%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO181+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 : n010.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 12:25:58 PM UTC 2026
% Result : Theorem 2.40s 0.75s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO181+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:06:09 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 2.40/0.75 % Refutation found
% 2.40/0.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.40/0.75 % SZS output start CNFRefutation for theBenchmark
% 2.40/0.75 fof(f1,axiom,(
% 2.40/0.75 (! [X] : ~ distinct_points(X,X) )),
% 2.40/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.75 fof(f4,axiom,(
% 2.40/0.75 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 2.40/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.75 fof(f7,axiom,(
% 2.40/0.75 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 2.40/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.75 fof(f9,axiom,(
% 2.40/0.75 (! [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) ) ) )),
% 2.40/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.75 fof(f10,axiom,(
% 2.40/0.75 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 2.40/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.75 fof(f11,axiom,(
% 2.40/0.75 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 2.40/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.75 fof(f13,conjecture,(
% 2.40/0.75 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(Y,line_connecting(X,Z)) ) ) )),
% 2.40/0.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.75 fof(f14,negated_conjecture,(
% 2.40/0.75 ~((! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(Y,line_connecting(X,Z)) ) ) ))),
% 2.40/0.75 inference(negated_conjecture,[status(cth)],[f13])).
% 2.40/0.75 fof(f15,plain,(
% 2.40/0.75 ![X0]: (~distinct_points(X0,X0))),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f1])).
% 2.40/0.75 fof(f18,plain,(
% 2.40/0.75 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 2.40/0.75 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 2.40/0.75 fof(f19,plain,(
% 2.40/0.75 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 2.40/0.75 inference(miniscoping,[status(thm)],[f18])).
% 2.40/0.75 fof(f20,plain,(
% 2.40/0.75 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f19])).
% 2.40/0.75 fof(f27,plain,(
% 2.40/0.75 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 2.40/0.75 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 2.40/0.75 fof(f28,plain,(
% 2.40/0.75 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 2.40/0.75 inference(miniscoping,[status(thm)],[f27])).
% 2.40/0.75 fof(f29,plain,(
% 2.40/0.75 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f28])).
% 2.40/0.75 fof(f30,plain,(
% 2.40/0.75 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f28])).
% 2.40/0.75 fof(f35,plain,(
% 2.40/0.75 ![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)))),
% 2.40/0.75 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 2.40/0.75 fof(f36,plain,(
% 2.40/0.75 ![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))),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f35])).
% 2.40/0.75 fof(f37,plain,(
% 2.40/0.75 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 2.40/0.75 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 2.40/0.75 fof(f38,plain,(
% 2.40/0.75 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 2.40/0.75 inference(miniscoping,[status(thm)],[f37])).
% 2.40/0.75 fof(f39,plain,(
% 2.40/0.75 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f38])).
% 2.40/0.75 fof(f40,plain,(
% 2.40/0.75 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 2.40/0.75 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 2.40/0.75 fof(f41,plain,(
% 2.40/0.75 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 2.40/0.75 inference(miniscoping,[status(thm)],[f40])).
% 2.40/0.75 fof(f42,plain,(
% 2.40/0.75 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f41])).
% 2.40/0.75 fof(f45,plain,(
% 2.40/0.75 (?[X,Y,Z]: (distinct_points(X,Y)&(apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(Y,line_connecting(X,Z)))))),
% 2.40/0.75 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 2.40/0.75 fof(f46,plain,(
% 2.40/0.75 ?[X,Y]: (distinct_points(X,Y)&(?[Z]: (apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(Y,line_connecting(X,Z)))))),
% 2.40/0.75 inference(miniscoping,[status(thm)],[f45])).
% 2.40/0.75 fof(f47,plain,(
% 2.40/0.75 (distinct_points(sK0_skl,sK1_skl)&(apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))&~apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))))),
% 2.40/0.75 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)],[f46])).
% 2.40/0.75 fof(f48,plain,(
% 2.40/0.75 distinct_points(sK0_skl,sK1_skl)),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f47])).
% 2.40/0.75 fof(f49,plain,(
% 2.40/0.75 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f47])).
% 2.40/0.75 fof(f50,plain,(
% 2.40/0.75 ~apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))),
% 2.40/0.75 inference(cnf_transformation,[status(thm)],[f47])).
% 2.40/0.75 fof(f51,plain,(
% 2.40/0.75 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 2.40/0.75 inference(resolution,[status(thm)],[f20,f48])).
% 2.40/0.75 fof(f52,plain,(
% 2.40/0.75 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 2.40/0.75 inference(resolution,[status(thm)],[f51,f20])).
% 2.40/0.75 fof(f56,plain,(
% 2.40/0.75 distinct_points(sK1_skl,sK0_skl)),
% 2.40/0.75 inference(resolution,[status(thm)],[f52,f15])).
% 2.40/0.75 fof(f72,definition,(
% 2.40/0.75 sQ2_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f74,plain,(
% 2.40/0.75 ~distinct_points(sK0_skl,sK1_skl)|sQ2_spl),
% 2.40/0.75 inference(component_clause,[status(thm)],[f72])).
% 2.40/0.75 fof(f79,definition,(
% 2.40/0.75 sQ4_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f80,plain,(
% 2.40/0.75 distinct_points(sK0_skl,sK0_skl)|~sQ4_spl),
% 2.40/0.75 inference(component_clause,[status(thm)],[f79])).
% 2.40/0.75 fof(f88,plain,(
% 2.40/0.75 ![X0]: (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl)))),
% 2.40/0.75 inference(resolution,[status(thm)],[f39,f49])).
% 2.40/0.75 fof(f139,definition,(
% 2.40/0.75 sQ7_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f140,plain,(
% 2.40/0.75 distinct_points(sK1_skl,sK1_skl)|~sQ7_spl),
% 2.40/0.75 inference(component_clause,[status(thm)],[f139])).
% 2.40/0.75 fof(f144,plain,(
% 2.40/0.75 ![X0]: (~distinct_points(sK0_skl,sK1_skl)|distinct_points(X0,sK0_skl)|distinct_points(sK2_skl,X0))),
% 2.40/0.75 inference(resolution,[status(thm)],[f29,f88])).
% 2.40/0.75 fof(f149,definition,(
% 2.40/0.75 ![X0]: (sQ9_spl <=> (distinct_points(X0,sK0_skl)|distinct_points(sK2_skl,X0)))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f150,plain,(
% 2.40/0.75 ![X0]: (distinct_points(X0,sK0_skl)|distinct_points(sK2_skl,X0)|~sQ9_spl)),
% 2.40/0.75 inference(component_clause,[status(thm)],[f149])).
% 2.40/0.75 fof(f152,plain,(
% 2.40/0.75 ~sQ2_spl|sQ9_spl),
% 2.40/0.75 inference(split_clause,[status(thm)],[f144,f72,f149])).
% 2.40/0.75 fof(f154,plain,(
% 2.40/0.75 $false|sQ2_spl),
% 2.40/0.75 inference(forward_subsumption_resolution,[status(thm)],[f74,f48])).
% 2.40/0.75 fof(f155,plain,(
% 2.40/0.75 sQ2_spl),
% 2.40/0.75 inference(contradiction_clause,[status(thm)],[f154])).
% 2.40/0.75 fof(f171,plain,(
% 2.40/0.75 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_points(X0,X1)|distinct_points(sK0_skl,X1)|~sQ9_spl)),
% 2.40/0.75 inference(resolution,[status(thm)],[f150,f20])).
% 2.40/0.75 fof(f187,plain,(
% 2.40/0.75 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,X0))),
% 2.40/0.75 inference(resolution,[status(thm)],[f42,f49])).
% 2.40/0.75 fof(f241,plain,(
% 2.40/0.75 ![X0]: (distinct_points(sK0_skl,sK2_skl)|distinct_points(sK2_skl,X0)|distinct_points(sK2_skl,X0)|~sQ9_spl)),
% 2.40/0.75 inference(resolution,[status(thm)],[f171,f20])).
% 2.40/0.75 fof(f252,definition,(
% 2.40/0.75 sQ12_spl <=> (distinct_points(sK0_skl,sK2_skl))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f255,definition,(
% 2.40/0.75 ![X0]: (sQ13_spl <=> (distinct_points(sK2_skl,X0)|distinct_points(sK2_skl,X0)))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f256,plain,(
% 2.40/0.75 ![X0]: (distinct_points(sK2_skl,X0)|distinct_points(sK2_skl,X0)|~sQ13_spl)),
% 2.40/0.75 inference(component_clause,[status(thm)],[f255])).
% 2.40/0.75 fof(f258,plain,(
% 2.40/0.75 sQ12_spl|sQ13_spl|~sQ9_spl),
% 2.40/0.75 inference(split_clause,[status(thm)],[f241,f252,f255,f149])).
% 2.40/0.75 fof(f260,definition,(
% 2.40/0.75 sQ14_spl <=> (distinct_points(sK2_skl,sK2_skl))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f261,plain,(
% 2.40/0.75 distinct_points(sK2_skl,sK2_skl)|~sQ14_spl),
% 2.40/0.75 inference(component_clause,[status(thm)],[f260])).
% 2.40/0.75 fof(f356,plain,(
% 2.40/0.75 ![X0]: (distinct_points(sK2_skl,X0)|~sQ13_spl)),
% 2.40/0.75 inference(duplicate_literals_removal,[status(thm)],[f256])).
% 2.40/0.75 fof(f358,plain,(
% 2.40/0.75 $false|~sQ13_spl),
% 2.40/0.75 inference(resolution,[status(thm)],[f356,f15])).
% 2.40/0.75 fof(f359,plain,(
% 2.40/0.75 ~sQ13_spl),
% 2.40/0.75 inference(contradiction_clause,[status(thm)],[f358])).
% 2.40/0.75 fof(f586,plain,(
% 2.40/0.75 $false|~sQ7_spl),
% 2.40/0.75 inference(forward_subsumption_resolution,[status(thm)],[f140,f15])).
% 2.40/0.75 fof(f587,plain,(
% 2.40/0.75 ~sQ7_spl),
% 2.40/0.75 inference(contradiction_clause,[status(thm)],[f586])).
% 2.40/0.75 fof(f655,plain,(
% 2.40/0.75 ![X0,X1,X2]: (~distinct_points(X0,X1)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X0,X2)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,X2)|apart_point_and_line(sK2_skl,X2))),
% 2.40/0.75 inference(resolution,[status(thm)],[f36,f187])).
% 2.40/0.75 fof(f814,plain,(
% 2.40/0.75 $false|~sQ14_spl),
% 2.40/0.75 inference(forward_subsumption_resolution,[status(thm)],[f261,f15])).
% 2.40/0.75 fof(f815,plain,(
% 2.40/0.75 ~sQ14_spl),
% 2.40/0.75 inference(contradiction_clause,[status(thm)],[f814])).
% 2.40/0.75 fof(f956,plain,(
% 2.40/0.75 ![X0]: (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_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(sK2_skl,X0))),
% 2.40/0.75 inference(resolution,[status(thm)],[f655,f56])).
% 2.40/0.75 fof(f1110,definition,(
% 2.40/0.75 sQ31_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f1111,plain,(
% 2.40/0.75 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ31_spl),
% 2.40/0.75 inference(component_clause,[status(thm)],[f1110])).
% 2.40/0.75 fof(f1117,definition,(
% 2.40/0.75 sQ33_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f1118,plain,(
% 2.40/0.75 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ33_spl),
% 2.40/0.75 inference(component_clause,[status(thm)],[f1117])).
% 2.40/0.75 fof(f1181,definition,(
% 2.40/0.75 ![X0]: (sQ47_spl <=> (apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK2_skl,X0)))),
% 2.40/0.75 introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 2.40/0.75 fof(f1182,plain,(
% 2.40/0.75 ![X0]: (apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK2_skl,X0)|~sQ47_spl)),
% 2.40/0.75 inference(component_clause,[status(thm)],[f1181])).
% 2.40/0.75 fof(f1184,plain,(
% 2.40/0.75 sQ33_spl|sQ47_spl|sQ31_spl),
% 2.40/0.75 inference(split_clause,[status(thm)],[f956,f1117,f1181,f1110])).
% 2.40/0.75 fof(f1456,plain,(
% 2.40/0.75 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ31_spl),
% 2.40/0.75 inference(resolution,[status(thm)],[f1111,f29])).
% 2.40/0.75 fof(f1460,plain,(
% 2.40/0.75 ~sQ2_spl|sQ4_spl|~sQ31_spl),
% 2.40/0.75 inference(split_clause,[status(thm)],[f1456,f72,f79,f1110])).
% 2.40/0.75 fof(f1461,plain,(
% 2.40/0.75 $false|~sQ4_spl),
% 2.40/0.75 inference(forward_subsumption_resolution,[status(thm)],[f80,f15])).
% 2.40/0.75 fof(f1462,plain,(
% 2.40/0.75 ~sQ4_spl),
% 2.40/0.75 inference(contradiction_clause,[status(thm)],[f1461])).
% 2.40/0.75 fof(f1471,plain,(
% 2.40/0.76 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ33_spl),
% 2.40/0.76 inference(resolution,[status(thm)],[f1118,f30])).
% 2.40/0.76 fof(f1475,plain,(
% 2.40/0.76 ~sQ2_spl|sQ7_spl|~sQ33_spl),
% 2.40/0.76 inference(split_clause,[status(thm)],[f1471,f72,f139,f1117])).
% 2.40/0.76 fof(f1486,plain,(
% 2.40/0.76 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl))|~sQ47_spl),
% 2.40/0.76 inference(resolution,[status(thm)],[f1182,f50])).
% 2.40/0.76 fof(f1491,definition,(
% 2.40/0.76 sQ89_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)))),
% 2.40/0.76 introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition])).
% 2.40/0.76 fof(f1492,plain,(
% 2.40/0.76 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|~sQ89_spl),
% 2.40/0.76 inference(component_clause,[status(thm)],[f1491])).
% 2.40/0.76 fof(f1494,definition,(
% 2.40/0.76 sQ90_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl)))),
% 2.40/0.76 introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition])).
% 2.40/0.76 fof(f1495,plain,(
% 2.40/0.76 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl))|~sQ90_spl),
% 2.40/0.76 inference(component_clause,[status(thm)],[f1494])).
% 2.40/0.76 fof(f1497,plain,(
% 2.40/0.76 sQ89_spl|sQ90_spl|~sQ47_spl),
% 2.40/0.76 inference(split_clause,[status(thm)],[f1486,f1491,f1494,f1181])).
% 2.40/0.76 fof(f1499,plain,(
% 2.40/0.76 ~distinct_points(sK0_skl,sK2_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ89_spl),
% 2.40/0.76 inference(resolution,[status(thm)],[f1492,f29])).
% 2.40/0.76 fof(f1503,plain,(
% 2.40/0.76 ~sQ12_spl|sQ4_spl|~sQ89_spl),
% 2.40/0.76 inference(split_clause,[status(thm)],[f1499,f252,f79,f1491])).
% 2.40/0.76 fof(f1504,plain,(
% 2.40/0.76 ~distinct_points(sK0_skl,sK2_skl)|distinct_points(sK2_skl,sK2_skl)|~sQ90_spl),
% 2.40/0.76 inference(resolution,[status(thm)],[f1495,f30])).
% 2.40/0.76 fof(f1508,plain,(
% 2.40/0.76 ~sQ12_spl|sQ14_spl|~sQ90_spl),
% 2.40/0.76 inference(split_clause,[status(thm)],[f1504,f252,f260,f1494])).
% 2.40/0.76 fof(f1510,plain,(
% 2.40/0.76 $false),
% 2.40/0.76 inference(sat_refutation,[status(thm)],[f152,f155,f258,f359,f587,f815,f1184,f1460,f1462,f1475,f1497,f1503,f1508])).
% 2.40/0.76 % SZS output end CNFRefutation for theBenchmark.p
% 2.40/0.77 % Elapsed time: 0.412460 seconds
% 2.40/0.77 % CPU time: 2.944661 seconds
% 2.40/0.77 % Total memory used: 43.832 MB
% 2.40/0.77 % Net memory used: 39.102 MB
%------------------------------------------------------------------------------