%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO202+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 : n001.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 12:26:04 PM UTC 2026
% Result : Theorem 1.33s 0.59s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+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
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 13:28:11 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 1.33/0.59 % Refutation found
% 1.33/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.33/0.59 % SZS output start CNFRefutation for theBenchmark
% 1.33/0.59 fof(f1,axiom,(
% 1.33/0.59 (! [X] : ~ distinct_points(X,X) )),
% 1.33/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.33/0.59 fof(f2,axiom,(
% 1.33/0.59 (! [X] : ~ distinct_lines(X,X) )),
% 1.33/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.33/0.59 fof(f3,axiom,(
% 1.33/0.59 (! [X] : ~ convergent_lines(X,X) )),
% 1.33/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.33/0.59 fof(f4,axiom,(
% 1.33/0.59 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 1.33/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.33/0.59 fof(f7,axiom,(
% 1.33/0.59 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 1.33/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.33/0.59 fof(f8,axiom,(
% 1.33/0.59 (! [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)) ) ) )),
% 1.33/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.33/0.59 fof(f9,axiom,(
% 1.33/0.59 (! [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) ) ) )),
% 1.33/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.33/0.59 fof(f12,axiom,(
% 1.33/0.59 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 1.33/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.33/0.59 fof(f13,conjecture,(
% 1.33/0.59 (! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ) )),
% 1.33/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.33/0.59 fof(f14,negated_conjecture,(
% 1.33/0.59 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ) ))),
% 1.33/0.59 inference(negated_conjecture,[status(cth)],[f13])).
% 1.33/0.59 fof(f15,plain,(
% 1.33/0.59 ![X0]: (~distinct_points(X0,X0))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f1])).
% 1.33/0.59 fof(f16,plain,(
% 1.33/0.59 ![X0]: (~distinct_lines(X0,X0))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f2])).
% 1.33/0.59 fof(f17,plain,(
% 1.33/0.59 ![X0]: (~convergent_lines(X0,X0))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f3])).
% 1.33/0.59 fof(f18,plain,(
% 1.33/0.59 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 1.33/0.59 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 1.33/0.59 fof(f19,plain,(
% 1.33/0.59 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 1.33/0.59 inference(miniscoping,[status(thm)],[f18])).
% 1.33/0.59 fof(f20,plain,(
% 1.33/0.59 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f19])).
% 1.33/0.59 fof(f27,plain,(
% 1.33/0.59 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 1.33/0.59 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 1.33/0.59 fof(f28,plain,(
% 1.33/0.59 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 1.33/0.59 inference(miniscoping,[status(thm)],[f27])).
% 1.33/0.59 fof(f29,plain,(
% 1.33/0.59 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f28])).
% 1.33/0.59 fof(f31,plain,(
% 1.33/0.59 ![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))))),
% 1.33/0.59 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 1.33/0.59 fof(f32,plain,(
% 1.33/0.59 ![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)))))),
% 1.33/0.59 inference(miniscoping,[status(thm)],[f31])).
% 1.33/0.59 fof(f33,plain,(
% 1.33/0.59 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f32])).
% 1.33/0.59 fof(f34,plain,(
% 1.33/0.59 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f32])).
% 1.33/0.59 fof(f35,plain,(
% 1.33/0.59 ![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)))),
% 1.33/0.59 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 1.33/0.59 fof(f36,plain,(
% 1.33/0.59 ![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))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f35])).
% 1.33/0.59 fof(f43,plain,(
% 1.33/0.59 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 1.33/0.59 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 1.33/0.59 fof(f44,plain,(
% 1.33/0.59 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f43])).
% 1.33/0.59 fof(f45,plain,(
% 1.33/0.59 (?[X,Y,Z]: (((distinct_points(X,Y)&distinct_points(X,Z))&convergent_lines(line_connecting(X,Y),line_connecting(X,Z)))&distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X)))),
% 1.33/0.59 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 1.33/0.59 fof(f46,plain,(
% 1.33/0.59 (((distinct_points(sK0_skl,sK1_skl)&distinct_points(sK0_skl,sK2_skl))&convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)))&distinct_points(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),sK0_skl))),
% 1.33/0.59 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])).
% 1.33/0.59 fof(f47,plain,(
% 1.33/0.59 distinct_points(sK0_skl,sK1_skl)),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f46])).
% 1.33/0.59 fof(f48,plain,(
% 1.33/0.59 distinct_points(sK0_skl,sK2_skl)),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f46])).
% 1.33/0.59 fof(f49,plain,(
% 1.33/0.59 convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f46])).
% 1.33/0.59 fof(f50,plain,(
% 1.33/0.59 distinct_points(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),sK0_skl)),
% 1.33/0.59 inference(cnf_transformation,[status(thm)],[f46])).
% 1.33/0.59 fof(f51,plain,(
% 1.33/0.59 ![X0]: (~apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|distinct_points(X0,intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))))),
% 1.33/0.59 inference(resolution,[status(thm)],[f33,f49])).
% 1.33/0.59 fof(f52,plain,(
% 1.33/0.59 ![X0]: (~apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))|distinct_points(X0,intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))))),
% 1.33/0.59 inference(resolution,[status(thm)],[f34,f49])).
% 1.33/0.59 fof(f53,plain,(
% 1.33/0.59 distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))),
% 1.33/0.59 inference(resolution,[status(thm)],[f44,f49])).
% 1.33/0.59 fof(f55,plain,(
% 1.33/0.59 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK2_skl,X0))),
% 1.33/0.59 inference(resolution,[status(thm)],[f20,f48])).
% 1.33/0.59 fof(f56,plain,(
% 1.33/0.59 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 1.33/0.59 inference(resolution,[status(thm)],[f20,f47])).
% 1.33/0.59 fof(f60,plain,(
% 1.33/0.59 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK2_skl,X1)|distinct_points(X0,X1))),
% 1.33/0.59 inference(resolution,[status(thm)],[f55,f20])).
% 1.33/0.59 fof(f62,plain,(
% 1.33/0.59 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 1.33/0.59 inference(resolution,[status(thm)],[f56,f20])).
% 1.33/0.59 fof(f68,plain,(
% 1.33/0.59 ![X0,X1]: (distinct_points(sK0_skl,sK2_skl)|distinct_points(sK2_skl,X0)|distinct_points(X1,X0))),
% 1.33/0.59 inference(resolution,[status(thm)],[f60,f20])).
% 1.33/0.59 fof(f77,definition,(
% 1.33/0.59 ![X0]: (sQ1_spl <=> (distinct_points(sK0_skl,X0)|distinct_points(sK0_skl,X0)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f78,plain,(
% 1.33/0.59 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK0_skl,X0)|~sQ1_spl)),
% 1.33/0.59 inference(component_clause,[status(thm)],[f77])).
% 1.33/0.59 fof(f81,definition,(
% 1.33/0.59 sQ2_spl <=> (distinct_points(sK0_skl,sK2_skl))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f84,definition,(
% 1.33/0.59 ![X0,X1]: (sQ3_spl <=> (distinct_points(sK2_skl,X0)|distinct_points(X1,X0)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f85,plain,(
% 1.33/0.59 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_points(X1,X0)|~sQ3_spl)),
% 1.33/0.59 inference(component_clause,[status(thm)],[f84])).
% 1.33/0.59 fof(f87,plain,(
% 1.33/0.59 sQ2_spl|sQ3_spl),
% 1.33/0.59 inference(split_clause,[status(thm)],[f68,f81,f84])).
% 1.33/0.59 fof(f113,plain,(
% 1.33/0.59 ![X0]: (distinct_points(sK0_skl,X0)|~sQ1_spl)),
% 1.33/0.59 inference(duplicate_literals_removal,[status(thm)],[f78])).
% 1.33/0.59 fof(f119,plain,(
% 1.33/0.59 ![X0,X1,X2]: (distinct_points(sK0_skl,X0)|distinct_points(X0,X1)|distinct_points(sK1_skl,X2)|distinct_points(X1,X2))),
% 1.33/0.59 inference(resolution,[status(thm)],[f62,f20])).
% 1.33/0.59 fof(f128,definition,(
% 1.33/0.59 sQ8_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f240,plain,(
% 1.33/0.59 $false|~sQ3_spl),
% 1.33/0.59 inference(resolution,[status(thm)],[f85,f15])).
% 1.33/0.59 fof(f244,plain,(
% 1.33/0.59 ~sQ3_spl),
% 1.33/0.59 inference(contradiction_clause,[status(thm)],[f240])).
% 1.33/0.59 fof(f325,definition,(
% 1.33/0.59 sQ19_spl <=> (distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK1_skl)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f326,plain,(
% 1.33/0.59 distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK1_skl))|~sQ19_spl),
% 1.33/0.59 inference(component_clause,[status(thm)],[f325])).
% 1.33/0.59 fof(f337,definition,(
% 1.33/0.59 ![X0,X1]: (sQ22_spl <=> (convergent_lines(line_connecting(sK0_skl,sK2_skl),X0)|convergent_lines(X1,X0)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f338,plain,(
% 1.33/0.59 ![X0,X1]: (convergent_lines(line_connecting(sK0_skl,sK2_skl),X0)|convergent_lines(X1,X0)|~sQ22_spl)),
% 1.33/0.59 inference(component_clause,[status(thm)],[f337])).
% 1.33/0.59 fof(f403,plain,(
% 1.33/0.59 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(X0,X1)|distinct_points(X1,sK1_skl))),
% 1.33/0.59 inference(resolution,[status(thm)],[f119,f15])).
% 1.33/0.59 fof(f514,plain,(
% 1.33/0.59 ![X0,X1]: (~distinct_lines(X0,X1)|apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),X0)|apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),X1)|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK0_skl,X1))),
% 1.33/0.59 inference(resolution,[status(thm)],[f36,f50])).
% 1.33/0.59 fof(f625,plain,(
% 1.33/0.59 apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))),
% 1.33/0.59 inference(resolution,[status(thm)],[f514,f53])).
% 1.33/0.59 fof(f626,definition,(
% 1.33/0.59 sQ37_spl <=> (apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK1_skl)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f627,plain,(
% 1.33/0.59 apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK1_skl))|~sQ37_spl),
% 1.33/0.59 inference(component_clause,[status(thm)],[f626])).
% 1.33/0.59 fof(f629,definition,(
% 1.33/0.59 sQ38_spl <=> (apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK2_skl)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f630,plain,(
% 1.33/0.59 apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK2_skl))|~sQ38_spl),
% 1.33/0.59 inference(component_clause,[status(thm)],[f629])).
% 1.33/0.59 fof(f632,definition,(
% 1.33/0.59 sQ39_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f633,plain,(
% 1.33/0.59 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ39_spl),
% 1.33/0.59 inference(component_clause,[status(thm)],[f632])).
% 1.33/0.59 fof(f635,definition,(
% 1.33/0.59 sQ40_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f636,plain,(
% 1.33/0.59 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|~sQ40_spl),
% 1.33/0.59 inference(component_clause,[status(thm)],[f635])).
% 1.33/0.59 fof(f638,plain,(
% 1.33/0.59 sQ37_spl|sQ38_spl|sQ39_spl|sQ40_spl),
% 1.33/0.59 inference(split_clause,[status(thm)],[f625,f626,f629,f632,f635])).
% 1.33/0.59 fof(f1024,plain,(
% 1.33/0.59 $false|~sQ1_spl),
% 1.33/0.59 inference(resolution,[status(thm)],[f113,f15])).
% 1.33/0.59 fof(f1026,plain,(
% 1.33/0.59 ~sQ1_spl),
% 1.33/0.59 inference(contradiction_clause,[status(thm)],[f1024])).
% 1.33/0.59 fof(f1088,plain,(
% 1.33/0.59 distinct_points(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)))|~sQ38_spl),
% 1.33/0.59 inference(resolution,[status(thm)],[f630,f52])).
% 1.33/0.59 fof(f1096,plain,(
% 1.33/0.59 $false|~sQ38_spl),
% 1.33/0.59 inference(forward_subsumption_resolution,[status(thm)],[f1088,f15])).
% 1.33/0.59 fof(f1097,plain,(
% 1.33/0.59 ~sQ38_spl),
% 1.33/0.59 inference(contradiction_clause,[status(thm)],[f1096])).
% 1.33/0.59 fof(f1123,definition,(
% 1.33/0.59 sQ86_spl <=> (convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK1_skl)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f1124,plain,(
% 1.33/0.59 convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK1_skl))|~sQ86_spl),
% 1.33/0.59 inference(component_clause,[status(thm)],[f1123])).
% 1.33/0.59 fof(f1153,plain,(
% 1.33/0.59 distinct_points(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)))|~sQ37_spl),
% 1.33/0.59 inference(resolution,[status(thm)],[f627,f51])).
% 1.33/0.59 fof(f1161,plain,(
% 1.33/0.59 $false|~sQ37_spl),
% 1.33/0.59 inference(forward_subsumption_resolution,[status(thm)],[f1153,f15])).
% 1.33/0.59 fof(f1162,plain,(
% 1.33/0.59 ~sQ37_spl),
% 1.33/0.59 inference(contradiction_clause,[status(thm)],[f1161])).
% 1.33/0.59 fof(f1169,plain,(
% 1.33/0.59 ~distinct_points(sK0_skl,sK2_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ40_spl),
% 1.33/0.59 inference(resolution,[status(thm)],[f636,f29])).
% 1.33/0.59 fof(f1176,definition,(
% 1.33/0.59 sQ90_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f1177,plain,(
% 1.33/0.59 distinct_points(sK0_skl,sK0_skl)|~sQ90_spl),
% 1.33/0.59 inference(component_clause,[status(thm)],[f1176])).
% 1.33/0.59 fof(f1179,plain,(
% 1.33/0.59 ~sQ2_spl|sQ90_spl|~sQ40_spl),
% 1.33/0.59 inference(split_clause,[status(thm)],[f1169,f81,f1176,f635])).
% 1.33/0.59 fof(f1186,plain,(
% 1.33/0.59 $false|~sQ90_spl),
% 1.33/0.59 inference(forward_subsumption_resolution,[status(thm)],[f1177,f15])).
% 1.33/0.59 fof(f1187,plain,(
% 1.33/0.59 ~sQ90_spl),
% 1.33/0.59 inference(contradiction_clause,[status(thm)],[f1186])).
% 1.33/0.59 fof(f1279,plain,(
% 1.33/0.59 $false|~sQ22_spl),
% 1.33/0.59 inference(resolution,[status(thm)],[f338,f17])).
% 1.33/0.59 fof(f1286,plain,(
% 1.33/0.59 ~sQ22_spl),
% 1.33/0.59 inference(contradiction_clause,[status(thm)],[f1279])).
% 1.33/0.59 fof(f1469,definition,(
% 1.33/0.59 sQ99_spl <=> (convergent_lines(line_connecting(sK0_skl,sK2_skl),line_connecting(sK0_skl,sK2_skl)))),
% 1.33/0.59 introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition])).
% 1.33/0.59 fof(f1470,plain,(
% 1.33/0.59 convergent_lines(line_connecting(sK0_skl,sK2_skl),line_connecting(sK0_skl,sK2_skl))|~sQ99_spl),
% 1.33/0.59 inference(component_clause,[status(thm)],[f1469])).
% 1.33/0.59 fof(f1473,plain,(
% 1.33/0.59 $false|~sQ86_spl),
% 1.33/0.59 inference(forward_subsumption_resolution,[status(thm)],[f1124,f17])).
% 1.33/0.59 fof(f1474,plain,(
% 1.33/0.59 ~sQ86_spl),
% 1.33/0.59 inference(contradiction_clause,[status(thm)],[f1473])).
% 1.33/0.59 fof(f1475,plain,(
% 1.33/0.59 $false|~sQ19_spl),
% 1.33/0.59 inference(forward_subsumption_resolution,[status(thm)],[f326,f16])).
% 1.33/0.59 fof(f1476,plain,(
% 1.33/0.59 ~sQ19_spl),
% 1.33/0.59 inference(contradiction_clause,[status(thm)],[f1475])).
% 1.33/0.59 fof(f1478,plain,(
% 1.33/0.59 $false|~sQ99_spl),
% 1.33/0.59 inference(forward_subsumption_resolution,[status(thm)],[f1470,f17])).
% 1.33/0.59 fof(f1479,plain,(
% 1.33/0.59 ~sQ99_spl),
% 1.33/0.59 inference(contradiction_clause,[status(thm)],[f1478])).
% 1.33/0.59 fof(f1575,plain,(
% 1.33/0.59 ![X0]: (distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,X0)|distinct_points(sK0_skl,X0))),
% 1.33/0.59 inference(resolution,[status(thm)],[f403,f20])).
% 1.33/0.59 fof(f1589,plain,(
% 1.33/0.59 sQ8_spl|sQ1_spl),
% 1.33/0.59 inference(split_clause,[status(thm)],[f1575,f128,f77])).
% 1.33/0.59 fof(f2231,plain,(
% 1.33/0.59 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ39_spl),
% 1.33/0.59 inference(resolution,[status(thm)],[f633,f29])).
% 1.33/0.59 fof(f2240,plain,(
% 1.33/0.59 ~sQ8_spl|sQ90_spl|~sQ39_spl),
% 1.33/0.59 inference(split_clause,[status(thm)],[f2231,f128,f1176,f632])).
% 1.33/0.59 fof(f2258,plain,(
% 1.33/0.59 $false),
% 1.33/0.59 inference(sat_refutation,[status(thm)],[f87,f244,f638,f1026,f1097,f1162,f1179,f1187,f1286,f1474,f1476,f1479,f1589,f2240])).
% 1.33/0.59 % SZS output end CNFRefutation for theBenchmark.p
% 1.33/0.62 % Elapsed time: 0.244190 seconds
% 1.33/0.62 % CPU time: 1.679302 seconds
% 1.33/0.62 % Total memory used: 36.075 MB
% 1.33/0.62 % Net memory used: 32.175 MB
%------------------------------------------------------------------------------