%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO205+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 : n015.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 12:26:05 PM UTC 2026
% Result : Theorem 0.08s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO205+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 13:29:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.51 % Refutation found
% 0.08/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.51 fof(f2,axiom,(
% 0.08/0.51 (! [X] : ~ distinct_lines(X,X) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f3,axiom,(
% 0.08/0.51 (! [X] : ~ convergent_lines(X,X) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f5,axiom,(
% 0.08/0.51 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f6,axiom,(
% 0.08/0.51 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f9,axiom,(
% 0.08/0.51 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f10,axiom,(
% 0.08/0.51 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f11,axiom,(
% 0.08/0.51 (! [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) ) ) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f13,axiom,(
% 0.08/0.51 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f14,axiom,(
% 0.08/0.51 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f15,conjecture,(
% 0.08/0.51 (! [X,Y,Z] :( ( convergent_lines(X,Y)& ~ distinct_lines(Y,Z) )=> ( convergent_lines(X,Z)& ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z)) ) ) )),
% 0.08/0.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.51 fof(f16,negated_conjecture,(
% 0.08/0.51 ~((! [X,Y,Z] :( ( convergent_lines(X,Y)& ~ distinct_lines(Y,Z) )=> ( convergent_lines(X,Z)& ~ distinct_points(intersection_point(X,Y),intersection_point(X,Z)) ) ) ))),
% 0.08/0.51 inference(negated_conjecture,[status(cth)],[f15])).
% 0.08/0.51 fof(f18,plain,(
% 0.08/0.51 ![X0]: (~distinct_lines(X0,X0))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f2])).
% 0.08/0.51 fof(f19,plain,(
% 0.08/0.51 ![X0]: (~convergent_lines(X0,X0))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f3])).
% 0.08/0.51 fof(f23,plain,(
% 0.08/0.51 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 0.08/0.51 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.08/0.51 fof(f24,plain,(
% 0.08/0.51 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 0.08/0.51 inference(miniscoping,[status(thm)],[f23])).
% 0.08/0.51 fof(f25,plain,(
% 0.08/0.51 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f24])).
% 0.08/0.51 fof(f26,plain,(
% 0.08/0.51 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.08/0.51 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.08/0.51 fof(f27,plain,(
% 0.08/0.51 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.08/0.51 inference(miniscoping,[status(thm)],[f26])).
% 0.08/0.51 fof(f28,plain,(
% 0.08/0.51 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f27])).
% 0.08/0.51 fof(f33,plain,(
% 0.08/0.51 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.08/0.51 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.08/0.51 fof(f34,plain,(
% 0.08/0.51 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f33])).
% 0.08/0.51 fof(f35,plain,(
% 0.08/0.51 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.08/0.51 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.08/0.51 fof(f36,plain,(
% 0.08/0.51 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f35])).
% 0.08/0.51 fof(f37,plain,(
% 0.08/0.51 ![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)))),
% 0.08/0.51 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.08/0.51 fof(f38,plain,(
% 0.08/0.51 ![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))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f37])).
% 0.08/0.51 fof(f42,plain,(
% 0.08/0.51 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.08/0.51 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.08/0.51 fof(f43,plain,(
% 0.08/0.51 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.08/0.51 inference(miniscoping,[status(thm)],[f42])).
% 0.08/0.51 fof(f44,plain,(
% 0.08/0.51 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f43])).
% 0.08/0.51 fof(f45,plain,(
% 0.08/0.51 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.08/0.51 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.08/0.51 fof(f46,plain,(
% 0.08/0.51 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.08/0.51 inference(miniscoping,[status(thm)],[f45])).
% 0.08/0.51 fof(f47,plain,(
% 0.08/0.51 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f46])).
% 0.08/0.51 fof(f48,plain,(
% 0.08/0.51 (?[X,Y,Z]: ((convergent_lines(X,Y)&~distinct_lines(Y,Z))&(~convergent_lines(X,Z)|distinct_points(intersection_point(X,Y),intersection_point(X,Z)))))),
% 0.08/0.51 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.08/0.51 fof(f49,plain,(
% 0.08/0.51 ((convergent_lines(sK0_skl,sK1_skl)&~distinct_lines(sK1_skl,sK2_skl))&(~convergent_lines(sK0_skl,sK2_skl)|distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))))),
% 0.08/0.51 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)],[f48])).
% 0.08/0.51 fof(f50,plain,(
% 0.08/0.51 convergent_lines(sK0_skl,sK1_skl)),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f49])).
% 0.08/0.51 fof(f51,plain,(
% 0.08/0.51 ~distinct_lines(sK1_skl,sK2_skl)),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f49])).
% 0.08/0.51 fof(f52,plain,(
% 0.08/0.51 ~convergent_lines(sK0_skl,sK2_skl)|distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))),
% 0.08/0.51 inference(cnf_transformation,[status(thm)],[f49])).
% 0.08/0.51 fof(f53,definition,(
% 0.08/0.51 sQ0_spl <=> (convergent_lines(sK0_skl,sK2_skl))),
% 0.08/0.51 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/0.51 fof(f55,plain,(
% 0.08/0.51 ~convergent_lines(sK0_skl,sK2_skl)|sQ0_spl),
% 0.08/0.51 inference(component_clause,[status(thm)],[f53])).
% 0.08/0.51 fof(f56,definition,(
% 0.08/0.51 sQ1_spl <=> (distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))),
% 0.08/0.51 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.08/0.51 fof(f57,plain,(
% 0.08/0.51 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))|~sQ1_spl),
% 0.08/0.51 inference(component_clause,[status(thm)],[f56])).
% 0.08/0.51 fof(f59,plain,(
% 0.08/0.51 ~sQ0_spl|sQ1_spl),
% 0.08/0.51 inference(split_clause,[status(thm)],[f52,f53,f56])).
% 0.08/0.51 fof(f73,plain,(
% 0.08/0.51 ![X0]: (distinct_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.08/0.51 inference(resolution,[status(thm)],[f47,f50])).
% 0.08/0.51 fof(f75,plain,(
% 0.08/0.51 convergent_lines(sK0_skl,sK2_skl)),
% 0.08/0.51 inference(resolution,[status(thm)],[f73,f51])).
% 0.08/0.51 fof(f78,plain,(
% 0.08/0.51 $false|sQ0_spl),
% 0.08/0.51 inference(forward_subsumption_resolution,[status(thm)],[f75,f55])).
% 0.08/0.51 fof(f79,plain,(
% 0.08/0.51 sQ0_spl),
% 0.08/0.51 inference(contradiction_clause,[status(thm)],[f78])).
% 0.08/0.51 fof(f80,plain,(
% 0.08/0.51 ![X0,X1]: (~distinct_lines(X0,X1)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)|~sQ1_spl)),
% 0.08/0.51 inference(resolution,[status(thm)],[f57,f38])).
% 0.08/0.51 fof(f83,plain,(
% 0.08/0.51 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK2_skl,X0))),
% 0.08/0.51 inference(resolution,[status(thm)],[f75,f28])).
% 0.08/0.51 fof(f101,definition,(
% 0.08/0.51 sQ5_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.08/0.51 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.08/0.51 fof(f102,plain,(
% 0.08/0.51 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ5_spl),
% 0.08/0.51 inference(component_clause,[status(thm)],[f101])).
% 0.08/0.51 fof(f107,definition,(
% 0.08/0.51 sQ7_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl))),
% 0.08/0.51 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.08/0.51 fof(f108,plain,(
% 0.08/0.51 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|~sQ7_spl),
% 0.08/0.51 inference(component_clause,[status(thm)],[f107])).
% 0.08/0.51 fof(f111,definition,(
% 0.08/0.51 sQ8_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 0.08/0.51 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.08/0.51 fof(f112,plain,(
% 0.08/0.51 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ8_spl),
% 0.08/0.51 inference(component_clause,[status(thm)],[f111])).
% 0.08/0.51 fof(f114,definition,(
% 0.08/0.51 sQ9_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl))),
% 0.08/0.51 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.08/0.51 fof(f115,plain,(
% 0.08/0.51 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)|~sQ9_spl),
% 0.08/0.51 inference(component_clause,[status(thm)],[f114])).
% 0.08/0.51 fof(f120,plain,(
% 0.08/0.51 convergent_lines(sK2_skl,sK0_skl)),
% 0.08/0.51 inference(resolution,[status(thm)],[f83,f19])).
% 0.08/0.51 fof(f121,plain,(
% 0.08/0.51 ![X0]: (distinct_lines(sK0_skl,X0)|convergent_lines(sK2_skl,X0))),
% 0.08/0.51 inference(resolution,[status(thm)],[f120,f47])).
% 0.08/0.51 fof(f123,plain,(
% 0.08/0.51 ![X0]: (distinct_lines(sK1_skl,X0)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)|~sQ9_spl)),
% 0.08/0.51 inference(resolution,[status(thm)],[f115,f44])).
% 0.08/0.51 fof(f125,plain,(
% 0.08/0.51 ~convergent_lines(sK0_skl,sK1_skl)|~sQ8_spl),
% 0.08/0.51 inference(resolution,[status(thm)],[f112,f36])).
% 0.08/0.51 fof(f128,plain,(
% 0.08/0.51 $false|~sQ8_spl),
% 0.08/0.51 inference(forward_subsumption_resolution,[status(thm)],[f125,f50])).
% 0.08/0.51 fof(f129,plain,(
% 0.08/0.51 ~sQ8_spl),
% 0.08/0.51 inference(contradiction_clause,[status(thm)],[f128])).
% 0.08/0.51 fof(f130,plain,(
% 0.08/0.51 ~convergent_lines(sK0_skl,sK2_skl)|~sQ7_spl),
% 0.08/0.51 inference(resolution,[status(thm)],[f108,f34])).
% 0.08/0.51 fof(f133,plain,(
% 0.08/0.51 ~sQ0_spl|~sQ7_spl),
% 0.08/0.51 inference(split_clause,[status(thm)],[f130,f53,f107])).
% 0.08/0.51 fof(f135,plain,(
% 0.08/0.51 ![X0,X1]: (convergent_lines(sK2_skl,X0)|distinct_lines(sK0_skl,X1)|distinct_lines(X0,X1))),
% 0.08/0.51 inference(resolution,[status(thm)],[f121,f25])).
% 0.08/0.51 fof(f181,plain,(
% 0.08/0.51 ~convergent_lines(sK0_skl,sK1_skl)|~sQ5_spl),
% 0.08/0.51 inference(resolution,[status(thm)],[f102,f34])).
% 0.08/0.51 fof(f184,plain,(
% 0.08/0.51 $false|~sQ5_spl),
% 0.08/0.51 inference(forward_subsumption_resolution,[status(thm)],[f181,f50])).
% 0.08/0.51 fof(f185,plain,(
% 0.08/0.51 ~sQ5_spl),
% 0.08/0.51 inference(contradiction_clause,[status(thm)],[f184])).
% 0.08/0.51 fof(f225,definition,(
% 0.08/0.51 sQ21_spl <=> (distinct_lines(sK1_skl,sK2_skl))),
% 0.08/0.51 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.08/0.51 fof(f226,plain,(
% 0.08/0.51 distinct_lines(sK1_skl,sK2_skl)|~sQ21_spl),
% 0.08/0.51 inference(component_clause,[status(thm)],[f225])).
% 0.08/0.51 fof(f700,plain,(
% 0.08/0.51 distinct_lines(sK1_skl,sK2_skl)|~convergent_lines(sK0_skl,sK2_skl)|~sQ9_spl),
% 0.08/0.51 inference(resolution,[status(thm)],[f123,f36])).
% 0.08/0.51 fof(f706,plain,(
% 0.08/0.51 sQ21_spl|~sQ0_spl|~sQ9_spl),
% 0.08/0.51 inference(split_clause,[status(thm)],[f700,f225,f53,f114])).
% 0.08/0.51 fof(f711,plain,(
% 0.08/0.51 $false|~sQ21_spl),
% 0.08/0.51 inference(forward_subsumption_resolution,[status(thm)],[f226,f51])).
% 0.08/0.51 fof(f712,plain,(
% 0.08/0.51 ~sQ21_spl),
% 0.08/0.51 inference(contradiction_clause,[status(thm)],[f711])).
% 0.08/0.51 fof(f721,definition,(
% 0.08/0.51 sQ65_spl <=> (distinct_lines(sK2_skl,sK1_skl))),
% 0.08/0.51 introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 0.08/0.51 fof(f722,plain,(
% 0.08/0.51 distinct_lines(sK2_skl,sK1_skl)|~sQ65_spl),
% 0.08/0.51 inference(component_clause,[status(thm)],[f721])).
% 0.08/0.51 fof(f723,plain,(
% 0.08/0.51 ~distinct_lines(sK2_skl,sK1_skl)|sQ65_spl),
% 0.08/0.51 inference(component_clause,[status(thm)],[f721])).
% 0.08/0.51 fof(f806,plain,(
% 0.08/0.51 ![X0]: (distinct_lines(sK2_skl,X0)|distinct_lines(sK1_skl,X0)|~sQ65_spl)),
% 0.08/0.51 inference(resolution,[status(thm)],[f722,f25])).
% 0.08/0.51 fof(f814,plain,(
% 0.08/0.51 distinct_lines(sK2_skl,sK2_skl)|~sQ65_spl),
% 0.08/0.51 inference(resolution,[status(thm)],[f806,f51])).
% 0.08/0.51 fof(f819,plain,(
% 0.08/0.52 $false|~sQ65_spl),
% 0.08/0.52 inference(forward_subsumption_resolution,[status(thm)],[f814,f18])).
% 0.08/0.52 fof(f820,plain,(
% 0.08/0.52 ~sQ65_spl),
% 0.08/0.52 inference(contradiction_clause,[status(thm)],[f819])).
% 0.08/0.52 fof(f828,plain,(
% 0.08/0.52 convergent_lines(sK2_skl,sK2_skl)|distinct_lines(sK0_skl,sK1_skl)|sQ65_spl),
% 0.08/0.52 inference(resolution,[status(thm)],[f723,f135])).
% 0.08/0.52 fof(f841,definition,(
% 0.08/0.52 sQ76_spl <=> (convergent_lines(sK2_skl,sK2_skl))),
% 0.08/0.52 introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition])).
% 0.08/0.52 fof(f842,plain,(
% 0.08/0.52 convergent_lines(sK2_skl,sK2_skl)|~sQ76_spl),
% 0.08/0.52 inference(component_clause,[status(thm)],[f841])).
% 0.08/0.52 fof(f844,definition,(
% 0.08/0.52 sQ77_spl <=> (distinct_lines(sK0_skl,sK1_skl))),
% 0.08/0.52 introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition])).
% 0.08/0.52 fof(f845,plain,(
% 0.08/0.52 distinct_lines(sK0_skl,sK1_skl)|~sQ77_spl),
% 0.08/0.52 inference(component_clause,[status(thm)],[f844])).
% 0.08/0.52 fof(f847,plain,(
% 0.08/0.52 sQ76_spl|sQ77_spl|sQ65_spl),
% 0.08/0.52 inference(split_clause,[status(thm)],[f828,f841,f844,f721])).
% 0.08/0.52 fof(f850,plain,(
% 0.08/0.52 $false|~sQ76_spl),
% 0.08/0.52 inference(forward_subsumption_resolution,[status(thm)],[f842,f19])).
% 0.08/0.52 fof(f851,plain,(
% 0.08/0.52 ~sQ76_spl),
% 0.08/0.52 inference(contradiction_clause,[status(thm)],[f850])).
% 0.08/0.52 fof(f853,plain,(
% 0.08/0.52 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)|~sQ77_spl|~sQ1_spl),
% 0.08/0.52 inference(resolution,[status(thm)],[f845,f80])).
% 0.08/0.52 fof(f859,plain,(
% 0.08/0.52 sQ5_spl|sQ8_spl|sQ7_spl|sQ9_spl|~sQ77_spl|~sQ1_spl),
% 0.08/0.52 inference(split_clause,[status(thm)],[f853,f101,f111,f107,f114,f844,f56])).
% 0.08/0.52 fof(f860,plain,(
% 0.08/0.52 $false),
% 0.08/0.52 inference(sat_refutation,[status(thm)],[f59,f79,f129,f133,f185,f706,f712,f820,f847,f851,f859])).
% 0.08/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.53 % Elapsed time: 0.156232 seconds
% 0.08/0.53 % CPU time: 1.043054 seconds
% 0.08/0.53 % Total memory used: 28.892 MB
% 0.08/0.53 % Net memory used: 26.242 MB
%------------------------------------------------------------------------------