%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO180+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 : n016.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 12:25:58 PM UTC 2026
% Result : Theorem 0.14s 10.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO180+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
% 0.10/10.38 % Computer : n016.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sun Sep 20 13:15:02 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.39 % Drodi V4.1.1
% 0.14/10.51 % Refutation found
% 0.14/10.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.51 % SZS output start CNFRefutation for theBenchmark
% 0.14/10.51 fof(f1,axiom,(
% 0.14/10.51 (! [X] : ~ distinct_points(X,X) )),
% 0.14/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/10.51 fof(f4,axiom,(
% 0.14/10.51 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.14/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/10.51 fof(f7,axiom,(
% 0.14/10.51 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.14/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/10.51 fof(f8,axiom,(
% 0.14/10.51 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.14/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/10.51 fof(f11,axiom,(
% 0.14/10.51 (! [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) ) ) )),
% 0.14/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/10.51 fof(f12,axiom,(
% 0.14/10.51 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 0.14/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/10.51 fof(f13,axiom,(
% 0.14/10.51 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.14/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/10.51 fof(f15,conjecture,(
% 0.14/10.51 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(X,line_connecting(Z,Y)) ) ) )),
% 0.14/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.14/10.51 fof(f16,negated_conjecture,(
% 0.14/10.51 ~((! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(X,line_connecting(Z,Y)) ) ) ))),
% 0.14/10.51 inference(negated_conjecture,[status(cth)],[f15])).
% 0.14/10.51 fof(f17,plain,(
% 0.14/10.51 ![X0]: (~distinct_points(X0,X0))),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/10.51 fof(f20,plain,(
% 0.14/10.51 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.14/10.51 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.14/10.51 fof(f21,plain,(
% 0.14/10.51 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.14/10.51 inference(miniscoping,[status(thm)],[f20])).
% 0.14/10.51 fof(f22,plain,(
% 0.14/10.51 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/10.51 fof(f29,plain,(
% 0.14/10.51 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.14/10.51 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.14/10.51 fof(f30,plain,(
% 0.14/10.51 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f29])).
% 0.14/10.51 fof(f31,plain,(
% 0.14/10.51 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.14/10.51 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.14/10.51 fof(f32,plain,(
% 0.14/10.51 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f31])).
% 0.14/10.51 fof(f37,plain,(
% 0.14/10.51 ![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)))),
% 0.14/10.51 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.14/10.51 fof(f38,plain,(
% 0.14/10.51 ![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))),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f37])).
% 0.14/10.51 fof(f39,plain,(
% 0.14/10.51 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 0.14/10.51 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.14/10.51 fof(f40,plain,(
% 0.14/10.51 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 0.14/10.51 inference(miniscoping,[status(thm)],[f39])).
% 0.14/10.51 fof(f41,plain,(
% 0.14/10.51 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f40])).
% 0.14/10.51 fof(f42,plain,(
% 0.14/10.51 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.14/10.51 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.14/10.51 fof(f43,plain,(
% 0.14/10.51 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.14/10.51 inference(miniscoping,[status(thm)],[f42])).
% 0.14/10.51 fof(f44,plain,(
% 0.14/10.51 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/10.51 fof(f48,plain,(
% 0.14/10.51 (?[X,Y,Z]: (distinct_points(X,Y)&(apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(X,line_connecting(Z,Y)))))),
% 0.14/10.51 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.14/10.51 fof(f49,plain,(
% 0.14/10.51 ?[X,Y]: (distinct_points(X,Y)&(?[Z]: (apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(X,line_connecting(Z,Y)))))),
% 0.14/10.51 inference(miniscoping,[status(thm)],[f48])).
% 0.14/10.51 fof(f50,plain,(
% 0.14/10.51 (distinct_points(sK0_skl,sK1_skl)&(apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))&~apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl))))),
% 0.14/10.51 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)],[f49])).
% 0.14/10.51 fof(f51,plain,(
% 0.14/10.51 distinct_points(sK0_skl,sK1_skl)),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f50])).
% 0.14/10.51 fof(f52,plain,(
% 0.14/10.51 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f50])).
% 0.14/10.51 fof(f53,plain,(
% 0.14/10.51 ~apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl))),
% 0.14/10.51 inference(cnf_transformation,[status(thm)],[f50])).
% 0.14/10.51 fof(f54,plain,(
% 0.14/10.51 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.14/10.51 inference(resolution,[status(thm)],[f22,f51])).
% 0.14/10.51 fof(f55,plain,(
% 0.14/10.51 ![X0,X1]: (distinct_points(sK1_skl,X0)|distinct_points(sK0_skl,X1)|distinct_points(X0,X1))),
% 0.14/10.51 inference(resolution,[status(thm)],[f54,f22])).
% 0.14/10.51 fof(f56,plain,(
% 0.14/10.51 distinct_points(sK1_skl,sK0_skl)),
% 0.14/10.51 inference(resolution,[status(thm)],[f54,f17])).
% 0.14/10.51 fof(f58,plain,(
% 0.14/10.51 ![X0]: (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/10.51 inference(resolution,[status(thm)],[f41,f52])).
% 0.14/10.51 fof(f59,plain,(
% 0.14/10.51 ![X0]: (distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.14/10.51 inference(resolution,[status(thm)],[f55,f22])).
% 0.14/10.51 fof(f70,definition,(
% 0.14/10.51 sQ0_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.14/10.51 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/10.51 fof(f73,definition,(
% 0.14/10.51 ![X0]: (sQ1_spl <=> (distinct_points(sK1_skl,X0)|distinct_points(sK1_skl,X0)))),
% 0.14/10.51 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/10.51 fof(f74,plain,(
% 0.14/10.51 ![X0]: (distinct_points(sK1_skl,X0)|distinct_points(sK1_skl,X0)|~sQ1_spl)),
% 0.14/10.51 inference(component_clause,[status(thm)],[f73])).
% 0.14/10.51 fof(f76,plain,(
% 0.14/10.51 sQ0_spl|sQ1_spl),
% 0.14/10.51 inference(split_clause,[status(thm)],[f59,f70,f73])).
% 0.14/10.51 fof(f92,plain,(
% 0.14/10.51 distinct_points(sK2_skl,sK1_skl)|~distinct_points(sK0_skl,sK1_skl)),
% 0.14/10.51 inference(resolution,[status(thm)],[f58,f32])).
% 0.14/10.51 fof(f95,definition,(
% 0.14/10.51 sQ5_spl <=> (distinct_points(sK2_skl,sK1_skl))),
% 0.14/10.51 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/10.51 fof(f96,plain,(
% 0.14/10.51 distinct_points(sK2_skl,sK1_skl)|~sQ5_spl),
% 0.14/10.51 inference(component_clause,[status(thm)],[f95])).
% 0.14/10.51 fof(f98,plain,(
% 0.14/10.51 sQ5_spl|~sQ0_spl),
% 0.14/10.51 inference(split_clause,[status(thm)],[f92,f95,f70])).
% 0.14/10.51 fof(f103,plain,(
% 0.14/10.51 ![X0]: (distinct_points(sK1_skl,X0)|~sQ1_spl)),
% 0.14/10.51 inference(duplicate_literals_removal,[status(thm)],[f74])).
% 0.14/10.51 fof(f105,plain,(
% 0.14/10.51 $false|~sQ1_spl),
% 0.14/10.51 inference(resolution,[status(thm)],[f103,f17])).
% 0.14/10.51 fof(f106,plain,(
% 0.14/10.51 ~sQ1_spl),
% 0.14/10.51 inference(contradiction_clause,[status(thm)],[f105])).
% 0.14/10.51 fof(f157,plain,(
% 0.14/10.51 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,X0))),
% 0.14/10.51 inference(resolution,[status(thm)],[f44,f52])).
% 0.14/10.51 fof(f232,plain,(
% 0.14/10.51 ![X0,X1,X2]: (apart_point_and_line(sK2_skl,X0)|~distinct_points(X1,X2)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,X0)|apart_point_and_line(X2,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X2,X0))),
% 0.14/10.51 inference(resolution,[status(thm)],[f157,f38])).
% 0.14/10.51 fof(f508,plain,(
% 0.14/10.51 ![X0]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,X0))),
% 0.14/10.51 inference(resolution,[status(thm)],[f232,f56])).
% 0.14/10.51 fof(f578,definition,(
% 0.14/10.51 sQ21_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/10.51 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.14/10.51 fof(f579,plain,(
% 0.14/10.51 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ21_spl),
% 0.14/10.51 inference(component_clause,[status(thm)],[f578])).
% 0.14/10.51 fof(f585,definition,(
% 0.14/10.51 sQ23_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/10.51 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.14/10.51 fof(f586,plain,(
% 0.14/10.51 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ23_spl),
% 0.14/10.51 inference(component_clause,[status(thm)],[f585])).
% 0.14/10.51 fof(f638,definition,(
% 0.14/10.51 ![X0]: (sQ35_spl <=> (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)))),
% 0.14/10.51 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.14/10.51 fof(f639,plain,(
% 0.14/10.51 ![X0]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|~sQ35_spl)),
% 0.14/10.51 inference(component_clause,[status(thm)],[f638])).
% 0.14/10.51 fof(f641,plain,(
% 0.14/10.51 sQ35_spl|sQ23_spl|sQ21_spl),
% 0.14/10.51 inference(split_clause,[status(thm)],[f508,f638,f585,f578])).
% 0.14/10.51 fof(f765,plain,(
% 0.14/10.51 ~distinct_points(sK0_skl,sK1_skl)|~sQ23_spl),
% 0.14/10.51 inference(resolution,[status(thm)],[f586,f32])).
% 0.14/10.51 fof(f768,plain,(
% 0.14/10.51 $false|~sQ23_spl),
% 0.14/10.51 inference(forward_subsumption_resolution,[status(thm)],[f765,f51])).
% 0.14/10.51 fof(f769,plain,(
% 0.14/10.51 ~sQ23_spl),
% 0.14/10.51 inference(contradiction_clause,[status(thm)],[f768])).
% 0.14/10.51 fof(f771,plain,(
% 0.14/10.51 ~distinct_points(sK0_skl,sK1_skl)|~sQ21_spl),
% 0.14/10.51 inference(resolution,[status(thm)],[f579,f30])).
% 0.14/10.51 fof(f774,plain,(
% 0.14/10.51 $false|~sQ21_spl),
% 0.14/10.51 inference(forward_subsumption_resolution,[status(thm)],[f771,f51])).
% 0.14/10.51 fof(f775,plain,(
% 0.14/10.51 ~sQ21_spl),
% 0.14/10.51 inference(contradiction_clause,[status(thm)],[f774])).
% 0.14/10.51 fof(f938,plain,(
% 0.14/10.51 apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl))|apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl))|~sQ35_spl),
% 0.14/10.51 inference(resolution,[status(thm)],[f639,f53])).
% 0.14/10.51 fof(f943,definition,(
% 0.14/10.51 sQ69_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)))),
% 0.14/10.51 introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition])).
% 0.14/10.51 fof(f944,plain,(
% 0.14/10.51 apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl))|~sQ69_spl),
% 0.14/10.51 inference(component_clause,[status(thm)],[f943])).
% 0.14/10.51 fof(f946,definition,(
% 0.14/10.51 sQ70_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl)))),
% 0.14/10.51 introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 0.14/10.51 fof(f947,plain,(
% 0.14/10.51 apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl))|~sQ70_spl),
% 0.14/10.51 inference(component_clause,[status(thm)],[f946])).
% 0.14/10.51 fof(f949,plain,(
% 0.14/10.51 sQ69_spl|sQ70_spl|~sQ35_spl),
% 0.14/10.51 inference(split_clause,[status(thm)],[f938,f943,f946,f638])).
% 0.14/10.51 fof(f950,plain,(
% 0.14/10.51 ~distinct_points(sK2_skl,sK1_skl)|~sQ69_spl),
% 0.14/10.51 inference(resolution,[status(thm)],[f944,f30])).
% 0.14/10.51 fof(f953,plain,(
% 0.14/10.51 $false|~sQ5_spl|~sQ69_spl),
% 0.14/10.51 inference(forward_subsumption_resolution,[status(thm)],[f950,f96])).
% 0.14/10.51 fof(f954,plain,(
% 0.14/10.51 ~sQ5_spl|~sQ69_spl),
% 0.14/10.51 inference(contradiction_clause,[status(thm)],[f953])).
% 0.14/10.51 fof(f955,plain,(
% 0.14/10.51 ~distinct_points(sK2_skl,sK1_skl)|~sQ70_spl),
% 0.14/10.51 inference(resolution,[status(thm)],[f947,f32])).
% 0.14/10.51 fof(f958,plain,(
% 0.14/10.51 $false|~sQ5_spl|~sQ70_spl),
% 0.14/10.51 inference(forward_subsumption_resolution,[status(thm)],[f955,f96])).
% 0.14/10.51 fof(f959,plain,(
% 0.14/10.51 ~sQ5_spl|~sQ70_spl),
% 0.14/10.51 inference(contradiction_clause,[status(thm)],[f958])).
% 0.14/10.51 fof(f960,plain,(
% 0.14/10.51 $false),
% 0.14/10.51 inference(sat_refutation,[status(thm)],[f76,f98,f106,f641,f769,f775,f949,f954,f959])).
% 0.14/10.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/10.53 % Elapsed time: 0.132963 seconds
% 0.14/10.53 % CPU time: 0.946147 seconds
% 0.14/10.53 % Total memory used: 28.664 MB
% 0.14/10.53 % Net memory used: 26.229 MB
%------------------------------------------------------------------------------