%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO192+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 : n013.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 12:26:01 PM UTC 2026
% Result : Theorem 0.09s 5.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO192+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
% 0.09/5.37 % Computer : n013.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 13:16:12 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/5.39 fof(f1,axiom,(
% 0.09/5.39 (! [X] : ~ distinct_points(X,X) )),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f2,axiom,(
% 0.09/5.39 (! [X] : ~ distinct_lines(X,X) )),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f5,axiom,(
% 0.09/5.39 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f6,axiom,(
% 0.09/5.39 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f8,axiom,(
% 0.09/5.39 (! [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)) ) ) )),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f11,axiom,(
% 0.09/5.39 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f12,axiom,(
% 0.09/5.39 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f13,conjecture,(
% 0.09/5.39 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( apart_point_and_line(intersection_point(X,Y),Z)=> ( distinct_lines(X,Z)& distinct_lines(Y,Z) ) ) ) )),
% 0.09/5.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f14,negated_conjecture,(
% 0.09/5.39 ~((! [X,Y,Z] :( convergent_lines(X,Y)=> ( apart_point_and_line(intersection_point(X,Y),Z)=> ( distinct_lines(X,Z)& distinct_lines(Y,Z) ) ) ) ))),
% 0.09/5.39 inference(negated_conjecture,[status(cth)],[f13])).
% 0.09/5.39 fof(f15,plain,(
% 0.09/5.39 ![X0]: (~distinct_points(X0,X0))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/5.39 fof(f16,plain,(
% 0.09/5.39 ![X0]: (~distinct_lines(X0,X0))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/5.39 fof(f21,plain,(
% 0.09/5.39 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 0.09/5.39 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.09/5.39 fof(f22,plain,(
% 0.09/5.39 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 0.09/5.39 inference(miniscoping,[status(thm)],[f21])).
% 0.09/5.39 fof(f23,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f22])).
% 0.09/5.39 fof(f24,plain,(
% 0.09/5.39 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.09/5.39 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.09/5.39 fof(f25,plain,(
% 0.09/5.39 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.09/5.39 inference(miniscoping,[status(thm)],[f24])).
% 0.09/5.39 fof(f26,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f25])).
% 0.09/5.39 fof(f31,plain,(
% 0.09/5.39 ![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))))),
% 0.09/5.39 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.09/5.39 fof(f32,plain,(
% 0.09/5.39 ![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)))))),
% 0.09/5.39 inference(miniscoping,[status(thm)],[f31])).
% 0.09/5.39 fof(f33,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f32])).
% 0.09/5.39 fof(f34,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f32])).
% 0.09/5.39 fof(f40,plain,(
% 0.09/5.39 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.09/5.39 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.09/5.39 fof(f41,plain,(
% 0.09/5.39 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.09/5.39 inference(miniscoping,[status(thm)],[f40])).
% 0.09/5.39 fof(f42,plain,(
% 0.09/5.39 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f41])).
% 0.09/5.39 fof(f43,plain,(
% 0.09/5.39 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 0.09/5.39 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.09/5.39 fof(f44,plain,(
% 0.09/5.39 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f43])).
% 0.09/5.39 fof(f45,plain,(
% 0.09/5.39 (?[X,Y,Z]: (convergent_lines(X,Y)&(apart_point_and_line(intersection_point(X,Y),Z)&(~distinct_lines(X,Z)|~distinct_lines(Y,Z)))))),
% 0.09/5.39 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.09/5.39 fof(f46,plain,(
% 0.09/5.39 ?[X,Y]: (convergent_lines(X,Y)&(?[Z]: (apart_point_and_line(intersection_point(X,Y),Z)&(~distinct_lines(X,Z)|~distinct_lines(Y,Z)))))),
% 0.09/5.39 inference(miniscoping,[status(thm)],[f45])).
% 0.09/5.39 fof(f47,plain,(
% 0.09/5.39 (convergent_lines(sK0_skl,sK1_skl)&(apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)&(~distinct_lines(sK0_skl,sK2_skl)|~distinct_lines(sK1_skl,sK2_skl))))),
% 0.09/5.39 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)],[f46])).
% 0.09/5.39 fof(f48,plain,(
% 0.09/5.39 convergent_lines(sK0_skl,sK1_skl)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f47])).
% 0.09/5.39 fof(f49,plain,(
% 0.09/5.39 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f47])).
% 0.09/5.39 fof(f50,plain,(
% 0.09/5.39 ~distinct_lines(sK0_skl,sK2_skl)|~distinct_lines(sK1_skl,sK2_skl)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f47])).
% 0.09/5.39 fof(f51,definition,(
% 0.09/5.39 sQ0_spl <=> (distinct_lines(sK0_skl,sK2_skl))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f53,plain,(
% 0.09/5.39 ~distinct_lines(sK0_skl,sK2_skl)|sQ0_spl),
% 0.09/5.39 inference(component_clause,[status(thm)],[f51])).
% 0.09/5.39 fof(f54,definition,(
% 0.09/5.39 sQ1_spl <=> (distinct_lines(sK1_skl,sK2_skl))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f57,plain,(
% 0.09/5.39 ~sQ0_spl|~sQ1_spl),
% 0.09/5.39 inference(split_clause,[status(thm)],[f50,f51,f54])).
% 0.09/5.39 fof(f62,plain,(
% 0.09/5.39 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.09/5.39 inference(resolution,[status(thm)],[f26,f48])).
% 0.09/5.39 fof(f63,plain,(
% 0.09/5.39 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.09/5.39 inference(resolution,[status(thm)],[f15,f34])).
% 0.09/5.39 fof(f64,plain,(
% 0.09/5.39 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.09/5.39 inference(resolution,[status(thm)],[f15,f33])).
% 0.09/5.39 fof(f65,plain,(
% 0.09/5.39 ![X0,X1]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X1)|convergent_lines(X0,X1))),
% 0.09/5.39 inference(resolution,[status(thm)],[f62,f26])).
% 0.09/5.39 fof(f75,plain,(
% 0.09/5.39 ![X0]: (distinct_lines(sK2_skl,X0)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0))),
% 0.09/5.39 inference(resolution,[status(thm)],[f42,f49])).
% 0.09/5.39 fof(f130,plain,(
% 0.09/5.39 ![X0]: (convergent_lines(sK0_skl,sK1_skl)|distinct_lines(sK1_skl,X0))),
% 0.09/5.39 inference(resolution,[status(thm)],[f65,f44])).
% 0.09/5.39 fof(f145,definition,(
% 0.09/5.39 sQ9_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f152,definition,(
% 0.09/5.39 ![X0]: (sQ11_spl <=> (distinct_lines(sK1_skl,X0)))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f153,plain,(
% 0.09/5.39 ![X0]: (distinct_lines(sK1_skl,X0)|~sQ11_spl)),
% 0.09/5.39 inference(component_clause,[status(thm)],[f152])).
% 0.09/5.39 fof(f155,plain,(
% 0.09/5.39 sQ9_spl|sQ11_spl),
% 0.09/5.39 inference(split_clause,[status(thm)],[f130,f145,f152])).
% 0.09/5.39 fof(f196,plain,(
% 0.09/5.39 distinct_lines(sK2_skl,sK0_skl)|~convergent_lines(sK0_skl,sK1_skl)),
% 0.09/5.39 inference(resolution,[status(thm)],[f75,f64])).
% 0.09/5.39 fof(f197,plain,(
% 0.09/5.39 distinct_lines(sK2_skl,sK1_skl)|~convergent_lines(sK0_skl,sK1_skl)),
% 0.09/5.39 inference(resolution,[status(thm)],[f75,f63])).
% 0.09/5.39 fof(f204,definition,(
% 0.09/5.39 sQ14_spl <=> (distinct_lines(sK2_skl,sK0_skl))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f205,plain,(
% 0.09/5.39 distinct_lines(sK2_skl,sK0_skl)|~sQ14_spl),
% 0.09/5.39 inference(component_clause,[status(thm)],[f204])).
% 0.09/5.39 fof(f207,plain,(
% 0.09/5.39 sQ14_spl|~sQ9_spl),
% 0.09/5.39 inference(split_clause,[status(thm)],[f196,f204,f145])).
% 0.14/5.41 fof(f208,definition,(
% 0.14/5.41 sQ15_spl <=> (distinct_lines(sK2_skl,sK1_skl))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f209,plain,(
% 0.14/5.41 distinct_lines(sK2_skl,sK1_skl)|~sQ15_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f208])).
% 0.14/5.41 fof(f211,plain,(
% 0.14/5.41 sQ15_spl|~sQ9_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f197,f208,f145])).
% 0.14/5.41 fof(f213,plain,(
% 0.14/5.41 $false|~sQ11_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f153,f16])).
% 0.14/5.41 fof(f214,plain,(
% 0.14/5.41 ~sQ11_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f213])).
% 0.14/5.41 fof(f215,plain,(
% 0.14/5.41 ![X0]: (distinct_lines(sK2_skl,X0)|distinct_lines(sK0_skl,X0)|~sQ14_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f205,f23])).
% 0.14/5.41 fof(f237,plain,(
% 0.14/5.41 distinct_lines(sK0_skl,sK2_skl)|~sQ14_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f215,f16])).
% 0.14/5.41 fof(f238,plain,(
% 0.14/5.41 $false|sQ0_spl|~sQ14_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f237,f53])).
% 0.14/5.41 fof(f239,plain,(
% 0.14/5.41 sQ0_spl|~sQ14_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f238])).
% 0.14/5.41 fof(f241,plain,(
% 0.14/5.41 ![X0]: (distinct_lines(sK2_skl,X0)|distinct_lines(sK1_skl,X0)|~sQ15_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f209,f23])).
% 0.14/5.41 fof(f245,plain,(
% 0.14/5.41 distinct_lines(sK1_skl,sK2_skl)|~sQ15_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f241,f16])).
% 0.14/5.41 fof(f246,plain,(
% 0.14/5.41 sQ1_spl|~sQ15_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f245,f54,f208])).
% 0.14/5.41 fof(f247,plain,(
% 0.14/5.41 $false),
% 0.14/5.41 inference(sat_refutation,[status(thm)],[f57,f155,f207,f211,f214,f239,f246])).
% 0.14/5.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/5.41 % Elapsed time: 0.039120 seconds
% 0.14/5.41 % CPU time: 0.129397 seconds
% 0.14/5.41 % Total memory used: 12.576 MB
% 0.14/5.41 % Net memory used: 12.267 MB
%------------------------------------------------------------------------------