%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO197+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 : n020.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 12:26:03 PM UTC 2026
% Result : Theorem 1.38s 0.81s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO197+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
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 13:21:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 1.38/0.81 % Refutation found
% 1.38/0.81 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.38/0.81 % SZS output start CNFRefutation for theBenchmark
% 1.38/0.81 fof(f1,axiom,(
% 1.38/0.81 (! [X] : ~ distinct_points(X,X) )),
% 1.38/0.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.38/0.81 fof(f8,axiom,(
% 1.38/0.81 (! [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)) ) ) )),
% 1.38/0.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.38/0.81 fof(f9,axiom,(
% 1.38/0.81 (! [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) ) ) )),
% 1.38/0.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.38/0.81 fof(f10,axiom,(
% 1.38/0.81 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 1.38/0.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.38/0.81 fof(f12,axiom,(
% 1.38/0.81 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 1.38/0.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.38/0.81 fof(f13,conjecture,(
% 1.38/0.81 (! [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(Z,Y),X) ) )),
% 1.38/0.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.38/0.81 fof(f14,negated_conjecture,(
% 1.38/0.81 ~((! [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(Z,Y),X) ) ))),
% 1.38/0.81 inference(negated_conjecture,[status(cth)],[f13])).
% 1.38/0.81 fof(f15,plain,(
% 1.38/0.81 ![X0]: (~distinct_points(X0,X0))),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f1])).
% 1.38/0.81 fof(f31,plain,(
% 1.38/0.81 ![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))))),
% 1.38/0.81 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 1.38/0.81 fof(f32,plain,(
% 1.38/0.81 ![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)))))),
% 1.38/0.81 inference(miniscoping,[status(thm)],[f31])).
% 1.38/0.81 fof(f33,plain,(
% 1.38/0.81 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f32])).
% 1.38/0.81 fof(f34,plain,(
% 1.38/0.81 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f32])).
% 1.38/0.81 fof(f35,plain,(
% 1.38/0.81 ![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)))),
% 1.38/0.81 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 1.38/0.81 fof(f36,plain,(
% 1.38/0.81 ![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))),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f35])).
% 1.38/0.81 fof(f37,plain,(
% 1.38/0.81 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 1.38/0.81 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 1.38/0.81 fof(f38,plain,(
% 1.38/0.81 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 1.38/0.81 inference(miniscoping,[status(thm)],[f37])).
% 1.38/0.81 fof(f39,plain,(
% 1.38/0.81 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f38])).
% 1.38/0.81 fof(f43,plain,(
% 1.38/0.81 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 1.38/0.81 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 1.38/0.81 fof(f44,plain,(
% 1.38/0.81 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f43])).
% 1.38/0.81 fof(f45,plain,(
% 1.38/0.81 (?[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(Z,Y),X)))),
% 1.38/0.81 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 1.38/0.81 fof(f46,plain,(
% 1.38/0.81 ((((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(sK2_skl,sK1_skl),sK0_skl))),
% 1.38/0.81 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])).
% 1.38/0.81 fof(f47,plain,(
% 1.38/0.81 convergent_lines(sK0_skl,sK1_skl)),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f46])).
% 1.38/0.81 fof(f48,plain,(
% 1.38/0.81 convergent_lines(sK2_skl,sK1_skl)),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f46])).
% 1.38/0.81 fof(f50,plain,(
% 1.38/0.81 ~apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f46])).
% 1.38/0.81 fof(f51,plain,(
% 1.38/0.81 apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK0_skl)),
% 1.38/0.81 inference(cnf_transformation,[status(thm)],[f46])).
% 1.38/0.81 fof(f60,plain,(
% 1.38/0.81 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 1.38/0.81 inference(resolution,[status(thm)],[f15,f34])).
% 1.38/0.81 fof(f61,plain,(
% 1.38/0.81 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 1.38/0.81 inference(resolution,[status(thm)],[f15,f33])).
% 1.38/0.81 fof(f63,plain,(
% 1.38/0.81 distinct_lines(sK2_skl,sK1_skl)),
% 1.38/0.81 inference(resolution,[status(thm)],[f44,f48])).
% 1.38/0.81 fof(f149,plain,(
% 1.38/0.81 ![X0]: (distinct_points(intersection_point(sK2_skl,sK1_skl),X0)|apart_point_and_line(X0,sK0_skl))),
% 1.38/0.81 inference(resolution,[status(thm)],[f39,f51])).
% 1.38/0.81 fof(f183,plain,(
% 1.38/0.81 ![X0,X1,X2]: (apart_point_and_line(X0,sK0_skl)|~distinct_lines(X1,X2)|apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X1)|apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X2)|apart_point_and_line(X0,X1)|apart_point_and_line(X0,X2))),
% 1.38/0.81 inference(resolution,[status(thm)],[f149,f36])).
% 1.38/0.81 fof(f322,plain,(
% 1.38/0.81 ![X0]: (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl)|apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK1_skl))),
% 1.38/0.81 inference(resolution,[status(thm)],[f183,f63])).
% 1.38/0.81 fof(f340,definition,(
% 1.38/0.81 sQ22_spl <=> (apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl))),
% 1.38/0.81 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 1.38/0.81 fof(f341,plain,(
% 1.38/0.81 apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl)|~sQ22_spl),
% 1.38/0.81 inference(component_clause,[status(thm)],[f340])).
% 1.38/0.81 fof(f347,definition,(
% 1.38/0.81 sQ24_spl <=> (apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl))),
% 1.38/0.81 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 1.38/0.81 fof(f348,plain,(
% 1.38/0.81 apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl)|~sQ24_spl),
% 1.38/0.81 inference(component_clause,[status(thm)],[f347])).
% 1.38/0.81 fof(f360,definition,(
% 1.38/0.81 ![X0]: (sQ27_spl <=> (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK1_skl)))),
% 1.38/0.81 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 1.38/0.81 fof(f361,plain,(
% 1.38/0.81 ![X0]: (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK1_skl)|~sQ27_spl)),
% 1.38/0.81 inference(component_clause,[status(thm)],[f360])).
% 1.38/0.81 fof(f363,plain,(
% 1.38/0.81 sQ27_spl|sQ24_spl|sQ22_spl),
% 1.38/0.81 inference(split_clause,[status(thm)],[f322,f360,f347,f340])).
% 1.38/0.81 fof(f396,plain,(
% 1.38/0.81 ~convergent_lines(sK2_skl,sK1_skl)|~sQ24_spl),
% 1.38/0.81 inference(resolution,[status(thm)],[f348,f61])).
% 1.38/0.81 fof(f403,plain,(
% 1.38/0.81 $false|~sQ24_spl),
% 1.38/0.81 inference(forward_subsumption_resolution,[status(thm)],[f396,f48])).
% 1.38/0.81 fof(f404,plain,(
% 1.38/0.81 ~sQ24_spl),
% 1.38/0.81 inference(contradiction_clause,[status(thm)],[f403])).
% 1.38/0.81 fof(f406,plain,(
% 1.38/0.81 ~convergent_lines(sK2_skl,sK1_skl)|~sQ22_spl),
% 1.38/0.81 inference(resolution,[status(thm)],[f341,f60])).
% 1.38/0.81 fof(f413,plain,(
% 1.38/0.81 $false|~sQ22_spl),
% 1.38/0.81 inference(forward_subsumption_resolution,[status(thm)],[f406,f48])).
% 1.38/0.81 fof(f414,plain,(
% 1.38/0.81 ~sQ22_spl),
% 1.38/0.81 inference(contradiction_clause,[status(thm)],[f413])).
% 1.38/0.81 fof(f3943,definition,(
% 1.38/0.81 sQ355_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 1.38/0.81 introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition])).
% 3.06/0.82 fof(f3944,plain,(
% 3.06/0.82 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ355_spl),
% 3.06/0.82 inference(component_clause,[status(thm)],[f3943])).
% 3.06/0.82 fof(f3989,plain,(
% 3.06/0.82 ~convergent_lines(sK0_skl,sK1_skl)|~sQ355_spl),
% 3.06/0.82 inference(resolution,[status(thm)],[f3944,f61])).
% 3.06/0.82 fof(f3996,plain,(
% 3.06/0.82 $false|~sQ355_spl),
% 3.06/0.82 inference(forward_subsumption_resolution,[status(thm)],[f3989,f47])).
% 3.06/0.82 fof(f3997,plain,(
% 3.06/0.82 ~sQ355_spl),
% 3.06/0.82 inference(contradiction_clause,[status(thm)],[f3996])).
% 3.06/0.82 fof(f4416,plain,(
% 3.06/0.82 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ27_spl),
% 3.06/0.82 inference(resolution,[status(thm)],[f361,f50])).
% 3.06/0.82 fof(f4426,definition,(
% 3.06/0.82 sQ400_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 3.06/0.82 introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition])).
% 3.06/0.82 fof(f4427,plain,(
% 3.06/0.82 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ400_spl),
% 3.06/0.82 inference(component_clause,[status(thm)],[f4426])).
% 3.06/0.82 fof(f4429,plain,(
% 3.06/0.82 sQ355_spl|sQ400_spl|~sQ27_spl),
% 3.06/0.82 inference(split_clause,[status(thm)],[f4416,f3943,f4426,f360])).
% 3.06/0.82 fof(f4430,plain,(
% 3.06/0.82 ~convergent_lines(sK0_skl,sK1_skl)|~sQ400_spl),
% 3.06/0.82 inference(resolution,[status(thm)],[f4427,f60])).
% 3.06/0.82 fof(f4437,plain,(
% 3.06/0.82 $false|~sQ400_spl),
% 3.06/0.82 inference(forward_subsumption_resolution,[status(thm)],[f4430,f47])).
% 3.06/0.82 fof(f4438,plain,(
% 3.06/0.82 ~sQ400_spl),
% 3.06/0.82 inference(contradiction_clause,[status(thm)],[f4437])).
% 3.06/0.82 fof(f4439,plain,(
% 3.06/0.82 $false),
% 3.06/0.82 inference(sat_refutation,[status(thm)],[f363,f404,f414,f3997,f4429,f4438])).
% 3.06/0.82 % SZS output end CNFRefutation for theBenchmark.p
% 3.06/0.83 % Elapsed time: 0.469242 seconds
% 3.06/0.83 % CPU time: 3.459905 seconds
% 3.06/0.83 % Total memory used: 52.428 MB
% 3.06/0.83 % Net memory used: 44.863 MB
%------------------------------------------------------------------------------