%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO186+1 : 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 : n003.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 0.10s 0.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO186+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 13:08:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.45 % Refutation found
% 0.10/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.45 fof(f3,axiom,(
% 0.10/0.45 (! [X] : ~ convergent_lines(X,X) )),
% 0.10/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.45 fof(f9,axiom,(
% 0.10/0.45 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.10/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.45 fof(f10,axiom,(
% 0.10/0.45 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.10/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.45 fof(f11,axiom,(
% 0.10/0.45 (! [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) ) ) )),
% 0.10/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.45 fof(f14,axiom,(
% 0.10/0.45 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.10/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.45 fof(f15,conjecture,(
% 0.10/0.45 (! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& ~ apart_point_and_line(X,U)& ~ apart_point_and_line(X,V) )=> ~ distinct_points(X,intersection_point(U,V)) ) )),
% 0.10/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.45 fof(f16,negated_conjecture,(
% 0.10/0.45 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& ~ apart_point_and_line(X,U)& ~ apart_point_and_line(X,V) )=> ~ distinct_points(X,intersection_point(U,V)) ) ))),
% 0.10/0.45 inference(negated_conjecture,[status(cth)],[f15])).
% 0.10/0.45 fof(f19,plain,(
% 0.10/0.45 ![X0]: (~convergent_lines(X0,X0))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.45 fof(f33,plain,(
% 0.10/0.45 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.10/0.45 fof(f34,plain,(
% 0.10/0.45 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f33])).
% 0.10/0.45 fof(f35,plain,(
% 0.10/0.45 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.10/0.45 fof(f36,plain,(
% 0.10/0.45 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f35])).
% 0.10/0.45 fof(f37,plain,(
% 0.10/0.45 ![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)))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.10/0.45 fof(f38,plain,(
% 0.10/0.45 ![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))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f37])).
% 0.10/0.45 fof(f45,plain,(
% 0.10/0.45 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.10/0.45 fof(f46,plain,(
% 0.10/0.45 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.10/0.45 inference(miniscoping,[status(thm)],[f45])).
% 0.10/0.45 fof(f47,plain,(
% 0.10/0.45 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.10/0.45 inference(cnf_transformation,[status(thm)],[f46])).
% 0.10/0.45 fof(f48,plain,(
% 0.10/0.45 (?[X,Y,U,V]: ((((distinct_points(X,Y)&convergent_lines(U,V))&~apart_point_and_line(X,U))&~apart_point_and_line(X,V))&distinct_points(X,intersection_point(U,V))))),
% 0.10/0.45 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.10/0.45 fof(f49,plain,(
% 0.10/0.45 ?[X,U,V]: (((((?[Y]: distinct_points(X,Y))&convergent_lines(U,V))&~apart_point_and_line(X,U))&~apart_point_and_line(X,V))&distinct_points(X,intersection_point(U,V)))),
% 0.10/0.45 inference(miniscoping,[status(thm)],[f48])).
% 0.10/0.45 fof(f50,plain,(
% 0.10/0.45 ((((distinct_points(sK0_skl,sK3_skl)&convergent_lines(sK1_skl,sK2_skl))&~apart_point_and_line(sK0_skl,sK1_skl))&~apart_point_and_line(sK0_skl,sK2_skl))&distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)))),
% 0.10/0.45 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)],[f49])).
% 0.10/0.46 fof(f52,plain,(
% 0.10/0.46 convergent_lines(sK1_skl,sK2_skl)),
% 0.10/0.46 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.46 fof(f53,plain,(
% 0.10/0.46 ~apart_point_and_line(sK0_skl,sK1_skl)),
% 0.10/0.46 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.46 fof(f54,plain,(
% 0.10/0.46 ~apart_point_and_line(sK0_skl,sK2_skl)),
% 0.10/0.46 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.46 fof(f55,plain,(
% 0.10/0.46 distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))),
% 0.10/0.46 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.46 fof(f65,plain,(
% 0.10/0.46 ![X0]: (distinct_lines(sK2_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.10/0.46 inference(resolution,[status(thm)],[f47,f52])).
% 0.10/0.46 fof(f70,plain,(
% 0.10/0.46 distinct_lines(sK2_skl,sK1_skl)),
% 0.10/0.46 inference(resolution,[status(thm)],[f65,f19])).
% 0.10/0.46 fof(f71,plain,(
% 0.10/0.46 ![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))),
% 0.10/0.46 inference(resolution,[status(thm)],[f70,f38])).
% 0.10/0.46 fof(f231,plain,(
% 0.10/0.46 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)),
% 0.10/0.46 inference(resolution,[status(thm)],[f71,f55])).
% 0.10/0.46 fof(f243,definition,(
% 0.10/0.46 sQ19_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f244,plain,(
% 0.10/0.46 apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK2_skl)|~sQ19_spl),
% 0.10/0.46 inference(component_clause,[status(thm)],[f243])).
% 0.10/0.46 fof(f246,definition,(
% 0.10/0.46 sQ20_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f247,plain,(
% 0.10/0.46 apart_point_and_line(intersection_point(sK1_skl,sK2_skl),sK1_skl)|~sQ20_spl),
% 0.10/0.46 inference(component_clause,[status(thm)],[f246])).
% 0.10/0.46 fof(f267,definition,(
% 0.10/0.46 sQ26_spl <=> (apart_point_and_line(sK0_skl,sK2_skl))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f268,plain,(
% 0.10/0.46 apart_point_and_line(sK0_skl,sK2_skl)|~sQ26_spl),
% 0.10/0.46 inference(component_clause,[status(thm)],[f267])).
% 0.10/0.46 fof(f270,definition,(
% 0.10/0.46 sQ27_spl <=> (apart_point_and_line(sK0_skl,sK1_skl))),
% 0.10/0.46 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.10/0.46 fof(f271,plain,(
% 0.10/0.46 apart_point_and_line(sK0_skl,sK1_skl)|~sQ27_spl),
% 0.10/0.46 inference(component_clause,[status(thm)],[f270])).
% 0.10/0.46 fof(f283,plain,(
% 0.10/0.46 sQ26_spl|sQ27_spl|sQ19_spl|sQ20_spl),
% 0.10/0.46 inference(split_clause,[status(thm)],[f231,f267,f270,f243,f246])).
% 0.10/0.46 fof(f307,plain,(
% 0.10/0.46 $false|~sQ27_spl),
% 0.10/0.46 inference(forward_subsumption_resolution,[status(thm)],[f271,f53])).
% 0.10/0.46 fof(f308,plain,(
% 0.10/0.46 ~sQ27_spl),
% 0.10/0.46 inference(contradiction_clause,[status(thm)],[f307])).
% 0.10/0.46 fof(f309,plain,(
% 0.10/0.46 $false|~sQ26_spl),
% 0.10/0.46 inference(forward_subsumption_resolution,[status(thm)],[f268,f54])).
% 0.10/0.46 fof(f310,plain,(
% 0.10/0.46 ~sQ26_spl),
% 0.10/0.46 inference(contradiction_clause,[status(thm)],[f309])).
% 0.10/0.46 fof(f627,plain,(
% 0.10/0.46 ~convergent_lines(sK1_skl,sK2_skl)|~sQ19_spl),
% 0.10/0.46 inference(resolution,[status(thm)],[f244,f36])).
% 0.10/0.46 fof(f630,plain,(
% 0.10/0.46 $false|~sQ19_spl),
% 0.10/0.46 inference(forward_subsumption_resolution,[status(thm)],[f627,f52])).
% 0.10/0.46 fof(f631,plain,(
% 0.10/0.46 ~sQ19_spl),
% 0.10/0.46 inference(contradiction_clause,[status(thm)],[f630])).
% 0.10/0.46 fof(f712,plain,(
% 0.10/0.46 ~convergent_lines(sK1_skl,sK2_skl)|~sQ20_spl),
% 0.10/0.46 inference(resolution,[status(thm)],[f247,f34])).
% 0.10/0.46 fof(f715,plain,(
% 0.10/0.46 $false|~sQ20_spl),
% 0.10/0.46 inference(forward_subsumption_resolution,[status(thm)],[f712,f52])).
% 0.10/0.46 fof(f716,plain,(
% 0.10/0.46 ~sQ20_spl),
% 0.10/0.46 inference(contradiction_clause,[status(thm)],[f715])).
% 0.10/0.46 fof(f717,plain,(
% 0.10/0.46 $false),
% 0.10/0.46 inference(sat_refutation,[status(thm)],[f283,f308,f310,f631,f716])).
% 0.10/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.47 % Elapsed time: 0.097957 seconds
% 0.10/0.47 % CPU time: 0.546175 seconds
% 0.10/0.47 % Total memory used: 22.906 MB
% 0.10/0.47 % Net memory used: 21.318 MB
%------------------------------------------------------------------------------