%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO187+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 : n026.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 1.33s 0.78s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO187+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 : n026.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 13:10:21 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 1.33/0.78 % Refutation found
% 1.33/0.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.33/0.78 % SZS output start CNFRefutation for theBenchmark
% 1.33/0.78 fof(f1,axiom,(
% 1.33/0.78 (! [X] : ~ distinct_points(X,X) )),
% 1.33/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.33/0.78 fof(f4,axiom,(
% 1.33/0.78 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 1.33/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.33/0.78 fof(f7,axiom,(
% 1.33/0.78 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 1.33/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.33/0.78 fof(f9,axiom,(
% 1.33/0.78 (! [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) ) ) )),
% 1.33/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.33/0.78 fof(f11,axiom,(
% 1.33/0.78 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 1.33/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.33/0.78 fof(f13,conjecture,(
% 1.33/0.78 (! [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)) ) ) )),
% 1.33/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.33/0.78 fof(f14,negated_conjecture,(
% 1.33/0.78 ~((! [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)) ) ) ))),
% 1.33/0.78 inference(negated_conjecture,[status(cth)],[f13])).
% 1.33/0.78 fof(f15,plain,(
% 1.33/0.78 ![X0]: (~distinct_points(X0,X0))),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f1])).
% 1.33/0.78 fof(f18,plain,(
% 1.33/0.78 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 1.33/0.78 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 1.33/0.78 fof(f19,plain,(
% 1.33/0.78 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 1.33/0.78 inference(miniscoping,[status(thm)],[f18])).
% 1.33/0.78 fof(f20,plain,(
% 1.33/0.78 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f19])).
% 1.33/0.78 fof(f27,plain,(
% 1.33/0.78 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 1.33/0.78 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 1.33/0.78 fof(f28,plain,(
% 1.33/0.78 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 1.33/0.78 inference(miniscoping,[status(thm)],[f27])).
% 1.33/0.78 fof(f29,plain,(
% 1.33/0.78 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f28])).
% 1.33/0.78 fof(f30,plain,(
% 1.33/0.78 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f28])).
% 1.33/0.78 fof(f35,plain,(
% 1.33/0.78 ![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)))),
% 1.33/0.78 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 1.33/0.78 fof(f36,plain,(
% 1.33/0.78 ![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))),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f35])).
% 1.33/0.78 fof(f40,plain,(
% 1.33/0.78 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 1.33/0.78 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 1.33/0.78 fof(f41,plain,(
% 1.33/0.78 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 1.33/0.78 inference(miniscoping,[status(thm)],[f40])).
% 1.33/0.78 fof(f42,plain,(
% 1.33/0.78 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f41])).
% 1.33/0.78 fof(f45,plain,(
% 1.33/0.78 (?[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)))))),
% 1.33/0.78 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 1.33/0.78 fof(f46,plain,(
% 1.33/0.78 ((((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))))),
% 1.33/0.78 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])).
% 1.33/0.78 fof(f47,plain,(
% 1.33/0.78 distinct_points(sK0_skl,sK1_skl)),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f46])).
% 1.33/0.78 fof(f48,plain,(
% 1.33/0.78 distinct_points(sK2_skl,sK3_skl)),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f46])).
% 1.33/0.78 fof(f49,plain,(
% 1.33/0.78 ~apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f46])).
% 1.33/0.78 fof(f50,plain,(
% 1.33/0.78 ~apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f46])).
% 1.33/0.78 fof(f51,plain,(
% 1.33/0.78 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))),
% 1.33/0.78 inference(cnf_transformation,[status(thm)],[f46])).
% 1.33/0.78 fof(f52,definition,(
% 1.33/0.78 sQ0_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f53,plain,(
% 1.33/0.78 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|~sQ0_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f52])).
% 1.33/0.78 fof(f55,definition,(
% 1.33/0.78 sQ1_spl <=> (apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f56,plain,(
% 1.33/0.78 apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))|~sQ1_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f55])).
% 1.33/0.78 fof(f58,plain,(
% 1.33/0.78 sQ0_spl|sQ1_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f51,f52,f55])).
% 1.33/0.78 fof(f59,plain,(
% 1.33/0.78 ![X0]: (distinct_points(sK2_skl,X0)|distinct_points(sK3_skl,X0))),
% 1.33/0.78 inference(resolution,[status(thm)],[f20,f48])).
% 1.33/0.78 fof(f60,plain,(
% 1.33/0.78 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 1.33/0.78 inference(resolution,[status(thm)],[f20,f47])).
% 1.33/0.78 fof(f63,definition,(
% 1.33/0.78 sQ2_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f65,plain,(
% 1.33/0.78 ~distinct_points(sK0_skl,sK1_skl)|sQ2_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f63])).
% 1.33/0.78 fof(f74,plain,(
% 1.33/0.78 $false|sQ2_spl),
% 1.33/0.78 inference(forward_subsumption_resolution,[status(thm)],[f65,f47])).
% 1.33/0.78 fof(f75,plain,(
% 1.33/0.78 sQ2_spl),
% 1.33/0.78 inference(contradiction_clause,[status(thm)],[f74])).
% 1.33/0.78 fof(f79,plain,(
% 1.33/0.78 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_points(sK3_skl,X1)|distinct_points(X0,X1))),
% 1.33/0.78 inference(resolution,[status(thm)],[f59,f20])).
% 1.33/0.78 fof(f127,plain,(
% 1.33/0.78 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK3_skl,X0)|~sQ1_spl)),
% 1.33/0.78 inference(resolution,[status(thm)],[f42,f56])).
% 1.33/0.78 fof(f129,plain,(
% 1.33/0.78 ![X0,X1,X2]: (apart_point_and_line(sK3_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)|~sQ1_spl)),
% 1.33/0.78 inference(resolution,[status(thm)],[f127,f36])).
% 1.33/0.78 fof(f139,plain,(
% 1.33/0.78 ![X0]: (distinct_points(sK2_skl,X0)|distinct_points(X0,sK3_skl))),
% 1.33/0.78 inference(resolution,[status(thm)],[f79,f15])).
% 1.33/0.78 fof(f149,definition,(
% 1.33/0.78 sQ13_spl <=> (distinct_points(sK2_skl,sK3_skl))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f236,plain,(
% 1.33/0.78 ![X0,X1]: (apart_point_and_line(sK3_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(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,X0)|distinct_points(sK0_skl,X1)|~sQ1_spl)),
% 1.33/0.78 inference(resolution,[status(thm)],[f129,f60])).
% 1.33/0.78 fof(f267,definition,(
% 1.33/0.78 sQ24_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f268,plain,(
% 1.33/0.78 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ24_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f267])).
% 1.33/0.78 fof(f270,definition,(
% 1.33/0.78 sQ25_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f271,plain,(
% 1.33/0.78 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ25_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f270])).
% 1.33/0.78 fof(f286,definition,(
% 1.33/0.78 ![X0,X1]: (sQ29_spl <=> (apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,X0)|distinct_points(sK0_skl,X1)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f287,plain,(
% 1.33/0.78 ![X0,X1]: (apart_point_and_line(sK3_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,X0)|distinct_points(sK0_skl,X1)|~sQ29_spl)),
% 1.33/0.78 inference(component_clause,[status(thm)],[f286])).
% 1.33/0.78 fof(f289,plain,(
% 1.33/0.78 sQ29_spl|sQ24_spl|~sQ1_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f236,f286,f267,f55])).
% 1.33/0.78 fof(f369,plain,(
% 1.33/0.78 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,X0)|~sQ0_spl)),
% 1.33/0.78 inference(resolution,[status(thm)],[f53,f42])).
% 1.33/0.78 fof(f382,plain,(
% 1.33/0.78 ![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)|~sQ0_spl)),
% 1.33/0.78 inference(resolution,[status(thm)],[f369,f36])).
% 1.33/0.78 fof(f391,plain,(
% 1.33/0.78 ![X0,X1]: (distinct_points(X0,sK3_skl)|distinct_points(sK2_skl,X1)|distinct_points(X0,X1))),
% 1.33/0.78 inference(resolution,[status(thm)],[f139,f20])).
% 1.33/0.78 fof(f449,plain,(
% 1.33/0.78 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ24_spl),
% 1.33/0.78 inference(resolution,[status(thm)],[f268,f30])).
% 1.33/0.78 fof(f453,definition,(
% 1.33/0.78 sQ49_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f454,plain,(
% 1.33/0.78 distinct_points(sK1_skl,sK1_skl)|~sQ49_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f453])).
% 1.33/0.78 fof(f456,plain,(
% 1.33/0.78 ~sQ2_spl|sQ49_spl|~sQ24_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f449,f63,f453,f267])).
% 1.33/0.78 fof(f458,plain,(
% 1.33/0.78 $false|~sQ49_spl),
% 1.33/0.78 inference(forward_subsumption_resolution,[status(thm)],[f454,f15])).
% 1.33/0.78 fof(f459,plain,(
% 1.33/0.78 ~sQ49_spl),
% 1.33/0.78 inference(contradiction_clause,[status(thm)],[f458])).
% 1.33/0.78 fof(f529,plain,(
% 1.33/0.78 ![X0,X1]: (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(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,X0)|distinct_points(sK0_skl,X1)|~sQ0_spl)),
% 1.33/0.78 inference(resolution,[status(thm)],[f382,f60])).
% 1.33/0.78 fof(f577,definition,(
% 1.33/0.78 ![X0,X1]: (sQ54_spl <=> (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,X0)|distinct_points(sK0_skl,X1)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f578,plain,(
% 1.33/0.78 ![X0,X1]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,X0)|distinct_points(sK0_skl,X1)|~sQ54_spl)),
% 1.33/0.78 inference(component_clause,[status(thm)],[f577])).
% 1.33/0.78 fof(f580,plain,(
% 1.33/0.78 sQ54_spl|sQ24_spl|~sQ0_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f529,f577,f267,f52])).
% 1.33/0.78 fof(f683,plain,(
% 1.33/0.78 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ25_spl),
% 1.33/0.78 inference(resolution,[status(thm)],[f271,f29])).
% 1.33/0.78 fof(f687,definition,(
% 1.33/0.78 sQ74_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f688,plain,(
% 1.33/0.78 distinct_points(sK0_skl,sK0_skl)|~sQ74_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f687])).
% 1.33/0.78 fof(f690,plain,(
% 1.33/0.78 ~sQ2_spl|sQ74_spl|~sQ25_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f683,f63,f687,f270])).
% 1.33/0.78 fof(f691,plain,(
% 1.33/0.78 $false|~sQ74_spl),
% 1.33/0.78 inference(forward_subsumption_resolution,[status(thm)],[f688,f15])).
% 1.33/0.78 fof(f692,plain,(
% 1.33/0.78 ~sQ74_spl),
% 1.33/0.78 inference(contradiction_clause,[status(thm)],[f691])).
% 1.33/0.78 fof(f705,plain,(
% 1.33/0.78 ![X0,X1]: (distinct_points(sK2_skl,sK3_skl)|distinct_points(sK2_skl,X0)|distinct_points(X1,X0))),
% 1.33/0.78 inference(resolution,[status(thm)],[f391,f20])).
% 1.33/0.78 fof(f725,definition,(
% 1.33/0.78 ![X0,X1]: (sQ78_spl <=> (distinct_points(sK2_skl,X0)|distinct_points(X1,X0)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f726,plain,(
% 1.33/0.78 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_points(X1,X0)|~sQ78_spl)),
% 1.33/0.78 inference(component_clause,[status(thm)],[f725])).
% 1.33/0.78 fof(f728,plain,(
% 1.33/0.78 sQ13_spl|sQ78_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f705,f149,f725])).
% 1.33/0.78 fof(f780,plain,(
% 1.33/0.78 $false|~sQ78_spl),
% 1.33/0.78 inference(resolution,[status(thm)],[f726,f15])).
% 1.33/0.78 fof(f790,plain,(
% 1.33/0.78 ~sQ78_spl),
% 1.33/0.78 inference(contradiction_clause,[status(thm)],[f780])).
% 1.33/0.78 fof(f2157,definition,(
% 1.33/0.78 sQ192_spl <=> (distinct_points(sK2_skl,sK2_skl))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f2158,plain,(
% 1.33/0.78 distinct_points(sK2_skl,sK2_skl)|~sQ192_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f2157])).
% 1.33/0.78 fof(f2752,definition,(
% 1.33/0.78 sQ211_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f2753,plain,(
% 1.33/0.78 apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl))|~sQ211_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f2752])).
% 1.33/0.78 fof(f2755,definition,(
% 1.33/0.78 sQ212_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f2756,plain,(
% 1.33/0.78 apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))|~sQ212_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f2755])).
% 1.33/0.78 fof(f2797,plain,(
% 1.33/0.78 apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|distinct_points(sK0_skl,sK0_skl)|~sQ54_spl),
% 1.33/0.78 inference(resolution,[status(thm)],[f578,f49])).
% 1.33/0.78 fof(f2837,plain,(
% 1.33/0.78 sQ211_spl|sQ212_spl|sQ25_spl|sQ74_spl|~sQ54_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f2797,f2752,f2755,f270,f687,f577])).
% 1.33/0.78 fof(f2838,plain,(
% 1.33/0.78 $false|~sQ212_spl),
% 1.33/0.78 inference(forward_subsumption_resolution,[status(thm)],[f2756,f50])).
% 1.33/0.78 fof(f2839,plain,(
% 1.33/0.78 ~sQ212_spl),
% 1.33/0.78 inference(contradiction_clause,[status(thm)],[f2838])).
% 1.33/0.78 fof(f3154,plain,(
% 1.33/0.78 ~distinct_points(sK2_skl,sK3_skl)|distinct_points(sK2_skl,sK2_skl)|~sQ211_spl),
% 1.33/0.78 inference(resolution,[status(thm)],[f2753,f29])).
% 1.33/0.78 fof(f3158,plain,(
% 1.33/0.78 ~sQ13_spl|sQ192_spl|~sQ211_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f3154,f149,f2157,f2752])).
% 1.33/0.78 fof(f3159,plain,(
% 1.33/0.78 $false|~sQ192_spl),
% 1.33/0.78 inference(forward_subsumption_resolution,[status(thm)],[f2158,f15])).
% 1.33/0.78 fof(f3160,plain,(
% 1.33/0.78 ~sQ192_spl),
% 1.33/0.78 inference(contradiction_clause,[status(thm)],[f3159])).
% 1.33/0.78 fof(f4049,definition,(
% 1.33/0.78 sQ274_spl <=> (apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl)))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f4050,plain,(
% 1.33/0.78 apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl))|~sQ274_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f4049])).
% 1.33/0.78 fof(f4158,plain,(
% 1.33/0.78 apart_point_and_line(sK3_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|distinct_points(sK0_skl,sK0_skl)|~sQ29_spl),
% 1.33/0.78 inference(resolution,[status(thm)],[f287,f49])).
% 1.33/0.78 fof(f4190,plain,(
% 1.33/0.78 sQ274_spl|sQ212_spl|sQ25_spl|sQ74_spl|~sQ29_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f4158,f4049,f2755,f270,f687,f286])).
% 1.33/0.78 fof(f4446,plain,(
% 1.33/0.78 ~distinct_points(sK2_skl,sK3_skl)|distinct_points(sK3_skl,sK3_skl)|~sQ274_spl),
% 1.33/0.78 inference(resolution,[status(thm)],[f4050,f30])).
% 1.33/0.78 fof(f4450,definition,(
% 1.33/0.78 sQ286_spl <=> (distinct_points(sK3_skl,sK3_skl))),
% 1.33/0.78 introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition])).
% 1.33/0.78 fof(f4451,plain,(
% 1.33/0.78 distinct_points(sK3_skl,sK3_skl)|~sQ286_spl),
% 1.33/0.78 inference(component_clause,[status(thm)],[f4450])).
% 1.33/0.78 fof(f4453,plain,(
% 1.33/0.78 ~sQ13_spl|sQ286_spl|~sQ274_spl),
% 1.33/0.78 inference(split_clause,[status(thm)],[f4446,f149,f4450,f4049])).
% 1.33/0.78 fof(f4455,plain,(
% 1.33/0.78 $false|~sQ286_spl),
% 1.33/0.78 inference(forward_subsumption_resolution,[status(thm)],[f4451,f15])).
% 1.33/0.78 fof(f4456,plain,(
% 1.33/0.78 ~sQ286_spl),
% 1.33/0.78 inference(contradiction_clause,[status(thm)],[f4455])).
% 1.33/0.78 fof(f4457,plain,(
% 1.33/0.78 $false),
% 1.33/0.78 inference(sat_refutation,[status(thm)],[f58,f75,f289,f456,f459,f580,f690,f692,f728,f790,f2837,f2839,f3158,f3160,f4190,f4453,f4456])).
% 1.33/0.78 % SZS output end CNFRefutation for theBenchmark.p
% 2.25/0.79 % Elapsed time: 0.429108 seconds
% 2.25/0.79 % CPU time: 3.070193 seconds
% 2.25/0.79 % Total memory used: 45.026 MB
% 2.25/0.79 % Net memory used: 39.506 MB
%------------------------------------------------------------------------------