%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO199+1 : 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 : n017.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 2.62s 0.82s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO199+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:15:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 2.62/0.82 % Refutation found
% 2.62/0.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.62/0.82 % SZS output start CNFRefutation for theBenchmark
% 2.62/0.82 fof(f3,axiom,(
% 2.62/0.82 (! [X] : ~ convergent_lines(X,X) )),
% 2.62/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.62/0.82 fof(f6,axiom,(
% 2.62/0.82 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 2.62/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.62/0.82 fof(f9,axiom,(
% 2.62/0.82 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 2.62/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.62/0.82 fof(f10,axiom,(
% 2.62/0.82 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 2.62/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.62/0.82 fof(f11,axiom,(
% 2.62/0.82 (! [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) ) ) )),
% 2.62/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.62/0.82 fof(f12,axiom,(
% 2.62/0.82 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 2.62/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.62/0.82 fof(f14,axiom,(
% 2.62/0.82 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 2.62/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.62/0.82 fof(f15,conjecture,(
% 2.62/0.82 (! [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) ) )),
% 2.62/0.82 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.62/0.82 fof(f16,negated_conjecture,(
% 2.62/0.82 ~((! [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) ) ))),
% 2.62/0.82 inference(negated_conjecture,[status(cth)],[f15])).
% 2.62/0.82 fof(f19,plain,(
% 2.62/0.82 ![X0]: (~convergent_lines(X0,X0))),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f3])).
% 2.62/0.82 fof(f26,plain,(
% 2.62/0.82 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 2.62/0.82 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 2.62/0.82 fof(f27,plain,(
% 2.62/0.82 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 2.62/0.82 inference(miniscoping,[status(thm)],[f26])).
% 2.62/0.82 fof(f28,plain,(
% 2.62/0.82 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f27])).
% 2.62/0.82 fof(f33,plain,(
% 2.62/0.82 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 2.62/0.82 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 2.62/0.82 fof(f34,plain,(
% 2.62/0.82 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f33])).
% 2.62/0.82 fof(f35,plain,(
% 2.62/0.82 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 2.62/0.82 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 2.62/0.82 fof(f36,plain,(
% 2.62/0.82 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f35])).
% 2.62/0.82 fof(f37,plain,(
% 2.62/0.82 ![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)))),
% 2.62/0.82 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 2.62/0.82 fof(f38,plain,(
% 2.62/0.82 ![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))),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f37])).
% 2.62/0.82 fof(f39,plain,(
% 2.62/0.82 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 2.62/0.82 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 2.62/0.82 fof(f40,plain,(
% 2.62/0.82 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 2.62/0.82 inference(miniscoping,[status(thm)],[f39])).
% 2.62/0.82 fof(f41,plain,(
% 2.62/0.82 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f40])).
% 2.62/0.82 fof(f45,plain,(
% 2.62/0.82 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 2.62/0.82 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 2.62/0.82 fof(f46,plain,(
% 2.62/0.82 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 2.62/0.82 inference(miniscoping,[status(thm)],[f45])).
% 2.62/0.82 fof(f47,plain,(
% 2.62/0.82 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f46])).
% 2.62/0.82 fof(f48,plain,(
% 2.62/0.82 (?[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)))),
% 2.62/0.82 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 2.62/0.82 fof(f49,plain,(
% 2.62/0.82 ((((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))),
% 2.62/0.82 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)],[f48])).
% 2.62/0.82 fof(f50,plain,(
% 2.62/0.82 convergent_lines(sK0_skl,sK1_skl)),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f49])).
% 2.62/0.82 fof(f53,plain,(
% 2.62/0.82 ~apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f49])).
% 2.62/0.82 fof(f54,plain,(
% 2.62/0.82 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK2_skl)),
% 2.62/0.82 inference(cnf_transformation,[status(thm)],[f49])).
% 2.62/0.82 fof(f57,plain,(
% 2.62/0.82 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 2.62/0.82 inference(resolution,[status(thm)],[f28,f50])).
% 2.62/0.82 fof(f63,plain,(
% 2.62/0.82 ![X0,X1]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X1)|convergent_lines(X0,X1))),
% 2.62/0.82 inference(resolution,[status(thm)],[f57,f28])).
% 2.62/0.82 fof(f141,plain,(
% 2.62/0.82 convergent_lines(sK1_skl,sK0_skl)),
% 2.62/0.82 inference(resolution,[status(thm)],[f63,f19])).
% 2.62/0.82 fof(f146,plain,(
% 2.62/0.82 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(X0,sK1_skl))),
% 2.62/0.82 inference(resolution,[status(thm)],[f63,f19])).
% 2.62/0.82 fof(f171,plain,(
% 2.62/0.82 ![X0]: (distinct_points(intersection_point(sK1_skl,sK0_skl),X0)|apart_point_and_line(X0,sK2_skl))),
% 2.62/0.82 inference(resolution,[status(thm)],[f41,f54])).
% 2.62/0.82 fof(f189,plain,(
% 2.62/0.82 ![X0,X1]: (distinct_lines(sK1_skl,X0)|convergent_lines(X1,X0)|convergent_lines(sK0_skl,X1))),
% 2.62/0.82 inference(resolution,[status(thm)],[f47,f146])).
% 2.62/0.82 fof(f332,plain,(
% 2.62/0.82 ![X0,X1,X2]: (apart_point_and_line(X0,sK2_skl)|~distinct_lines(X1,X2)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X2)|apart_point_and_line(X0,X1)|apart_point_and_line(X0,X2))),
% 2.62/0.82 inference(resolution,[status(thm)],[f171,f38])).
% 2.62/0.82 fof(f353,plain,(
% 2.62/0.82 distinct_lines(sK1_skl,sK0_skl)),
% 2.62/0.82 inference(resolution,[status(thm)],[f189,f19])).
% 2.62/0.82 fof(f584,plain,(
% 2.62/0.82 ![X0]: (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl))),
% 2.62/0.82 inference(resolution,[status(thm)],[f332,f353])).
% 2.62/0.82 fof(f636,definition,(
% 2.62/0.82 ![X0]: (sQ31_spl <=> (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)))),
% 2.62/0.82 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 2.62/0.82 fof(f637,plain,(
% 2.62/0.82 ![X0]: (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)|~sQ31_spl)),
% 2.62/0.82 inference(component_clause,[status(thm)],[f636])).
% 2.62/0.82 fof(f639,definition,(
% 2.62/0.82 sQ32_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl))),
% 2.62/0.82 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 2.62/0.82 fof(f640,plain,(
% 2.62/0.82 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|~sQ32_spl),
% 2.62/0.82 inference(component_clause,[status(thm)],[f639])).
% 2.62/0.82 fof(f642,definition,(
% 2.62/0.82 sQ33_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl))),
% 2.62/0.83 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 2.62/0.83 fof(f643,plain,(
% 2.62/0.83 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|~sQ33_spl),
% 2.62/0.83 inference(component_clause,[status(thm)],[f642])).
% 2.62/0.83 fof(f645,plain,(
% 2.62/0.83 sQ31_spl|sQ32_spl|sQ33_spl),
% 2.62/0.83 inference(split_clause,[status(thm)],[f584,f636,f639,f642])).
% 2.62/0.83 fof(f794,plain,(
% 2.62/0.83 ~convergent_lines(sK1_skl,sK0_skl)|~sQ32_spl),
% 2.62/0.83 inference(resolution,[status(thm)],[f640,f34])).
% 2.62/0.83 fof(f797,plain,(
% 2.62/0.83 $false|~sQ32_spl),
% 2.62/0.83 inference(forward_subsumption_resolution,[status(thm)],[f794,f141])).
% 2.62/0.83 fof(f798,plain,(
% 2.62/0.83 ~sQ32_spl),
% 2.62/0.83 inference(contradiction_clause,[status(thm)],[f797])).
% 2.62/0.83 fof(f799,plain,(
% 2.62/0.83 ~convergent_lines(sK1_skl,sK0_skl)|~sQ33_spl),
% 2.62/0.83 inference(resolution,[status(thm)],[f643,f36])).
% 2.62/0.83 fof(f802,plain,(
% 2.62/0.83 $false|~sQ33_spl),
% 2.62/0.83 inference(forward_subsumption_resolution,[status(thm)],[f799,f141])).
% 2.62/0.83 fof(f803,plain,(
% 2.62/0.83 ~sQ33_spl),
% 2.62/0.83 inference(contradiction_clause,[status(thm)],[f802])).
% 2.62/0.83 fof(f1154,plain,(
% 2.62/0.83 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ31_spl),
% 2.62/0.83 inference(resolution,[status(thm)],[f637,f53])).
% 2.62/0.83 fof(f1159,definition,(
% 2.62/0.83 sQ86_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 2.62/0.83 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 2.62/0.83 fof(f1160,plain,(
% 2.62/0.83 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ86_spl),
% 2.62/0.83 inference(component_clause,[status(thm)],[f1159])).
% 2.62/0.83 fof(f1162,definition,(
% 2.62/0.83 sQ87_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 2.62/0.83 introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition])).
% 2.62/0.83 fof(f1163,plain,(
% 2.62/0.83 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ87_spl),
% 2.62/0.83 inference(component_clause,[status(thm)],[f1162])).
% 2.62/0.83 fof(f1165,plain,(
% 2.62/0.83 sQ86_spl|sQ87_spl|~sQ31_spl),
% 2.62/0.83 inference(split_clause,[status(thm)],[f1154,f1159,f1162,f636])).
% 2.62/0.83 fof(f1166,plain,(
% 2.62/0.83 ~convergent_lines(sK0_skl,sK1_skl)|~sQ86_spl),
% 2.62/0.83 inference(resolution,[status(thm)],[f1160,f36])).
% 2.62/0.83 fof(f1169,plain,(
% 2.62/0.83 $false|~sQ86_spl),
% 2.62/0.83 inference(forward_subsumption_resolution,[status(thm)],[f1166,f50])).
% 2.62/0.83 fof(f1170,plain,(
% 2.62/0.83 ~sQ86_spl),
% 2.62/0.83 inference(contradiction_clause,[status(thm)],[f1169])).
% 2.62/0.83 fof(f1171,plain,(
% 2.62/0.83 ~convergent_lines(sK0_skl,sK1_skl)|~sQ87_spl),
% 2.62/0.83 inference(resolution,[status(thm)],[f1163,f34])).
% 2.62/0.83 fof(f1174,plain,(
% 2.62/0.83 $false|~sQ87_spl),
% 2.62/0.83 inference(forward_subsumption_resolution,[status(thm)],[f1171,f50])).
% 2.62/0.83 fof(f1175,plain,(
% 2.62/0.83 ~sQ87_spl),
% 2.62/0.83 inference(contradiction_clause,[status(thm)],[f1174])).
% 2.62/0.83 fof(f1176,plain,(
% 2.62/0.83 $false),
% 2.62/0.83 inference(sat_refutation,[status(thm)],[f645,f798,f803,f1165,f1170,f1175])).
% 2.62/0.83 % SZS output end CNFRefutation for theBenchmark.p
% 1.34/0.84 % Elapsed time: 0.460294 seconds
% 1.34/0.84 % CPU time: 3.341578 seconds
% 1.34/0.84 % Total memory used: 41.833 MB
% 1.34/0.84 % Net memory used: 35.215 MB
%------------------------------------------------------------------------------