%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO187+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 12:26:00 PM UTC 2026
% Result : Theorem 3.88s 1.21s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 20 13:07:58 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.41 % Drodi V4.1.1
% 3.88/1.21 % Refutation found
% 3.88/1.21 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.88/1.21 % SZS output start CNFRefutation for theBenchmark
% 3.88/1.21 fof(f1,axiom,(
% 3.88/1.21 (! [X] : ~ distinct_points(X,X) )),
% 3.88/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.88/1.21 fof(f4,axiom,(
% 3.88/1.21 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 3.88/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.88/1.21 fof(f7,axiom,(
% 3.88/1.21 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 3.88/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.88/1.21 fof(f8,axiom,(
% 3.88/1.21 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 3.88/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.88/1.21 fof(f11,axiom,(
% 3.88/1.21 (! [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) ) ) )),
% 3.88/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.88/1.21 fof(f12,axiom,(
% 3.88/1.21 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 3.88/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.88/1.21 fof(f13,axiom,(
% 3.88/1.21 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 3.88/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.88/1.21 fof(f15,conjecture,(
% 3.88/1.21 (! [X,Y,U,V] :( ( distinct_points(X,Y)& distinct_points(U,V)& ~ apart_point_and_line(X,line_connecting(U,V))& ~ apart_point_and_line(Y,line_connecting(U,V)) )=> ( ~ apart_point_and_line(U,line_connecting(X,Y))& ~ apart_point_and_line(V,line_connecting(X,Y)) ) ) )),
% 3.88/1.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.88/1.21 fof(f16,negated_conjecture,(
% 3.88/1.21 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& distinct_points(U,V)& ~ apart_point_and_line(X,line_connecting(U,V))& ~ apart_point_and_line(Y,line_connecting(U,V)) )=> ( ~ apart_point_and_line(U,line_connecting(X,Y))& ~ apart_point_and_line(V,line_connecting(X,Y)) ) ) ))),
% 3.88/1.21 inference(negated_conjecture,[status(cth)],[f15])).
% 3.88/1.21 fof(f17,plain,(
% 3.88/1.21 ![X0]: (~distinct_points(X0,X0))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f1])).
% 3.88/1.21 fof(f20,plain,(
% 3.88/1.21 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 3.88/1.21 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 3.88/1.21 fof(f21,plain,(
% 3.88/1.21 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 3.88/1.21 inference(miniscoping,[status(thm)],[f20])).
% 3.88/1.21 fof(f22,plain,(
% 3.88/1.21 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f21])).
% 3.88/1.21 fof(f29,plain,(
% 3.88/1.21 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 3.88/1.21 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 3.88/1.21 fof(f30,plain,(
% 3.88/1.21 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f29])).
% 3.88/1.21 fof(f31,plain,(
% 3.88/1.21 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 3.88/1.21 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 3.88/1.21 fof(f32,plain,(
% 3.88/1.21 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f31])).
% 3.88/1.21 fof(f37,plain,(
% 3.88/1.21 ![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)))),
% 3.88/1.21 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 3.88/1.21 fof(f38,plain,(
% 3.88/1.21 ![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))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f37])).
% 3.88/1.21 fof(f39,plain,(
% 3.88/1.21 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 3.88/1.21 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 3.88/1.21 fof(f40,plain,(
% 3.88/1.21 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 3.88/1.21 inference(miniscoping,[status(thm)],[f39])).
% 3.88/1.21 fof(f41,plain,(
% 3.88/1.21 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f40])).
% 3.88/1.21 fof(f42,plain,(
% 3.88/1.21 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 3.88/1.21 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 3.88/1.21 fof(f43,plain,(
% 3.88/1.21 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 3.88/1.21 inference(miniscoping,[status(thm)],[f42])).
% 3.88/1.21 fof(f44,plain,(
% 3.88/1.21 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f43])).
% 3.88/1.21 fof(f48,plain,(
% 3.88/1.21 (?[X,Y,U,V]: ((((distinct_points(X,Y)&distinct_points(U,V))&~apart_point_and_line(X,line_connecting(U,V)))&~apart_point_and_line(Y,line_connecting(U,V)))&(apart_point_and_line(U,line_connecting(X,Y))|apart_point_and_line(V,line_connecting(X,Y)))))),
% 3.88/1.21 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 3.88/1.21 fof(f49,plain,(
% 3.88/1.21 ((((distinct_points(sK0_skl,sK1_skl)&distinct_points(sK2_skl,sK3_skl))&~apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)))&~apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)))&(apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))))),
% 3.88/1.21 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(U,sK2_skl),skolemize(V,sK3_skl)],[f48])).
% 3.88/1.21 fof(f50,plain,(
% 3.88/1.21 distinct_points(sK0_skl,sK1_skl)),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f49])).
% 3.88/1.21 fof(f51,plain,(
% 3.88/1.21 distinct_points(sK2_skl,sK3_skl)),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f49])).
% 3.88/1.21 fof(f52,plain,(
% 3.88/1.21 ~apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f49])).
% 3.88/1.21 fof(f53,plain,(
% 3.88/1.21 ~apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f49])).
% 3.88/1.21 fof(f54,plain,(
% 3.88/1.21 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))),
% 3.88/1.21 inference(cnf_transformation,[status(thm)],[f49])).
% 3.88/1.21 fof(f55,definition,(
% 3.88/1.21 sQ0_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f56,plain,(
% 3.88/1.21 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|~sQ0_spl),
% 3.88/1.21 inference(component_clause,[status(thm)],[f55])).
% 3.88/1.21 fof(f58,definition,(
% 3.88/1.21 sQ1_spl <=> (apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f59,plain,(
% 3.88/1.21 apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))|~sQ1_spl),
% 3.88/1.21 inference(component_clause,[status(thm)],[f58])).
% 3.88/1.21 fof(f61,plain,(
% 3.88/1.21 sQ0_spl|sQ1_spl),
% 3.88/1.21 inference(split_clause,[status(thm)],[f54,f55,f58])).
% 3.88/1.21 fof(f62,plain,(
% 3.88/1.21 ![X0]: (distinct_points(sK2_skl,X0)|distinct_points(sK3_skl,X0))),
% 3.88/1.21 inference(resolution,[status(thm)],[f22,f51])).
% 3.88/1.21 fof(f64,plain,(
% 3.88/1.21 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_points(sK3_skl,X1)|distinct_points(X0,X1))),
% 3.88/1.21 inference(resolution,[status(thm)],[f62,f22])).
% 3.88/1.21 fof(f75,plain,(
% 3.88/1.21 ![X0]: (distinct_points(sK2_skl,X0)|distinct_points(X0,sK3_skl))),
% 3.88/1.21 inference(resolution,[status(thm)],[f64,f17])).
% 3.88/1.21 fof(f85,definition,(
% 3.88/1.21 sQ4_spl <=> (distinct_points(sK2_skl,sK3_skl))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f93,plain,(
% 3.88/1.21 ![X0,X1]: (distinct_points(X0,sK3_skl)|distinct_points(sK2_skl,X1)|distinct_points(X0,X1))),
% 3.88/1.21 inference(resolution,[status(thm)],[f75,f22])).
% 3.88/1.21 fof(f129,plain,(
% 3.88/1.21 ![X0,X1]: (distinct_points(sK2_skl,sK3_skl)|distinct_points(sK2_skl,X0)|distinct_points(X1,X0))),
% 3.88/1.21 inference(resolution,[status(thm)],[f93,f22])).
% 3.88/1.21 fof(f135,definition,(
% 3.88/1.21 ![X0,X1]: (sQ10_spl <=> (distinct_points(sK2_skl,X0)|distinct_points(X1,X0)))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f136,plain,(
% 3.88/1.21 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_points(X1,X0)|~sQ10_spl)),
% 3.88/1.21 inference(component_clause,[status(thm)],[f135])).
% 3.88/1.21 fof(f138,plain,(
% 3.88/1.21 sQ4_spl|sQ10_spl),
% 3.88/1.21 inference(split_clause,[status(thm)],[f129,f85,f135])).
% 3.88/1.21 fof(f245,plain,(
% 3.88/1.21 $false|~sQ10_spl),
% 3.88/1.21 inference(resolution,[status(thm)],[f136,f17])).
% 3.88/1.21 fof(f249,plain,(
% 3.88/1.21 ~sQ10_spl),
% 3.88/1.21 inference(contradiction_clause,[status(thm)],[f245])).
% 3.88/1.21 fof(f272,plain,(
% 3.88/1.21 ![X0]: (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|~sQ0_spl)),
% 3.88/1.21 inference(resolution,[status(thm)],[f41,f56])).
% 3.88/1.21 fof(f559,plain,(
% 3.88/1.21 ![X0,X1]: (~distinct_lines(X0,X1)|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK0_skl,X1)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK1_skl,X1))),
% 3.88/1.21 inference(resolution,[status(thm)],[f38,f50])).
% 3.88/1.21 fof(f749,plain,(
% 3.88/1.21 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK3_skl,X0)|~sQ1_spl)),
% 3.88/1.21 inference(resolution,[status(thm)],[f59,f44])).
% 3.88/1.21 fof(f755,plain,(
% 3.88/1.21 ![X0]: (apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,X0)|~sQ1_spl)),
% 3.88/1.21 inference(resolution,[status(thm)],[f749,f559])).
% 3.88/1.21 fof(f762,definition,(
% 3.88/1.21 sQ33_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f763,plain,(
% 3.88/1.21 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ33_spl),
% 3.88/1.21 inference(component_clause,[status(thm)],[f762])).
% 3.88/1.21 fof(f775,definition,(
% 3.88/1.21 ![X0]: (sQ36_spl <=> (apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK1_skl,X0)))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f776,plain,(
% 3.88/1.21 ![X0]: (apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK1_skl,X0)|~sQ36_spl)),
% 3.88/1.21 inference(component_clause,[status(thm)],[f775])).
% 3.88/1.21 fof(f778,definition,(
% 3.88/1.21 sQ37_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f779,plain,(
% 3.88/1.21 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ37_spl),
% 3.88/1.21 inference(component_clause,[status(thm)],[f778])).
% 3.88/1.21 fof(f781,plain,(
% 3.88/1.21 sQ36_spl|sQ33_spl|sQ37_spl|~sQ1_spl),
% 3.88/1.21 inference(split_clause,[status(thm)],[f755,f775,f762,f778,f58])).
% 3.88/1.21 fof(f970,plain,(
% 3.88/1.21 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_lines(line_connecting(sK0_skl,sK1_skl),X1)|apart_point_and_line(X0,X1)|~sQ0_spl)),
% 3.88/1.21 inference(resolution,[status(thm)],[f272,f44])).
% 3.88/1.21 fof(f997,plain,(
% 3.88/1.21 ![X0,X1]: (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,X1)|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,X1)|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,X1)|~sQ0_spl)),
% 3.88/1.21 inference(resolution,[status(thm)],[f970,f559])).
% 3.88/1.21 fof(f1021,definition,(
% 3.88/1.21 ![X0,X1]: (sQ60_spl <=> (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,X1)|apart_point_and_line(sK0_skl,X1)|apart_point_and_line(sK1_skl,X1)))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f1022,plain,(
% 3.88/1.21 ![X0,X1]: (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,X1)|apart_point_and_line(sK0_skl,X1)|apart_point_and_line(sK1_skl,X1)|~sQ60_spl)),
% 3.88/1.21 inference(component_clause,[status(thm)],[f1021])).
% 3.88/1.21 fof(f1024,plain,(
% 3.88/1.21 sQ60_spl|sQ33_spl|sQ37_spl|~sQ0_spl),
% 3.88/1.21 inference(split_clause,[status(thm)],[f997,f1021,f762,f778,f55])).
% 3.88/1.21 fof(f1092,plain,(
% 3.88/1.21 ![X0]: (apart_point_and_line(sK0_skl,line_connecting(X0,sK3_skl))|apart_point_and_line(sK1_skl,line_connecting(X0,sK3_skl))|~distinct_points(X0,sK3_skl)|~sQ36_spl)),
% 3.88/1.21 inference(resolution,[status(thm)],[f776,f32])).
% 3.88/1.21 fof(f1196,definition,(
% 3.88/1.21 sQ66_spl <=> (distinct_points(sK2_skl,sK2_skl))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f1197,plain,(
% 3.88/1.21 distinct_points(sK2_skl,sK2_skl)|~sQ66_spl),
% 3.88/1.21 inference(component_clause,[status(thm)],[f1196])).
% 3.88/1.21 fof(f1560,plain,(
% 3.88/1.21 $false|~sQ66_spl),
% 3.88/1.21 inference(forward_subsumption_resolution,[status(thm)],[f1197,f17])).
% 3.88/1.21 fof(f1561,plain,(
% 3.88/1.21 ~sQ66_spl),
% 3.88/1.21 inference(contradiction_clause,[status(thm)],[f1560])).
% 3.88/1.21 fof(f2964,plain,(
% 3.88/1.21 apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))|~sQ36_spl),
% 3.88/1.21 inference(resolution,[status(thm)],[f1092,f51])).
% 3.88/1.21 fof(f3183,definition,(
% 3.88/1.21 sQ197_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f3184,plain,(
% 3.88/1.21 apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))|~sQ197_spl),
% 3.88/1.21 inference(component_clause,[status(thm)],[f3183])).
% 3.88/1.21 fof(f3186,definition,(
% 3.88/1.21 sQ198_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f3187,plain,(
% 3.88/1.21 apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))|~sQ198_spl),
% 3.88/1.21 inference(component_clause,[status(thm)],[f3186])).
% 3.88/1.21 fof(f3189,plain,(
% 3.88/1.21 sQ197_spl|sQ198_spl|~sQ36_spl),
% 3.88/1.21 inference(split_clause,[status(thm)],[f2964,f3183,f3186,f775])).
% 3.88/1.21 fof(f3384,plain,(
% 3.88/1.21 $false|~sQ198_spl),
% 3.88/1.21 inference(forward_subsumption_resolution,[status(thm)],[f3187,f53])).
% 3.88/1.21 fof(f3385,plain,(
% 3.88/1.21 ~sQ198_spl),
% 3.88/1.21 inference(contradiction_clause,[status(thm)],[f3384])).
% 3.88/1.21 fof(f3386,plain,(
% 3.88/1.21 $false|~sQ197_spl),
% 3.88/1.21 inference(forward_subsumption_resolution,[status(thm)],[f3184,f52])).
% 3.88/1.21 fof(f3387,plain,(
% 3.88/1.21 ~sQ197_spl),
% 3.88/1.21 inference(contradiction_clause,[status(thm)],[f3386])).
% 3.88/1.21 fof(f3392,plain,(
% 3.88/1.21 ~distinct_points(sK0_skl,sK1_skl)|~sQ33_spl),
% 3.88/1.21 inference(resolution,[status(thm)],[f763,f30])).
% 3.88/1.21 fof(f3395,plain,(
% 3.88/1.21 $false|~sQ33_spl),
% 3.88/1.21 inference(forward_subsumption_resolution,[status(thm)],[f3392,f50])).
% 3.88/1.21 fof(f3396,plain,(
% 3.88/1.21 ~sQ33_spl),
% 3.88/1.21 inference(contradiction_clause,[status(thm)],[f3395])).
% 3.88/1.21 fof(f3399,plain,(
% 3.88/1.21 ~distinct_points(sK0_skl,sK1_skl)|~sQ37_spl),
% 3.88/1.21 inference(resolution,[status(thm)],[f779,f32])).
% 3.88/1.21 fof(f3402,plain,(
% 3.88/1.21 $false|~sQ37_spl),
% 3.88/1.21 inference(forward_subsumption_resolution,[status(thm)],[f3399,f50])).
% 3.88/1.21 fof(f3403,plain,(
% 3.88/1.21 ~sQ37_spl),
% 3.88/1.21 inference(contradiction_clause,[status(thm)],[f3402])).
% 3.88/1.21 fof(f3696,definition,(
% 3.88/1.21 sQ225_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f3697,plain,(
% 3.88/1.21 distinct_points(sK0_skl,sK0_skl)|~sQ225_spl),
% 3.88/1.21 inference(component_clause,[status(thm)],[f3696])).
% 3.88/1.21 fof(f6827,plain,(
% 3.88/1.21 $false|~sQ225_spl),
% 3.88/1.21 inference(forward_subsumption_resolution,[status(thm)],[f3697,f17])).
% 3.88/1.21 fof(f6828,plain,(
% 3.88/1.21 ~sQ225_spl),
% 3.88/1.21 inference(contradiction_clause,[status(thm)],[f6827])).
% 3.88/1.21 fof(f7292,plain,(
% 3.88/1.21 ![X0]: (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))|~sQ60_spl)),
% 3.88/1.21 inference(resolution,[status(thm)],[f1022,f53])).
% 3.88/1.21 fof(f7321,definition,(
% 3.88/1.21 ![X0]: (sQ489_spl <=> (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,line_connecting(sK2_skl,sK3_skl))))),
% 3.88/1.21 introduced(definition,[new_symbols(definition,[sQ489_spl])],[split_symbol_definition])).
% 3.88/1.21 fof(f7322,plain,(
% 3.88/1.21 ![X0]: (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,line_connecting(sK2_skl,sK3_skl))|~sQ489_spl)),
% 3.88/1.21 inference(component_clause,[status(thm)],[f7321])).
% 3.88/1.21 fof(f7324,plain,(
% 3.88/1.21 sQ489_spl|sQ197_spl|~sQ60_spl),
% 3.88/1.21 inference(split_clause,[status(thm)],[f7292,f7321,f3183,f1021])).
% 3.88/1.21 fof(f7360,plain,(
% 3.88/1.21 distinct_points(sK2_skl,sK2_skl)|~distinct_points(sK2_skl,sK3_skl)|~sQ489_spl),
% 3.88/1.21 inference(resolution,[status(thm)],[f7322,f30])).
% 3.88/1.21 fof(f7364,plain,(
% 3.88/1.21 sQ66_spl|~sQ4_spl|~sQ489_spl),
% 3.88/1.21 inference(split_clause,[status(thm)],[f7360,f1196,f85,f7321])).
% 3.88/1.21 fof(f7365,plain,(
% 3.88/1.21 $false),
% 3.88/1.21 inference(sat_refutation,[status(thm)],[f61,f138,f249,f781,f1024,f1561,f3189,f3385,f3387,f3396,f3403,f6828,f7324,f7364])).
% 3.88/1.21 % SZS output end CNFRefutation for theBenchmark.p
% 3.88/1.25 % Elapsed time: 0.838894 seconds
% 3.88/1.25 % CPU time: 6.181947 seconds
% 3.88/1.25 % Total memory used: 49.507 MB
% 3.88/1.25 % Net memory used: 43.521 MB
%------------------------------------------------------------------------------