain,(
% 0.09/0.51 ![X0]: (~apart_point_and_line(X0,sK0_skl)|distinct_points(X0,intersection_point(sK0_skl,sK2_skl)))),
% 0.09/0.51 inference(resolution,[status(thm)],[f33,f49])).
% 0.09/0.51 fof(f57,plain,(
% 0.09/0.51 ![X0]: (~apart_point_and_line(X0,sK0_skl)|distinct_points(X0,intersection_point(sK0_skl,sK1_skl)))),
% 0.09/0.51 inference(resolution,[status(thm)],[f33,f47])).
% 0.09/0.51 fof(f60,plain,(
% 0.09/0.51 distinct_lines(sK0_skl,sK1_skl)),
% 0.09/0.51 inference(resolution,[status(thm)],[f44,f47])).
% 0.09/0.51 fof(f65,plain,(
% 0.09/0.51 ![X0]: (~apart_point_and_line(X0,sK2_skl)|distinct_points(X0,intersection_point(sK0_skl,sK2_skl)))),
% 0.09/0.51 inference(resolution,[status(thm)],[f34,f49])).
% 0.09/0.51 fof(f66,plain,(
% 0.09/0.51 ![X0]: (~apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK0_skl,sK1_skl)))),
% 0.09/0.51 inference(resolution,[status(thm)],[f34,f47])).
% 0.09/0.51 fof(f78,plain,(
% 0.09/0.51 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X1,sK0_skl)|apart_point_and_line(X1,sK1_skl))),
% 0.09/0.51 inference(resolution,[status(thm)],[f36,f60])).
% 0.09/0.51 fof(f112,plain,(
% 0.09/0.51 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))),
% 0.09/0.51 inference(resolution,[status(thm)],[f65,f50])).
% 0.09/0.51 fof(f193,definition,(
% 0.09/0.51 sQ11_spl <=> (distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl)))),
% 0.09/0.51 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.09/0.51 fof(f194,plain,(
% 0.09/0.51 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ11_spl),
% 0.09/0.51 inference(component_clause,[status(thm)],[f193])).
% 0.09/0.51 fof(f244,definition,(
% 0.09/0.51 sQ18_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.09/0.51 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.09/0.51 fof(f245,plain,(
% 0.09/0.51 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ18_spl),
% 0.09/0.51 inference(component_clause,[status(thm)],[f244])).
% 0.09/0.51 fof(f247,definition,(
% 0.09/0.51 sQ19_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 0.09/0.51 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.09/0.51 fof(f248,plain,(
% 0.09/0.51 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ19_spl),
% 0.09/0.51 inference(component_clause,[status(thm)],[f247])).
% 0.09/0.51 fof(f254,plain,(
% 0.09/0.51 $false|~sQ11_spl),
% 0.09/0.51 inference(forward_subsumption_resolution,[status(thm)],[f194,f15])).
% 0.09/0.51 fof(f255,plain,(
% 0.09/0.51 ~sQ11_spl),
% 0.09/0.51 inference(contradiction_clause,[status(thm)],[f254])).
% 0.09/0.51 fof(f267,plain,(
% 0.09/0.51 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ18_spl),
% 0.09/0.51 inference(resolution,[status(thm)],[f245,f57])).
% 0.09/0.51 fof(f272,plain,(
% 0.09/0.51 sQ11_spl|~sQ18_spl),
% 0.09/0.51 inference(split_clause,[status(thm)],[f267,f193,f244])).
% 0.09/0.51 fof(f280,plain,(
% 0.09/0.51 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ19_spl),
% 0.09/0.51 inference(resolution,[status(thm)],[f248,f66])).
% 0.09/0.51 fof(f285,plain,(
% 0.09/0.51 sQ11_spl|~sQ19_spl),
% 0.09/0.51 inference(split_clause,[status(thm)],[f280,f193,f247])).
% 0.09/0.51 fof(f440,plain,(
% 0.09/0.51 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)),
% 0.09/0.51 inference(resolution,[status(thm)],[f112,f78])).
% 0.09/0.51 fof(f442,definition,(
% 0.09/0.51 sQ42_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl))),
% 0.09/0.51 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.09/0.51 fof(f443,plain,(
% 0.09/0.51 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|~sQ42_spl),
% 0.09/0.51 inference(component_clause,[status(thm)],[f442])).
% 0.09/0.51 fof(f449,definition,(
% 0.09/0.51 sQ44_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl))),
% 0.09/0.51 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.09/0.51 fof(f450,plain,(
% 0.09/0.51 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)|~sQ44_spl),
% 0.09/0.51 inference(component_clause,[status(thm)],[f449])).
% 0.09/0.51 fof(f452,plain,(
% 0.09/0.51 sQ18_spl|sQ19_spl|sQ42_spl|sQ44_spl),
% 0.09/0.51 inference(split_clause,[status(thm)],[f440,f244,f247,f442,f449])).
% 0.09/0.51 fof(f581,plain,(
% 0.09/0.51 distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl))|~sQ42_spl),
% 0.09/0.51 inference(resolution,[status(thm)],[f443,f56])).
% 0.09/0.51 fof(f587,plain,(
% 0.09/0.51 $false|~sQ42_spl),
% 0.09/0.51 inference(forward_subsumption_resolution,[status(thm)],[f581,f15])).
% 0.09/0.51 fof(f588,plain,(
% 0.09/0.51 ~sQ42_spl),
% 0.09/0.51 inference(contradiction_clause,[status(thm)],[f587])).
% 0.09/0.51 fof(f589,plain,(
% 0.09/0.51 $false|~sQ44_spl),
% 0.09/0.51 inference(forward_subsumption_resolution,[status(thm)],[f450,f51])).
% 0.09/0.51 fof(f590,plain,(
% 0.09/0.51 ~sQ44_spl),
% 0.09/0.51 inference(contradiction_clause,[status(thm)],[f589])).
% 0.09/0.51 fof(f591,plain,(
% 0.09/0.51 $false),
% 0.09/0.51 inference(sat_refutation,[status(thm)],[f255,f272,f285,f452,f588,f590])).
% 0.09/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 1.04/0.53 % Elapsed time: 0.143931 seconds
% 1.04/0.53 % CPU time: 0.911752 seconds
% 1.04/0.53 % Total memory used: 28.992 MB
% 1.04/0.53 % Net memory used: 26.466 MB
%------------------------------------------------------------------------------