%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO190+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 : n009.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 12:26:01 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO190+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 : n009.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 13:34:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.41 fof(f1,axiom,(
% 0.12/0.41 (! [X] : ~ distinct_points(X,X) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f4,axiom,(
% 0.12/0.41 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f7,axiom,(
% 0.12/0.41 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f9,axiom,(
% 0.12/0.41 (! [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) ) ) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f11,axiom,(
% 0.12/0.41 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f13,conjecture,(
% 0.12/0.41 (! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& distinct_points(Y,Z)& ~ apart_point_and_line(Z,line_connecting(X,Y)) )=> ~ apart_point_and_line(Z,line_connecting(Y,X)) ) )),
% 0.12/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f14,negated_conjecture,(
% 0.12/0.41 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& distinct_points(Y,Z)& ~ apart_point_and_line(Z,line_connecting(X,Y)) )=> ~ apart_point_and_line(Z,line_connecting(Y,X)) ) ))),
% 0.12/0.41 inference(negated_conjecture,[status(cth)],[f13])).
% 0.12/0.41 fof(f15,plain,(
% 0.12/0.41 ![X0]: (~distinct_points(X0,X0))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.41 fof(f18,plain,(
% 0.12/0.41 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.12/0.41 fof(f19,plain,(
% 0.12/0.41 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f18])).
% 0.12/0.41 fof(f20,plain,(
% 0.12/0.41 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f19])).
% 0.12/0.41 fof(f27,plain,(
% 0.12/0.41 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.12/0.41 fof(f28,plain,(
% 0.12/0.41 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f27])).
% 0.12/0.41 fof(f29,plain,(
% 0.12/0.41 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f28])).
% 0.12/0.41 fof(f30,plain,(
% 0.12/0.41 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f28])).
% 0.12/0.41 fof(f35,plain,(
% 0.12/0.41 ![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)))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.12/0.41 fof(f36,plain,(
% 0.12/0.41 ![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))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f35])).
% 0.12/0.41 fof(f40,plain,(
% 0.12/0.41 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.12/0.41 fof(f41,plain,(
% 0.12/0.41 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f40])).
% 0.12/0.41 fof(f42,plain,(
% 0.12/0.41 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f41])).
% 0.12/0.41 fof(f45,plain,(
% 0.12/0.41 (?[X,Y,Z]: ((((distinct_points(X,Y)&distinct_points(X,Z))&distinct_points(Y,Z))&~apart_point_and_line(Z,line_connecting(X,Y)))&apart_point_and_line(Z,line_connecting(Y,X))))),
% 0.12/0.41 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.12/0.41 fof(f46,plain,(
% 0.12/0.41 ((((distinct_points(sK0_skl,sK1_skl)&distinct_points(sK0_skl,sK2_skl))&distinct_points(sK1_skl,sK2_skl))&~apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)))&apart_point_and_line(sK2_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.12/0.41 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])).
% 0.12/0.41 fof(f47,plain,(
% 0.12/0.41 distinct_points(sK0_skl,sK1_skl)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f46])).
% 0.12/0.41 fof(f50,plain,(
% 0.12/0.41 ~apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f46])).
% 0.12/0.41 fof(f51,plain,(
% 0.12/0.41 apart_point_and_line(sK2_skl,line_connecting(sK1_skl,sK0_skl))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f46])).
% 0.12/0.41 fof(f54,plain,(
% 0.12/0.41 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.12/0.41 inference(resolution,[status(thm)],[f20,f47])).
% 0.12/0.41 fof(f59,plain,(
% 0.12/0.41 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.12/0.41 inference(resolution,[status(thm)],[f54,f20])).
% 0.12/0.41 fof(f62,definition,(
% 0.12/0.41 sQ0_spl <=> (distinct_points(sK1_skl,sK0_skl))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f64,plain,(
% 0.12/0.41 ~distinct_points(sK1_skl,sK0_skl)|sQ0_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f62])).
% 0.12/0.41 fof(f74,plain,(
% 0.12/0.41 distinct_points(sK0_skl,sK0_skl)|sQ0_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f64,f54])).
% 0.12/0.41 fof(f75,plain,(
% 0.12/0.41 $false|sQ0_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f74,f15])).
% 0.12/0.41 fof(f76,plain,(
% 0.12/0.41 sQ0_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f75])).
% 0.12/0.41 fof(f127,plain,(
% 0.12/0.41 ![X0,X1]: (distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,X0)|distinct_points(X1,X0))),
% 0.12/0.41 inference(resolution,[status(thm)],[f59,f20])).
% 0.12/0.41 fof(f134,definition,(
% 0.12/0.41 sQ8_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f137,definition,(
% 0.12/0.41 ![X0,X1]: (sQ9_spl <=> (distinct_points(sK1_skl,X0)|distinct_points(X1,X0)))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f138,plain,(
% 0.12/0.41 ![X0,X1]: (distinct_points(sK1_skl,X0)|distinct_points(X1,X0)|~sQ9_spl)),
% 0.12/0.41 inference(component_clause,[status(thm)],[f137])).
% 0.12/0.41 fof(f140,plain,(
% 0.12/0.41 sQ8_spl|sQ9_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f127,f134,f137])).
% 0.12/0.41 fof(f192,plain,(
% 0.12/0.41 ![X0]: (distinct_lines(line_connecting(sK1_skl,sK0_skl),X0)|apart_point_and_line(sK2_skl,X0))),
% 0.12/0.41 inference(resolution,[status(thm)],[f42,f51])).
% 0.12/0.41 fof(f207,plain,(
% 0.12/0.41 $false|~sQ9_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f138,f15])).
% 0.12/0.41 fof(f211,plain,(
% 0.12/0.41 ~sQ9_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f207])).
% 0.12/0.41 fof(f230,plain,(
% 0.12/0.41 ![X0,X1,X2]: (apart_point_and_line(sK2_skl,X0)|~distinct_points(X1,X2)|apart_point_and_line(X1,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(X1,X0)|apart_point_and_line(X2,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(X2,X0))),
% 0.12/0.41 inference(resolution,[status(thm)],[f192,f36])).
% 0.12/0.41 fof(f446,plain,(
% 0.12/0.41 ![X0]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(sK1_skl,X0))),
% 0.12/0.41 inference(resolution,[status(thm)],[f230,f47])).
% 0.12/0.41 fof(f492,definition,(
% 0.12/0.41 sQ20_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f493,plain,(
% 0.12/0.41 apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|~sQ20_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f492])).
% 0.12/0.41 fof(f499,definition,(
% 0.12/0.41 sQ22_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f500,plain,(
% 0.12/0.41 apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))|~sQ22_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f499])).
% 0.12/0.41 fof(f545,definition,(
% 0.12/0.41 ![X0]: (sQ33_spl <=> (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f546,plain,(
% 0.12/0.41 ![X0]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|~sQ33_spl)),
% 0.12/0.41 inference(component_clause,[status(thm)],[f545])).
% 0.12/0.41 fof(f585,plain,(
% 0.12/0.41 sQ33_spl|sQ22_spl|sQ20_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f446,f545,f499,f492])).
% 0.12/0.41 fof(f659,plain,(
% 0.12/0.41 ~distinct_points(sK1_skl,sK0_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ20_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f493,f29])).
% 0.12/0.41 fof(f663,definition,(
% 0.12/0.41 sQ54_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f664,plain,(
% 0.12/0.41 distinct_points(sK1_skl,sK1_skl)|~sQ54_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f663])).
% 0.12/0.41 fof(f666,plain,(
% 0.12/0.41 ~sQ0_spl|sQ54_spl|~sQ20_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f659,f62,f663,f492])).
% 0.12/0.41 fof(f667,plain,(
% 0.12/0.41 $false|~sQ54_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f664,f15])).
% 0.12/0.41 fof(f668,plain,(
% 0.12/0.41 ~sQ54_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f667])).
% 0.12/0.41 fof(f670,plain,(
% 0.12/0.41 ~distinct_points(sK1_skl,sK0_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ22_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f500,f30])).
% 0.12/0.41 fof(f674,definition,(
% 0.12/0.41 sQ55_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f675,plain,(
% 0.12/0.41 distinct_points(sK0_skl,sK0_skl)|~sQ55_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f674])).
% 0.12/0.41 fof(f677,plain,(
% 0.12/0.41 ~sQ0_spl|sQ55_spl|~sQ22_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f670,f62,f674,f499])).
% 0.12/0.41 fof(f679,plain,(
% 0.12/0.41 $false|~sQ55_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f675,f15])).
% 0.12/0.41 fof(f680,plain,(
% 0.12/0.41 ~sQ55_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f679])).
% 0.12/0.41 fof(f935,plain,(
% 0.12/0.41 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ33_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f546,f50])).
% 0.12/0.41 fof(f940,definition,(
% 0.12/0.41 sQ71_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f941,plain,(
% 0.12/0.41 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ71_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f940])).
% 0.12/0.41 fof(f943,definition,(
% 0.12/0.41 sQ72_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f944,plain,(
% 0.12/0.41 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ72_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f943])).
% 0.12/0.41 fof(f946,plain,(
% 0.12/0.41 sQ71_spl|sQ72_spl|~sQ33_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f935,f940,f943,f545])).
% 0.12/0.41 fof(f947,plain,(
% 0.12/0.41 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ71_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f941,f30])).
% 0.12/0.41 fof(f951,plain,(
% 0.12/0.41 ~sQ8_spl|sQ54_spl|~sQ71_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f947,f134,f663,f940])).
% 0.12/0.41 fof(f954,plain,(
% 0.12/0.41 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ72_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f944,f29])).
% 0.12/0.41 fof(f958,plain,(
% 0.12/0.41 ~sQ8_spl|sQ55_spl|~sQ72_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f954,f134,f674,f943])).
% 0.12/0.41 fof(f959,plain,(
% 0.12/0.41 $false),
% 0.12/0.41 inference(sat_refutation,[status(thm)],[f76,f140,f211,f585,f666,f668,f677,f680,f946,f951,f958])).
% 0.12/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.42 % Elapsed time: 0.062002 seconds
% 0.12/0.42 % CPU time: 0.312405 seconds
% 0.12/0.42 % Total memory used: 20.483 MB
% 0.12/0.42 % Net memory used: 19.643 MB
%------------------------------------------------------------------------------