%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO198+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 : n003.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 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO198+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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 13:19:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.46 % Refutation found
% 0.14/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.46 fof(f1,axiom,(
% 0.14/0.46 (! [X] : ~ distinct_points(X,X) )),
% 0.14/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f8,axiom,(
% 0.14/0.46 (! [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)) ) ) )),
% 0.14/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f9,axiom,(
% 0.14/0.46 (! [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) ) ) )),
% 0.14/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f12,axiom,(
% 0.14/0.46 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 0.14/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f13,conjecture,(
% 0.14/0.46 (! [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(X,Z),Y) ) )),
% 0.14/0.46 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.46 fof(f14,negated_conjecture,(
% 0.14/0.46 ~((! [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(X,Z),Y) ) ))),
% 0.14/0.46 inference(negated_conjecture,[status(cth)],[f13])).
% 0.14/0.46 fof(f15,plain,(
% 0.14/0.46 ![X0]: (~distinct_points(X0,X0))),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.46 fof(f31,plain,(
% 0.14/0.46 ![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))))),
% 0.14/0.46 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.14/0.46 fof(f32,plain,(
% 0.14/0.46 ![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)))))),
% 0.14/0.46 inference(miniscoping,[status(thm)],[f31])).
% 0.14/0.46 fof(f33,plain,(
% 0.14/0.46 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f32])).
% 0.14/0.46 fof(f34,plain,(
% 0.14/0.46 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f32])).
% 0.14/0.46 fof(f35,plain,(
% 0.14/0.46 ![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)))),
% 0.14/0.46 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.14/0.46 fof(f36,plain,(
% 0.14/0.46 ![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))),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f35])).
% 0.14/0.46 fof(f43,plain,(
% 0.14/0.46 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 0.14/0.46 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.14/0.46 fof(f44,plain,(
% 0.14/0.46 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/0.46 fof(f45,plain,(
% 0.14/0.46 (?[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(X,Z),Y)))),
% 0.14/0.46 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.14/0.46 fof(f46,plain,(
% 0.14/0.46 ((((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(sK0_skl,sK2_skl),sK1_skl))),
% 0.14/0.46 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])).
% 0.14/0.46 fof(f47,plain,(
% 0.14/0.46 convergent_lines(sK0_skl,sK1_skl)),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.46 fof(f49,plain,(
% 0.14/0.46 convergent_lines(sK0_skl,sK2_skl)),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.46 fof(f50,plain,(
% 0.14/0.46 ~apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.46 fof(f51,plain,(
% 0.14/0.46 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)),
% 0.14/0.46 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.46 fof(f56,plain,(
% 0.14/0.46 ![X0]: (~apart_point_and_line(X0,sK0_skl)|distinct_points(X0,intersection_point(sK0_skl,sK2_skl)))),
% 0.14/0.46 inference(resolution,[status(thm)],[f33,f49])).
% 0.14/0.46 fof(f57,plain,(
% 0.14/0.46 ![X0]: (~apart_point_and_line(X0,sK0_skl)|distinct_points(X0,intersection_point(sK0_skl,sK1_skl)))),
% 0.14/0.46 inference(resolution,[status(thm)],[f33,f47])).
% 0.14/0.46 fof(f59,plain,(
% 0.14/0.46 distinct_lines(sK0_skl,sK2_skl)),
% 0.14/0.46 inference(resolution,[status(thm)],[f44,f49])).
% 0.14/0.46 fof(f65,plain,(
% 0.14/0.46 ![X0]: (~apart_point_and_line(X0,sK2_skl)|distinct_points(X0,intersection_point(sK0_skl,sK2_skl)))),
% 0.14/0.46 inference(resolution,[status(thm)],[f34,f49])).
% 0.14/0.46 fof(f66,plain,(
% 0.14/0.46 ![X0]: (~apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK0_skl,sK1_skl)))),
% 0.14/0.46 inference(resolution,[status(thm)],[f34,f47])).
% 0.14/0.46 fof(f79,plain,(
% 0.14/0.46 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X1,sK0_skl)|apart_point_and_line(X1,sK2_skl))),
% 0.14/0.46 inference(resolution,[status(thm)],[f36,f59])).
% 0.14/0.46 fof(f112,plain,(
% 0.14/0.46 distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK1_skl))),
% 0.14/0.46 inference(resolution,[status(thm)],[f66,f51])).
% 0.14/0.46 fof(f202,definition,(
% 0.14/0.46 sQ13_spl <=> (distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl)))),
% 0.14/0.46 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.14/0.46 fof(f203,plain,(
% 0.14/0.46 distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl))|~sQ13_spl),
% 0.14/0.46 inference(component_clause,[status(thm)],[f202])).
% 0.14/0.46 fof(f238,definition,(
% 0.14/0.46 sQ16_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl))),
% 0.14/0.46 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.14/0.46 fof(f239,plain,(
% 0.14/0.46 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|~sQ16_spl),
% 0.14/0.46 inference(component_clause,[status(thm)],[f238])).
% 0.14/0.46 fof(f250,plain,(
% 0.14/0.46 $false|~sQ13_spl),
% 0.14/0.46 inference(forward_subsumption_resolution,[status(thm)],[f203,f15])).
% 0.14/0.46 fof(f251,plain,(
% 0.14/0.46 ~sQ13_spl),
% 0.14/0.46 inference(contradiction_clause,[status(thm)],[f250])).
% 0.14/0.46 fof(f257,definition,(
% 0.14/0.46 sQ19_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl))),
% 0.14/0.46 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.14/0.46 fof(f258,plain,(
% 0.14/0.46 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl)|~sQ19_spl),
% 0.14/0.46 inference(component_clause,[status(thm)],[f257])).
% 0.14/0.46 fof(f265,plain,(
% 0.14/0.46 distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl))|~sQ16_spl),
% 0.14/0.46 inference(resolution,[status(thm)],[f239,f56])).
% 0.14/0.46 fof(f269,plain,(
% 0.14/0.46 sQ13_spl|~sQ16_spl),
% 0.14/0.46 inference(split_clause,[status(thm)],[f265,f202,f238])).
% 0.14/0.46 fof(f278,plain,(
% 0.14/0.46 distinct_points(intersection_point(sK0_skl,sK2_skl),intersection_point(sK0_skl,sK2_skl))|~sQ19_spl),
% 0.14/0.46 inference(resolution,[status(thm)],[f258,f65])).
% 0.14/0.46 fof(f283,plain,(
% 0.14/0.46 sQ13_spl|~sQ19_spl),
% 0.14/0.46 inference(split_clause,[status(thm)],[f278,f202,f257])).
% 0.14/0.46 fof(f437,plain,(
% 0.14/0.46 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 0.14/0.46 inference(resolution,[status(thm)],[f112,f79])).
% 0.14/0.46 fof(f439,definition,(
% 0.14/0.46 sQ41_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.14/0.46 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.14/0.46 fof(f440,plain,(
% 0.14/0.46 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ41_spl),
% 0.14/0.46 inference(component_clause,[status(thm)],[f439])).
% 0.14/0.46 fof(f442,definition,(
% 0.14/0.46 sQ42_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl))),
% 0.14/0.46 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.14/0.46 fof(f443,plain,(
% 0.14/0.46 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)|~sQ42_spl),
% 0.14/0.47 inference(component_clause,[status(thm)],[f442])).
% 0.14/0.47 fof(f445,plain,(
% 0.14/0.47 sQ16_spl|sQ19_spl|sQ41_spl|sQ42_spl),
% 0.14/0.47 inference(split_clause,[status(thm)],[f437,f238,f257,f439,f442])).
% 0.14/0.47 fof(f557,plain,(
% 0.14/0.47 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ41_spl),
% 0.14/0.47 inference(resolution,[status(thm)],[f440,f57])).
% 0.14/0.47 fof(f564,plain,(
% 0.14/0.47 $false|~sQ41_spl),
% 0.14/0.47 inference(forward_subsumption_resolution,[status(thm)],[f557,f15])).
% 0.14/0.47 fof(f565,plain,(
% 0.14/0.47 ~sQ41_spl),
% 0.14/0.47 inference(contradiction_clause,[status(thm)],[f564])).
% 0.14/0.47 fof(f566,plain,(
% 0.14/0.47 $false|~sQ42_spl),
% 0.14/0.47 inference(forward_subsumption_resolution,[status(thm)],[f443,f50])).
% 0.14/0.47 fof(f567,plain,(
% 0.14/0.47 ~sQ42_spl),
% 0.14/0.47 inference(contradiction_clause,[status(thm)],[f566])).
% 0.14/0.47 fof(f568,plain,(
% 0.14/0.47 $false),
% 0.14/0.47 inference(sat_refutation,[status(thm)],[f251,f269,f283,f445,f565,f567])).
% 0.14/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.48 % Elapsed time: 0.107523 seconds
% 0.14/0.48 % CPU time: 0.680760 seconds
% 0.14/0.48 % Total memory used: 26.152 MB
% 0.14/0.48 % Net memory used: 24.301 MB
%------------------------------------------------------------------------------