%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO195+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 : n012.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 2.24s 0.66s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO195+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 20 13:20:37 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 2.24/0.66 % Refutation found
% 2.24/0.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.24/0.66 % SZS output start CNFRefutation for theBenchmark
% 2.24/0.66 fof(f1,axiom,(
% 2.24/0.66 (! [X] : ~ distinct_points(X,X) )),
% 2.24/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.24/0.66 fof(f3,axiom,(
% 2.24/0.66 (! [X] : ~ convergent_lines(X,X) )),
% 2.24/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.24/0.66 fof(f6,axiom,(
% 2.24/0.66 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 2.24/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.24/0.66 fof(f8,axiom,(
% 2.24/0.66 (! [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)) ) ) )),
% 2.24/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.24/0.66 fof(f9,axiom,(
% 2.24/0.66 (! [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) ) ) )),
% 2.24/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.24/0.66 fof(f10,axiom,(
% 2.24/0.66 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 2.24/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.24/0.66 fof(f12,axiom,(
% 2.24/0.66 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 2.24/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.24/0.66 fof(f13,conjecture,(
% 2.24/0.66 (! [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(Y,X),Z) ) ) )),
% 2.24/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.24/0.66 fof(f14,negated_conjecture,(
% 2.24/0.66 ~((! [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(Y,X),Z) ) ) ))),
% 2.24/0.66 inference(negated_conjecture,[status(cth)],[f13])).
% 2.24/0.66 fof(f15,plain,(
% 2.24/0.66 ![X0]: (~distinct_points(X0,X0))),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f1])).
% 2.24/0.66 fof(f17,plain,(
% 2.24/0.66 ![X0]: (~convergent_lines(X0,X0))),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f3])).
% 2.24/0.66 fof(f24,plain,(
% 2.24/0.66 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 2.24/0.66 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 2.24/0.66 fof(f25,plain,(
% 2.24/0.66 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 2.24/0.66 inference(miniscoping,[status(thm)],[f24])).
% 2.24/0.66 fof(f26,plain,(
% 2.24/0.66 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f25])).
% 2.24/0.66 fof(f31,plain,(
% 2.24/0.66 ![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))))),
% 2.24/0.66 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 2.24/0.66 fof(f32,plain,(
% 2.24/0.66 ![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)))))),
% 2.24/0.66 inference(miniscoping,[status(thm)],[f31])).
% 2.24/0.66 fof(f33,plain,(
% 2.24/0.66 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f32])).
% 2.24/0.66 fof(f34,plain,(
% 2.24/0.66 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f32])).
% 2.24/0.66 fof(f35,plain,(
% 2.24/0.66 ![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)))),
% 2.24/0.66 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 2.24/0.66 fof(f36,plain,(
% 2.24/0.66 ![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))),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f35])).
% 2.24/0.66 fof(f37,plain,(
% 2.24/0.66 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 2.24/0.66 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 2.24/0.66 fof(f38,plain,(
% 2.24/0.66 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 2.24/0.66 inference(miniscoping,[status(thm)],[f37])).
% 2.24/0.66 fof(f39,plain,(
% 2.24/0.66 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f38])).
% 2.24/0.66 fof(f43,plain,(
% 2.24/0.66 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 2.24/0.66 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 2.24/0.66 fof(f44,plain,(
% 2.24/0.66 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f43])).
% 2.24/0.66 fof(f45,plain,(
% 2.24/0.66 (?[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(Y,X),Z))))),
% 2.24/0.66 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 2.24/0.66 fof(f46,plain,(
% 2.24/0.66 (((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(sK1_skl,sK0_skl),sK2_skl)))),
% 2.24/0.66 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])).
% 2.24/0.66 fof(f47,plain,(
% 2.24/0.66 convergent_lines(sK0_skl,sK1_skl)),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f46])).
% 2.24/0.66 fof(f50,plain,(
% 2.24/0.66 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f46])).
% 2.24/0.66 fof(f51,plain,(
% 2.24/0.66 ~apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK2_skl)),
% 2.24/0.66 inference(cnf_transformation,[status(thm)],[f46])).
% 2.24/0.66 fof(f52,plain,(
% 2.24/0.66 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 2.24/0.66 inference(resolution,[status(thm)],[f15,f34])).
% 2.24/0.66 fof(f53,plain,(
% 2.24/0.66 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 2.24/0.66 inference(resolution,[status(thm)],[f15,f33])).
% 2.24/0.66 fof(f56,plain,(
% 2.24/0.66 distinct_lines(sK0_skl,sK1_skl)),
% 2.24/0.66 inference(resolution,[status(thm)],[f44,f47])).
% 2.24/0.66 fof(f59,plain,(
% 2.24/0.66 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 2.24/0.66 inference(resolution,[status(thm)],[f26,f47])).
% 2.24/0.66 fof(f66,plain,(
% 2.24/0.66 ![X0,X1]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X1)|convergent_lines(X0,X1))),
% 2.24/0.66 inference(resolution,[status(thm)],[f59,f26])).
% 2.24/0.66 fof(f151,plain,(
% 2.24/0.66 convergent_lines(sK1_skl,sK0_skl)),
% 2.24/0.66 inference(resolution,[status(thm)],[f66,f17])).
% 2.24/0.66 fof(f489,plain,(
% 2.24/0.66 ![X0]: (distinct_points(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(X0,sK2_skl))),
% 2.24/0.66 inference(resolution,[status(thm)],[f39,f50])).
% 2.24/0.66 fof(f495,plain,(
% 2.24/0.66 ![X0,X1,X2]: (apart_point_and_line(X0,sK2_skl)|~distinct_lines(X1,X2)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X2)|apart_point_and_line(X0,X1)|apart_point_and_line(X0,X2))),
% 2.24/0.66 inference(resolution,[status(thm)],[f489,f36])).
% 2.24/0.66 fof(f675,plain,(
% 2.24/0.66 ![X0]: (apart_point_and_line(X0,sK2_skl)|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(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl))),
% 2.24/0.66 inference(resolution,[status(thm)],[f495,f56])).
% 2.24/0.66 fof(f709,definition,(
% 2.24/0.66 sQ46_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 2.24/0.66 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 2.24/0.66 fof(f710,plain,(
% 2.24/0.66 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ46_spl),
% 2.24/0.66 inference(component_clause,[status(thm)],[f709])).
% 2.24/0.66 fof(f721,definition,(
% 2.24/0.66 ![X0]: (sQ49_spl <=> (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)))),
% 2.24/0.66 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 2.24/0.66 fof(f722,plain,(
% 2.24/0.66 ![X0]: (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)|~sQ49_spl)),
% 2.24/0.66 inference(component_clause,[status(thm)],[f721])).
% 2.24/0.66 fof(f724,definition,(
% 2.24/0.66 sQ50_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 2.24/0.66 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 2.24/0.66 fof(f725,plain,(
% 2.24/0.66 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ50_spl),
% 2.24/0.66 inference(component_clause,[status(thm)],[f724])).
% 2.24/0.66 fof(f727,plain,(
% 2.24/0.66 sQ49_spl|sQ50_spl|sQ46_spl),
% 2.24/0.66 inference(split_clause,[status(thm)],[f675,f721,f724,f709])).
% 2.24/0.66 fof(f779,plain,(
% 2.24/0.66 ~convergent_lines(sK0_skl,sK1_skl)|~sQ50_spl),
% 2.24/0.66 inference(resolution,[status(thm)],[f725,f53])).
% 2.24/0.66 fof(f786,plain,(
% 2.24/0.66 $false|~sQ50_spl),
% 2.24/0.66 inference(forward_subsumption_resolution,[status(thm)],[f779,f47])).
% 2.24/0.66 fof(f787,plain,(
% 2.24/0.66 ~sQ50_spl),
% 2.24/0.66 inference(contradiction_clause,[status(thm)],[f786])).
% 2.24/0.66 fof(f789,plain,(
% 2.24/0.66 ~convergent_lines(sK0_skl,sK1_skl)|~sQ46_spl),
% 2.24/0.66 inference(resolution,[status(thm)],[f710,f52])).
% 2.24/0.66 fof(f796,plain,(
% 2.24/0.66 $false|~sQ46_spl),
% 2.24/0.66 inference(forward_subsumption_resolution,[status(thm)],[f789,f47])).
% 2.24/0.66 fof(f797,plain,(
% 2.24/0.66 ~sQ46_spl),
% 2.24/0.66 inference(contradiction_clause,[status(thm)],[f796])).
% 2.24/0.66 fof(f2663,plain,(
% 2.24/0.66 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|~sQ49_spl),
% 2.24/0.66 inference(resolution,[status(thm)],[f722,f51])).
% 2.24/0.66 fof(f2672,definition,(
% 2.24/0.66 sQ259_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl))),
% 2.24/0.66 introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition])).
% 2.24/0.66 fof(f2673,plain,(
% 2.24/0.66 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|~sQ259_spl),
% 2.24/0.66 inference(component_clause,[status(thm)],[f2672])).
% 2.24/0.66 fof(f2675,definition,(
% 2.24/0.66 sQ260_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl))),
% 2.24/0.66 introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition])).
% 2.24/0.66 fof(f2676,plain,(
% 2.24/0.66 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|~sQ260_spl),
% 2.24/0.66 inference(component_clause,[status(thm)],[f2675])).
% 2.24/0.66 fof(f2678,plain,(
% 2.24/0.66 sQ259_spl|sQ260_spl|~sQ49_spl),
% 2.24/0.66 inference(split_clause,[status(thm)],[f2663,f2672,f2675,f721])).
% 2.24/0.66 fof(f3412,plain,(
% 2.24/0.66 ~convergent_lines(sK1_skl,sK0_skl)|~sQ259_spl),
% 2.24/0.66 inference(resolution,[status(thm)],[f2673,f52])).
% 2.24/0.66 fof(f3419,plain,(
% 2.24/0.66 $false|~sQ259_spl),
% 2.24/0.66 inference(forward_subsumption_resolution,[status(thm)],[f3412,f151])).
% 2.24/0.66 fof(f3420,plain,(
% 2.24/0.66 ~sQ259_spl),
% 2.24/0.66 inference(contradiction_clause,[status(thm)],[f3419])).
% 2.24/0.66 fof(f3421,plain,(
% 2.24/0.66 ~convergent_lines(sK1_skl,sK0_skl)|~sQ260_spl),
% 2.24/0.66 inference(resolution,[status(thm)],[f2676,f53])).
% 2.24/0.66 fof(f3428,plain,(
% 2.24/0.66 $false|~sQ260_spl),
% 2.24/0.66 inference(forward_subsumption_resolution,[status(thm)],[f3421,f151])).
% 2.24/0.66 fof(f3429,plain,(
% 2.24/0.66 ~sQ260_spl),
% 2.24/0.66 inference(contradiction_clause,[status(thm)],[f3428])).
% 2.24/0.66 fof(f3430,plain,(
% 2.24/0.66 $false),
% 2.24/0.66 inference(sat_refutation,[status(thm)],[f727,f787,f797,f2678,f3420,f3429])).
% 2.24/0.66 % SZS output end CNFRefutation for theBenchmark.p
% 2.24/0.66 % Elapsed time: 0.356851 seconds
% 2.24/0.66 % CPU time: 2.667671 seconds
% 2.24/0.66 % Total memory used: 59.101 MB
% 2.24/0.66 % Net memory used: 50.391 MB
%------------------------------------------------------------------------------