%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO199+2 : 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 : n002.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 0.14s 0.98s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO199+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n002.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sun Sep 20 13:21:18 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.59 % Drodi V4.1.1
% 0.14/0.98 % Refutation found
% 0.14/0.98 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.98 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.98 fof(f1,axiom,(
% 0.14/0.98 (! [X] : ~ distinct_points(X,X) )),
% 0.14/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.98 fof(f3,axiom,(
% 0.14/0.98 (! [X] : ~ convergent_lines(X,X) )),
% 0.14/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.98 fof(f6,axiom,(
% 0.14/0.98 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.14/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.98 fof(f8,axiom,(
% 0.14/0.98 (! [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)) ) ) )),
% 0.14/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.98 fof(f9,axiom,(
% 0.14/0.98 (! [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) ) ) )),
% 0.14/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.98 fof(f10,axiom,(
% 0.14/0.98 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 0.14/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.98 fof(f12,axiom,(
% 0.14/0.98 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 0.14/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.98 fof(f13,conjecture,(
% 0.14/0.98 (! [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) ) )),
% 0.14/0.98 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.98 fof(f14,negated_conjecture,(
% 0.14/0.98 ~((! [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) ) ))),
% 0.14/0.98 inference(negated_conjecture,[status(cth)],[f13])).
% 0.14/0.98 fof(f15,plain,(
% 0.14/0.98 ![X0]: (~distinct_points(X0,X0))),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.98 fof(f17,plain,(
% 0.14/0.98 ![X0]: (~convergent_lines(X0,X0))),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.98 fof(f24,plain,(
% 0.14/0.98 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.14/0.98 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.14/0.98 fof(f25,plain,(
% 0.14/0.98 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.14/0.98 inference(miniscoping,[status(thm)],[f24])).
% 0.14/0.98 fof(f26,plain,(
% 0.14/0.98 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f25])).
% 0.14/0.98 fof(f31,plain,(
% 0.14/0.98 ![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))))),
% 0.14/0.98 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.14/0.98 fof(f32,plain,(
% 0.14/0.98 ![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)))))),
% 0.14/0.98 inference(miniscoping,[status(thm)],[f31])).
% 0.14/0.98 fof(f33,plain,(
% 0.14/0.98 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f32])).
% 0.14/0.98 fof(f34,plain,(
% 0.14/0.98 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f32])).
% 0.14/0.98 fof(f35,plain,(
% 0.14/0.98 ![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)))),
% 0.14/0.98 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.14/0.98 fof(f36,plain,(
% 0.14/0.98 ![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))),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f35])).
% 0.14/0.98 fof(f37,plain,(
% 0.14/0.98 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 0.14/0.98 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.14/0.98 fof(f38,plain,(
% 0.14/0.98 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 0.14/0.98 inference(miniscoping,[status(thm)],[f37])).
% 0.14/0.98 fof(f39,plain,(
% 0.14/0.98 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f38])).
% 0.14/0.98 fof(f43,plain,(
% 0.14/0.98 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 0.14/0.98 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.14/0.98 fof(f44,plain,(
% 0.14/0.98 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/0.98 fof(f45,plain,(
% 0.14/0.98 (?[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)))),
% 0.14/0.98 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.14/0.98 fof(f46,plain,(
% 0.14/0.98 ((((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))),
% 0.14/0.98 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])).
% 0.14/0.98 fof(f47,plain,(
% 0.14/0.98 convergent_lines(sK0_skl,sK1_skl)),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.98 fof(f50,plain,(
% 0.14/0.98 ~apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.98 fof(f51,plain,(
% 0.14/0.98 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK2_skl)),
% 0.14/0.98 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.98 fof(f54,plain,(
% 0.14/0.98 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.14/0.98 inference(resolution,[status(thm)],[f26,f47])).
% 0.14/0.98 fof(f60,plain,(
% 0.14/0.98 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.14/0.98 inference(resolution,[status(thm)],[f15,f34])).
% 0.14/0.98 fof(f61,plain,(
% 0.14/0.98 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.14/0.98 inference(resolution,[status(thm)],[f15,f33])).
% 0.14/0.98 fof(f67,plain,(
% 0.14/0.98 distinct_lines(sK0_skl,sK1_skl)),
% 0.14/0.98 inference(resolution,[status(thm)],[f44,f47])).
% 0.14/0.98 fof(f69,plain,(
% 0.14/0.98 ![X0,X1]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X1)|convergent_lines(X0,X1))),
% 0.14/0.98 inference(resolution,[status(thm)],[f54,f26])).
% 0.14/0.98 fof(f149,plain,(
% 0.14/0.98 ![X0]: (distinct_points(intersection_point(sK1_skl,sK0_skl),X0)|apart_point_and_line(X0,sK2_skl))),
% 0.14/0.98 inference(resolution,[status(thm)],[f39,f51])).
% 0.14/0.98 fof(f183,plain,(
% 0.14/0.98 ![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))),
% 0.14/0.98 inference(resolution,[status(thm)],[f149,f36])).
% 0.14/0.98 fof(f206,plain,(
% 0.14/0.98 convergent_lines(sK1_skl,sK0_skl)),
% 0.14/0.98 inference(resolution,[status(thm)],[f69,f17])).
% 0.14/0.98 fof(f311,plain,(
% 0.14/0.98 ![X0]: (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl))),
% 0.14/0.98 inference(resolution,[status(thm)],[f183,f67])).
% 0.14/0.98 fof(f328,definition,(
% 0.14/0.98 ![X0]: (sQ18_spl <=> (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)))),
% 0.14/0.98 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.14/0.98 fof(f329,plain,(
% 0.14/0.98 ![X0]: (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)|~sQ18_spl)),
% 0.14/0.98 inference(component_clause,[status(thm)],[f328])).
% 0.14/0.98 fof(f331,definition,(
% 0.14/0.98 sQ19_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl))),
% 0.14/0.98 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.14/0.98 fof(f332,plain,(
% 0.14/0.98 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|~sQ19_spl),
% 0.14/0.98 inference(component_clause,[status(thm)],[f331])).
% 0.14/0.98 fof(f334,definition,(
% 0.14/0.98 sQ20_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl))),
% 0.14/0.99 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.14/0.99 fof(f335,plain,(
% 0.14/0.99 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|~sQ20_spl),
% 0.14/0.99 inference(component_clause,[status(thm)],[f334])).
% 0.14/0.99 fof(f337,plain,(
% 0.14/0.99 sQ18_spl|sQ19_spl|sQ20_spl),
% 0.14/0.99 inference(split_clause,[status(thm)],[f311,f328,f331,f334])).
% 0.14/0.99 fof(f390,plain,(
% 0.14/0.99 ~convergent_lines(sK1_skl,sK0_skl)|~sQ19_spl),
% 0.14/0.99 inference(resolution,[status(thm)],[f332,f60])).
% 0.14/0.99 fof(f397,plain,(
% 0.14/0.99 $false|~sQ19_spl),
% 0.14/0.99 inference(forward_subsumption_resolution,[status(thm)],[f390,f206])).
% 0.14/0.99 fof(f398,plain,(
% 0.14/0.99 ~sQ19_spl),
% 0.14/0.99 inference(contradiction_clause,[status(thm)],[f397])).
% 0.14/0.99 fof(f400,plain,(
% 0.14/0.99 ~convergent_lines(sK1_skl,sK0_skl)|~sQ20_spl),
% 0.14/0.99 inference(resolution,[status(thm)],[f335,f61])).
% 0.14/0.99 fof(f407,plain,(
% 0.14/0.99 $false|~sQ20_spl),
% 0.14/0.99 inference(forward_subsumption_resolution,[status(thm)],[f400,f206])).
% 0.14/0.99 fof(f408,plain,(
% 0.14/0.99 ~sQ20_spl),
% 0.14/0.99 inference(contradiction_clause,[status(thm)],[f407])).
% 0.14/0.99 fof(f3499,plain,(
% 0.14/0.99 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ18_spl),
% 0.14/0.99 inference(resolution,[status(thm)],[f329,f50])).
% 0.14/0.99 fof(f3508,definition,(
% 0.14/0.99 sQ314_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.14/0.99 introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition])).
% 0.14/0.99 fof(f3509,plain,(
% 0.14/0.99 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ314_spl),
% 0.14/0.99 inference(component_clause,[status(thm)],[f3508])).
% 0.14/0.99 fof(f3511,definition,(
% 0.14/0.99 sQ315_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 0.14/0.99 introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition])).
% 0.14/0.99 fof(f3512,plain,(
% 0.14/0.99 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ315_spl),
% 0.14/0.99 inference(component_clause,[status(thm)],[f3511])).
% 0.14/0.99 fof(f3514,plain,(
% 0.14/0.99 sQ314_spl|sQ315_spl|~sQ18_spl),
% 0.14/0.99 inference(split_clause,[status(thm)],[f3499,f3508,f3511,f328])).
% 0.14/0.99 fof(f3653,plain,(
% 0.14/0.99 ~convergent_lines(sK0_skl,sK1_skl)|~sQ315_spl),
% 0.14/0.99 inference(resolution,[status(thm)],[f3512,f60])).
% 0.14/0.99 fof(f3660,plain,(
% 0.14/0.99 $false|~sQ315_spl),
% 0.14/0.99 inference(forward_subsumption_resolution,[status(thm)],[f3653,f47])).
% 0.14/0.99 fof(f3661,plain,(
% 0.14/0.99 ~sQ315_spl),
% 0.14/0.99 inference(contradiction_clause,[status(thm)],[f3660])).
% 0.14/0.99 fof(f3662,plain,(
% 0.14/0.99 ~convergent_lines(sK0_skl,sK1_skl)|~sQ314_spl),
% 0.14/0.99 inference(resolution,[status(thm)],[f3509,f61])).
% 0.14/0.99 fof(f3669,plain,(
% 0.14/0.99 $false|~sQ314_spl),
% 0.14/0.99 inference(forward_subsumption_resolution,[status(thm)],[f3662,f47])).
% 0.14/0.99 fof(f3670,plain,(
% 0.14/0.99 ~sQ314_spl),
% 0.14/0.99 inference(contradiction_clause,[status(thm)],[f3669])).
% 0.14/0.99 fof(f3671,plain,(
% 0.14/0.99 $false),
% 0.14/0.99 inference(sat_refutation,[status(thm)],[f337,f398,f408,f3514,f3661,f3670])).
% 0.14/0.99 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/1.00 % Elapsed time: 0.415057 seconds
% 0.14/1.00 % CPU time: 3.134129 seconds
% 0.14/1.00 % Total memory used: 49.637 MB
% 0.14/1.00 % Net memory used: 42.663 MB
%------------------------------------------------------------------------------