%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO177+2 : 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 : n011.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 12:25:57 PM UTC 2026
% Result : Theorem 5.56s 1.29s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO177+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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 12:59:25 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 5.56/1.29 % Refutation found
% 5.56/1.29 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.56/1.29 % SZS output start CNFRefutation for theBenchmark
% 5.56/1.29 fof(f1,axiom,(
% 5.56/1.29 (! [X] : ~ distinct_points(X,X) )),
% 5.56/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.56/1.29 fof(f4,axiom,(
% 5.56/1.29 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 5.56/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.56/1.29 fof(f7,axiom,(
% 5.56/1.29 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 5.56/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.56/1.29 fof(f9,axiom,(
% 5.56/1.29 (! [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) ) ) )),
% 5.56/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.56/1.29 fof(f11,axiom,(
% 5.56/1.29 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 5.56/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.56/1.29 fof(f13,conjecture,(
% 5.56/1.29 (! [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)) ) ) ) )),
% 5.56/1.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.56/1.29 fof(f14,negated_conjecture,(
% 5.56/1.29 ~((! [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)) ) ) ) ))),
% 5.56/1.29 inference(negated_conjecture,[status(cth)],[f13])).
% 5.56/1.29 fof(f15,plain,(
% 5.56/1.29 ![X0]: (~distinct_points(X0,X0))),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f1])).
% 5.56/1.29 fof(f18,plain,(
% 5.56/1.29 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 5.56/1.29 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 5.56/1.29 fof(f19,plain,(
% 5.56/1.29 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 5.56/1.29 inference(miniscoping,[status(thm)],[f18])).
% 5.56/1.29 fof(f20,plain,(
% 5.56/1.29 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f19])).
% 5.56/1.29 fof(f27,plain,(
% 5.56/1.29 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 5.56/1.29 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 5.56/1.29 fof(f28,plain,(
% 5.56/1.29 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 5.56/1.29 inference(miniscoping,[status(thm)],[f27])).
% 5.56/1.29 fof(f29,plain,(
% 5.56/1.29 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f28])).
% 5.56/1.29 fof(f30,plain,(
% 5.56/1.29 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f28])).
% 5.56/1.29 fof(f35,plain,(
% 5.56/1.29 ![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)))),
% 5.56/1.29 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 5.56/1.29 fof(f36,plain,(
% 5.56/1.29 ![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))),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f35])).
% 5.56/1.29 fof(f40,plain,(
% 5.56/1.29 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 5.56/1.29 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 5.56/1.29 fof(f41,plain,(
% 5.56/1.29 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 5.56/1.29 inference(miniscoping,[status(thm)],[f40])).
% 5.56/1.29 fof(f42,plain,(
% 5.56/1.29 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f41])).
% 5.56/1.29 fof(f45,plain,(
% 5.56/1.29 (?[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))))))),
% 5.56/1.29 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 5.56/1.29 fof(f46,plain,(
% 5.56/1.29 ((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)))))),
% 5.56/1.29 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)],[f45])).
% 5.56/1.29 fof(f47,plain,(
% 5.56/1.29 distinct_points(sK0_skl,sK1_skl)),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f46])).
% 5.56/1.29 fof(f48,plain,(
% 5.56/1.29 distinct_points(sK2_skl,sK3_skl)),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f46])).
% 5.56/1.29 fof(f49,plain,(
% 5.56/1.29 apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f46])).
% 5.56/1.29 fof(f50,plain,(
% 5.56/1.29 ~apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f46])).
% 5.56/1.29 fof(f51,plain,(
% 5.56/1.29 ~apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))),
% 5.56/1.29 inference(cnf_transformation,[status(thm)],[f46])).
% 5.56/1.29 fof(f52,definition,(
% 5.56/1.29 sQ0_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f53,plain,(
% 5.56/1.29 apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))|~sQ0_spl),
% 5.56/1.29 inference(component_clause,[status(thm)],[f52])).
% 5.56/1.29 fof(f55,definition,(
% 5.56/1.29 sQ1_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f56,plain,(
% 5.56/1.29 apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))|~sQ1_spl),
% 5.56/1.29 inference(component_clause,[status(thm)],[f55])).
% 5.56/1.29 fof(f58,plain,(
% 5.56/1.29 sQ0_spl|sQ1_spl),
% 5.56/1.29 inference(split_clause,[status(thm)],[f49,f52,f55])).
% 5.56/1.29 fof(f59,plain,(
% 5.56/1.29 ![X0]: (distinct_points(sK2_skl,X0)|distinct_points(sK3_skl,X0))),
% 5.56/1.29 inference(resolution,[status(thm)],[f20,f48])).
% 5.56/1.29 fof(f60,plain,(
% 5.56/1.29 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 5.56/1.29 inference(resolution,[status(thm)],[f20,f47])).
% 5.56/1.29 fof(f61,plain,(
% 5.56/1.29 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_points(sK3_skl,X1)|distinct_points(X0,X1))),
% 5.56/1.29 inference(resolution,[status(thm)],[f59,f20])).
% 5.56/1.29 fof(f63,plain,(
% 5.56/1.29 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 5.56/1.29 inference(resolution,[status(thm)],[f60,f20])).
% 5.56/1.29 fof(f68,plain,(
% 5.56/1.29 distinct_points(sK3_skl,sK2_skl)),
% 5.56/1.29 inference(resolution,[status(thm)],[f61,f15])).
% 5.56/1.29 fof(f70,plain,(
% 5.56/1.29 ![X0,X1]: (distinct_points(sK2_skl,sK3_skl)|distinct_points(sK3_skl,X0)|distinct_points(X1,X0))),
% 5.56/1.29 inference(resolution,[status(thm)],[f61,f20])).
% 5.56/1.29 fof(f83,definition,(
% 5.56/1.29 sQ4_spl <=> (distinct_points(sK2_skl,sK3_skl))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f86,definition,(
% 5.56/1.29 ![X0,X1]: (sQ5_spl <=> (distinct_points(sK3_skl,X0)|distinct_points(X1,X0)))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f87,plain,(
% 5.56/1.29 ![X0,X1]: (distinct_points(sK3_skl,X0)|distinct_points(X1,X0)|~sQ5_spl)),
% 5.56/1.29 inference(component_clause,[status(thm)],[f86])).
% 5.56/1.29 fof(f89,plain,(
% 5.56/1.29 sQ4_spl|sQ5_spl),
% 5.56/1.29 inference(split_clause,[status(thm)],[f70,f83,f86])).
% 5.56/1.29 fof(f102,plain,(
% 5.56/1.29 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(X0,sK1_skl))),
% 5.56/1.29 inference(resolution,[status(thm)],[f63,f15])).
% 5.56/1.29 fof(f112,definition,(
% 5.56/1.29 sQ8_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f120,plain,(
% 5.56/1.29 ![X0,X1]: (distinct_points(X0,sK1_skl)|distinct_points(sK0_skl,X1)|distinct_points(X0,X1))),
% 5.56/1.29 inference(resolution,[status(thm)],[f102,f20])).
% 5.56/1.29 fof(f132,plain,(
% 5.56/1.29 $false|~sQ5_spl),
% 5.56/1.29 inference(resolution,[status(thm)],[f87,f15])).
% 5.56/1.29 fof(f136,plain,(
% 5.56/1.29 ~sQ5_spl),
% 5.56/1.29 inference(contradiction_clause,[status(thm)],[f132])).
% 5.56/1.29 fof(f158,plain,(
% 5.56/1.29 ![X0]: (distinct_lines(line_connecting(sK2_skl,sK3_skl),X0)|apart_point_and_line(sK1_skl,X0)|~sQ1_spl)),
% 5.56/1.29 inference(resolution,[status(thm)],[f42,f56])).
% 5.56/1.29 fof(f182,plain,(
% 5.56/1.29 ![X0]: (distinct_points(X0,sK1_skl)|distinct_points(X0,sK0_skl))),
% 5.56/1.29 inference(resolution,[status(thm)],[f120,f15])).
% 5.56/1.29 fof(f189,plain,(
% 5.56/1.29 ![X0,X1]: (distinct_points(X0,sK0_skl)|distinct_points(X0,X1)|distinct_points(sK1_skl,X1))),
% 5.56/1.29 inference(resolution,[status(thm)],[f182,f20])).
% 5.56/1.29 fof(f217,plain,(
% 5.56/1.29 ![X0]: (distinct_lines(line_connecting(sK2_skl,sK3_skl),X0)|apart_point_and_line(sK0_skl,X0)|~sQ0_spl)),
% 5.56/1.29 inference(resolution,[status(thm)],[f53,f42])).
% 5.56/1.29 fof(f299,plain,(
% 5.56/1.29 ![X0]: (distinct_points(X0,sK0_skl)|distinct_points(sK1_skl,X0))),
% 5.56/1.29 inference(resolution,[status(thm)],[f189,f15])).
% 5.56/1.29 fof(f303,plain,(
% 5.56/1.29 ![X0,X1]: (distinct_points(sK1_skl,X0)|distinct_points(X0,X1)|distinct_points(sK0_skl,X1))),
% 5.56/1.29 inference(resolution,[status(thm)],[f299,f20])).
% 5.56/1.29 fof(f320,definition,(
% 5.56/1.29 ![X0]: (sQ20_spl <=> (distinct_points(sK1_skl,X0)|distinct_points(sK1_skl,X0)))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f321,plain,(
% 5.56/1.29 ![X0]: (distinct_points(sK1_skl,X0)|distinct_points(sK1_skl,X0)|~sQ20_spl)),
% 5.56/1.29 inference(component_clause,[status(thm)],[f320])).
% 5.56/1.29 fof(f341,plain,(
% 5.56/1.29 ![X0]: (distinct_points(sK1_skl,X0)|~sQ20_spl)),
% 5.56/1.29 inference(duplicate_literals_removal,[status(thm)],[f321])).
% 5.56/1.29 fof(f342,plain,(
% 5.56/1.29 ![X0,X1,X2]: (apart_point_and_line(sK1_skl,X0)|~distinct_points(X1,X2)|apart_point_and_line(X1,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(X1,X0)|apart_point_and_line(X2,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(X2,X0)|~sQ1_spl)),
% 5.56/1.29 inference(resolution,[status(thm)],[f158,f36])).
% 5.56/1.29 fof(f349,plain,(
% 5.56/1.29 ![X0]: (apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK2_skl,X0)|~sQ1_spl)),
% 5.56/1.29 inference(resolution,[status(thm)],[f342,f68])).
% 5.56/1.29 fof(f382,definition,(
% 5.56/1.29 sQ23_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl)))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f383,plain,(
% 5.56/1.29 apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl))|~sQ23_spl),
% 5.56/1.29 inference(component_clause,[status(thm)],[f382])).
% 5.56/1.29 fof(f397,definition,(
% 5.56/1.29 sQ27_spl <=> (apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl)))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f398,plain,(
% 5.56/1.29 apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl))|~sQ27_spl),
% 5.56/1.29 inference(component_clause,[status(thm)],[f397])).
% 5.56/1.29 fof(f401,definition,(
% 5.56/1.29 ![X0]: (sQ28_spl <=> (apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK2_skl,X0)))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f402,plain,(
% 5.56/1.29 ![X0]: (apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK2_skl,X0)|~sQ28_spl)),
% 5.56/1.29 inference(component_clause,[status(thm)],[f401])).
% 5.56/1.29 fof(f404,plain,(
% 5.56/1.29 sQ28_spl|sQ27_spl|sQ23_spl|~sQ1_spl),
% 5.56/1.29 inference(split_clause,[status(thm)],[f349,f401,f397,f382,f55])).
% 5.56/1.29 fof(f497,plain,(
% 5.56/1.29 $false|~sQ20_spl),
% 5.56/1.29 inference(resolution,[status(thm)],[f341,f15])).
% 5.56/1.29 fof(f502,plain,(
% 5.56/1.29 ~sQ20_spl),
% 5.56/1.29 inference(contradiction_clause,[status(thm)],[f497])).
% 5.56/1.29 fof(f523,plain,(
% 5.56/1.29 ~distinct_points(sK2_skl,sK3_skl)|distinct_points(sK2_skl,sK2_skl)|~sQ23_spl),
% 5.56/1.29 inference(resolution,[status(thm)],[f383,f29])).
% 5.56/1.29 fof(f527,definition,(
% 5.56/1.29 sQ47_spl <=> (distinct_points(sK2_skl,sK2_skl))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f528,plain,(
% 5.56/1.29 distinct_points(sK2_skl,sK2_skl)|~sQ47_spl),
% 5.56/1.29 inference(component_clause,[status(thm)],[f527])).
% 5.56/1.29 fof(f530,plain,(
% 5.56/1.29 ~sQ4_spl|sQ47_spl|~sQ23_spl),
% 5.56/1.29 inference(split_clause,[status(thm)],[f523,f83,f527,f382])).
% 5.56/1.29 fof(f531,plain,(
% 5.56/1.29 $false|~sQ47_spl),
% 5.56/1.29 inference(forward_subsumption_resolution,[status(thm)],[f528,f15])).
% 5.56/1.29 fof(f532,plain,(
% 5.56/1.29 ~sQ47_spl),
% 5.56/1.29 inference(contradiction_clause,[status(thm)],[f531])).
% 5.56/1.29 fof(f566,plain,(
% 5.56/1.29 ![X0,X1,X2]: (apart_point_and_line(sK0_skl,X0)|~distinct_points(X1,X2)|apart_point_and_line(X1,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(X1,X0)|apart_point_and_line(X2,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(X2,X0)|~sQ0_spl)),
% 5.56/1.29 inference(resolution,[status(thm)],[f217,f36])).
% 5.56/1.29 fof(f628,plain,(
% 5.56/1.29 ![X0]: (distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,X0)|distinct_points(sK1_skl,X0))),
% 5.56/1.29 inference(resolution,[status(thm)],[f303,f20])).
% 5.56/1.29 fof(f638,plain,(
% 5.56/1.29 sQ8_spl|sQ20_spl),
% 5.56/1.29 inference(split_clause,[status(thm)],[f628,f112,f320])).
% 5.56/1.29 fof(f756,plain,(
% 5.56/1.29 ![X0]: (apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK2_skl,X0)|~sQ0_spl)),
% 5.56/1.29 inference(resolution,[status(thm)],[f566,f68])).
% 5.56/1.29 fof(f925,definition,(
% 5.56/1.29 ![X0]: (sQ78_spl <=> (apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK2_skl,X0)))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f926,plain,(
% 5.56/1.29 ![X0]: (apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK2_skl,X0)|~sQ78_spl)),
% 5.56/1.29 inference(component_clause,[status(thm)],[f925])).
% 5.56/1.29 fof(f928,plain,(
% 5.56/1.29 sQ78_spl|sQ27_spl|sQ23_spl|~sQ0_spl),
% 5.56/1.29 inference(split_clause,[status(thm)],[f756,f925,f397,f382,f52])).
% 5.56/1.29 fof(f1059,plain,(
% 5.56/1.29 ~distinct_points(sK2_skl,sK3_skl)|distinct_points(sK3_skl,sK3_skl)|~sQ27_spl),
% 5.56/1.29 inference(resolution,[status(thm)],[f398,f30])).
% 5.56/1.29 fof(f1063,definition,(
% 5.56/1.29 sQ102_spl <=> (distinct_points(sK3_skl,sK3_skl))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f1064,plain,(
% 5.56/1.29 distinct_points(sK3_skl,sK3_skl)|~sQ102_spl),
% 5.56/1.29 inference(component_clause,[status(thm)],[f1063])).
% 5.56/1.29 fof(f1066,plain,(
% 5.56/1.29 ~sQ4_spl|sQ102_spl|~sQ27_spl),
% 5.56/1.29 inference(split_clause,[status(thm)],[f1059,f83,f1063,f397])).
% 5.56/1.29 fof(f1068,plain,(
% 5.56/1.29 $false|~sQ102_spl),
% 5.56/1.29 inference(forward_subsumption_resolution,[status(thm)],[f1064,f15])).
% 5.56/1.29 fof(f1069,plain,(
% 5.56/1.29 ~sQ102_spl),
% 5.56/1.29 inference(contradiction_clause,[status(thm)],[f1068])).
% 5.56/1.29 fof(f1134,definition,(
% 5.56/1.29 sQ105_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f1135,plain,(
% 5.56/1.29 distinct_points(sK1_skl,sK1_skl)|~sQ105_spl),
% 5.56/1.29 inference(component_clause,[status(thm)],[f1134])).
% 5.56/1.29 fof(f1356,definition,(
% 5.56/1.29 sQ114_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f1357,plain,(
% 5.56/1.29 distinct_points(sK0_skl,sK0_skl)|~sQ114_spl),
% 5.56/1.29 inference(component_clause,[status(thm)],[f1356])).
% 5.56/1.29 fof(f1695,plain,(
% 5.56/1.29 $false|~sQ105_spl),
% 5.56/1.29 inference(forward_subsumption_resolution,[status(thm)],[f1135,f15])).
% 5.56/1.29 fof(f1696,plain,(
% 5.56/1.29 ~sQ105_spl),
% 5.56/1.29 inference(contradiction_clause,[status(thm)],[f1695])).
% 5.56/1.29 fof(f1697,plain,(
% 5.56/1.29 $false|~sQ114_spl),
% 5.56/1.29 inference(forward_subsumption_resolution,[status(thm)],[f1357,f15])).
% 5.56/1.29 fof(f1698,plain,(
% 5.56/1.29 ~sQ114_spl),
% 5.56/1.29 inference(contradiction_clause,[status(thm)],[f1697])).
% 5.56/1.29 fof(f1865,definition,(
% 5.56/1.29 sQ144_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 5.56/1.29 introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition])).
% 5.56/1.29 fof(f1866,plain,(
% 5.56/1.29 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ144_spl),
% 5.56/1.29 inference(component_clause,[status(thm)],[f1865])).
% 5.56/1.29 fof(f3315,plain,(
% 5.56/1.29 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ144_spl),
% 5.56/1.29 inference(resolution,[status(thm)],[f1866,f29])).
% 5.56/1.30 fof(f3319,plain,(
% 5.56/1.30 ~sQ8_spl|sQ114_spl|~sQ144_spl),
% 5.56/1.30 inference(split_clause,[status(thm)],[f3315,f112,f1356,f1865])).
% 5.56/1.30 fof(f4452,plain,(
% 5.56/1.30 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|~sQ28_spl),
% 5.56/1.30 inference(resolution,[status(thm)],[f402,f51])).
% 5.56/1.30 fof(f4458,definition,(
% 5.56/1.30 sQ185_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 5.56/1.30 introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition])).
% 5.56/1.30 fof(f4459,plain,(
% 5.56/1.30 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ185_spl),
% 5.56/1.30 inference(component_clause,[status(thm)],[f4458])).
% 5.56/1.30 fof(f4461,definition,(
% 5.56/1.30 sQ186_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)))),
% 5.56/1.30 introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition])).
% 5.56/1.30 fof(f4462,plain,(
% 5.56/1.30 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|~sQ186_spl),
% 5.56/1.30 inference(component_clause,[status(thm)],[f4461])).
% 5.56/1.30 fof(f4464,plain,(
% 5.56/1.30 sQ185_spl|sQ186_spl|~sQ28_spl),
% 5.56/1.30 inference(split_clause,[status(thm)],[f4452,f4458,f4461,f401])).
% 5.56/1.30 fof(f4465,plain,(
% 5.56/1.30 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ185_spl),
% 5.56/1.30 inference(resolution,[status(thm)],[f4459,f30])).
% 5.56/1.30 fof(f4469,plain,(
% 5.56/1.30 ~sQ8_spl|sQ105_spl|~sQ185_spl),
% 5.56/1.30 inference(split_clause,[status(thm)],[f4465,f112,f1134,f4458])).
% 5.56/1.30 fof(f4471,plain,(
% 5.56/1.30 $false|~sQ186_spl),
% 5.56/1.30 inference(forward_subsumption_resolution,[status(thm)],[f4462,f50])).
% 5.56/1.30 fof(f4472,plain,(
% 5.56/1.30 ~sQ186_spl),
% 5.56/1.30 inference(contradiction_clause,[status(thm)],[f4471])).
% 5.56/1.30 fof(f5669,plain,(
% 5.56/1.30 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|~sQ78_spl),
% 5.56/1.30 inference(resolution,[status(thm)],[f926,f51])).
% 5.56/1.30 fof(f5675,plain,(
% 5.56/1.30 sQ144_spl|sQ186_spl|~sQ78_spl),
% 5.56/1.30 inference(split_clause,[status(thm)],[f5669,f1865,f4461,f925])).
% 5.56/1.30 fof(f5676,plain,(
% 5.56/1.30 $false),
% 5.56/1.30 inference(sat_refutation,[status(thm)],[f58,f89,f136,f404,f502,f530,f532,f638,f928,f1066,f1069,f1696,f1698,f3319,f4464,f4469,f4472,f5675])).
% 5.56/1.30 % SZS output end CNFRefutation for theBenchmark.p
% 5.56/1.33 % Elapsed time: 0.946616 seconds
% 5.56/1.33 % CPU time: 7.121399 seconds
% 5.56/1.33 % Total memory used: 52.538 MB
% 5.56/1.33 % Net memory used: 45.739 MB
%------------------------------------------------------------------------------