%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO178+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.08s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO178+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n003.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sun Sep 20 13:02:31 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.08/0.36 % Refutation found
% 0.08/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.36 fof(f7,axiom,(
% 0.08/0.36 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.08/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.36 fof(f8,axiom,(
% 0.08/0.36 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.08/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.36 fof(f12,axiom,(
% 0.08/0.36 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 0.08/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.36 fof(f36,conjecture,(
% 0.08/0.36 (! [X,Y,Z] :( ( distinct_points(X,Y)& apart_point_and_line(Z,line_connecting(X,Y)) )=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) )),
% 0.08/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.36 fof(f37,negated_conjecture,(
% 0.08/0.36 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& apart_point_and_line(Z,line_connecting(X,Y)) )=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ))),
% 0.08/0.36 inference(negated_conjecture,[status(cth)],[f36])).
% 0.08/0.36 fof(f50,plain,(
% 0.08/0.36 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.08/0.36 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.08/0.36 fof(f51,plain,(
% 0.08/0.36 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f50])).
% 0.08/0.36 fof(f52,plain,(
% 0.08/0.36 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.08/0.36 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.08/0.36 fof(f53,plain,(
% 0.08/0.36 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f52])).
% 0.08/0.36 fof(f60,plain,(
% 0.08/0.36 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 0.08/0.36 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.08/0.36 fof(f61,plain,(
% 0.08/0.36 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 0.08/0.36 inference(miniscoping,[status(thm)],[f60])).
% 0.08/0.36 fof(f62,plain,(
% 0.08/0.36 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f61])).
% 0.08/0.36 fof(f127,plain,(
% 0.08/0.36 (?[X,Y,Z]: ((distinct_points(X,Y)&apart_point_and_line(Z,line_connecting(X,Y)))&(~distinct_points(Z,X)|~distinct_points(Z,Y))))),
% 0.08/0.36 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.08/0.36 fof(f128,plain,(
% 0.08/0.36 ((distinct_points(sK0_skl,sK1_skl)&apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)))&(~distinct_points(sK2_skl,sK0_skl)|~distinct_points(sK2_skl,sK1_skl)))),
% 0.08/0.36 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)],[f127])).
% 0.08/0.36 fof(f129,plain,(
% 0.08/0.36 distinct_points(sK0_skl,sK1_skl)),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f128])).
% 0.08/0.36 fof(f130,plain,(
% 0.08/0.36 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f128])).
% 0.08/0.36 fof(f131,plain,(
% 0.08/0.36 ~distinct_points(sK2_skl,sK0_skl)|~distinct_points(sK2_skl,sK1_skl)),
% 0.08/0.36 inference(cnf_transformation,[status(thm)],[f128])).
% 0.08/0.36 fof(f142,definition,(
% 0.08/0.36 sQ0_spl <=> (distinct_points(sK2_skl,sK0_skl))),
% 0.08/0.36 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/0.36 fof(f145,definition,(
% 0.08/0.36 sQ1_spl <=> (distinct_points(sK2_skl,sK1_skl))),
% 0.08/0.36 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.08/0.36 fof(f148,plain,(
% 0.08/0.36 ~sQ0_spl|~sQ1_spl),
% 0.08/0.36 inference(split_clause,[status(thm)],[f131,f142,f145])).
% 0.08/0.36 fof(f152,plain,(
% 0.08/0.36 ![X0]: (distinct_points(sK2_skl,X0)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl)))),
% 0.08/0.36 inference(resolution,[status(thm)],[f62,f130])).
% 0.08/0.36 fof(f171,definition,(
% 0.08/0.36 sQ4_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.08/0.36 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.08/0.36 fof(f173,plain,(
% 0.08/0.36 ~distinct_points(sK0_skl,sK1_skl)|sQ4_spl),
% 0.08/0.36 inference(component_clause,[status(thm)],[f171])).
% 0.08/0.36 fof(f211,plain,(
% 0.08/0.36 distinct_points(sK2_skl,sK1_skl)|~distinct_points(sK0_skl,sK1_skl)),
% 0.08/0.37 inference(resolution,[status(thm)],[f152,f53])).
% 0.08/0.37 fof(f212,plain,(
% 0.08/0.37 distinct_points(sK2_skl,sK0_skl)|~distinct_points(sK0_skl,sK1_skl)),
% 0.08/0.37 inference(resolution,[status(thm)],[f152,f51])).
% 0.08/0.37 fof(f214,plain,(
% 0.08/0.37 sQ1_spl|~sQ4_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f211,f145,f171])).
% 0.08/0.37 fof(f215,plain,(
% 0.08/0.37 sQ0_spl|~sQ4_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f212,f142,f171])).
% 0.08/0.37 fof(f216,plain,(
% 0.08/0.37 $false|sQ4_spl),
% 0.08/0.37 inference(forward_subsumption_resolution,[status(thm)],[f173,f129])).
% 0.08/0.37 fof(f217,plain,(
% 0.08/0.37 sQ4_spl),
% 0.08/0.37 inference(contradiction_clause,[status(thm)],[f216])).
% 0.08/0.37 fof(f218,plain,(
% 0.08/0.37 $false),
% 0.08/0.37 inference(sat_refutation,[status(thm)],[f148,f214,f215,f217])).
% 0.08/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.39 % Elapsed time: 0.045433 seconds
% 0.11/0.39 % CPU time: 0.098186 seconds
% 0.11/0.39 % Total memory used: 13.771 MB
% 0.11/0.39 % Net memory used: 13.698 MB
%------------------------------------------------------------------------------