%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO204+1 : 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 : n002.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 12:26:05 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 13:27:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f4,axiom,(
% 0.10/0.40 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f7,axiom,(
% 0.10/0.40 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f8,axiom,(
% 0.10/0.40 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f11,axiom,(
% 0.10/0.40 (! [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) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f12,axiom,(
% 0.10/0.40 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f15,conjecture,(
% 0.10/0.40 (! [X,Y,Z] :( ( distinct_points(X,Y)& ~ distinct_points(Y,Z) )=> ( distinct_points(X,Z)& ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z)) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f16,negated_conjecture,(
% 0.10/0.40 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& ~ distinct_points(Y,Z) )=> ( distinct_points(X,Z)& ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z)) ) ) ))),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f15])).
% 0.10/0.40 fof(f20,plain,(
% 0.10/0.40 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.10/0.40 fof(f21,plain,(
% 0.10/0.40 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f20])).
% 0.10/0.40 fof(f22,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f21])).
% 0.10/0.40 fof(f29,plain,(
% 0.10/0.40 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.10/0.40 fof(f30,plain,(
% 0.10/0.40 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f29])).
% 0.10/0.40 fof(f31,plain,(
% 0.10/0.40 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.10/0.40 fof(f32,plain,(
% 0.10/0.40 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f31])).
% 0.10/0.40 fof(f37,plain,(
% 0.10/0.40 ![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)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.10/0.40 fof(f38,plain,(
% 0.10/0.40 ![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))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f37])).
% 0.10/0.40 fof(f39,plain,(
% 0.10/0.40 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.10/0.40 fof(f40,plain,(
% 0.10/0.40 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f39])).
% 0.10/0.40 fof(f41,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.10/0.40 fof(f48,plain,(
% 0.10/0.40 (?[X,Y,Z]: ((distinct_points(X,Y)&~distinct_points(Y,Z))&(~distinct_points(X,Z)|distinct_lines(line_connecting(X,Y),line_connecting(X,Z)))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.10/0.40 fof(f49,plain,(
% 0.10/0.40 ((distinct_points(sK0_skl,sK1_skl)&~distinct_points(sK1_skl,sK2_skl))&(~distinct_points(sK0_skl,sK2_skl)|distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))))),
% 0.10/0.40 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)],[f48])).
% 0.10/0.40 fof(f50,plain,(
% 0.10/0.40 distinct_points(sK0_skl,sK1_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.10/0.40 fof(f51,plain,(
% 0.10/0.40 ~distinct_points(sK1_skl,sK2_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.10/0.40 fof(f52,plain,(
% 0.10/0.40 ~distinct_points(sK0_skl,sK2_skl)|distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.10/0.40 fof(f53,definition,(
% 0.10/0.40 sQ0_spl <=> (distinct_points(sK0_skl,sK2_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f55,plain,(
% 0.10/0.40 ~distinct_points(sK0_skl,sK2_skl)|sQ0_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f53])).
% 0.10/0.40 fof(f56,definition,(
% 0.10/0.40 sQ1_spl <=> (distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f57,plain,(
% 0.10/0.40 distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))|~sQ1_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f56])).
% 0.10/0.40 fof(f59,plain,(
% 0.10/0.40 ~sQ0_spl|sQ1_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f52,f53,f56])).
% 0.10/0.40 fof(f60,plain,(
% 0.10/0.40 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f22,f50])).
% 0.10/0.40 fof(f61,plain,(
% 0.10/0.40 distinct_points(sK0_skl,sK2_skl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f60,f51])).
% 0.10/0.40 fof(f64,plain,(
% 0.10/0.40 $false|sQ0_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f61,f55])).
% 0.10/0.40 fof(f65,plain,(
% 0.10/0.40 sQ0_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f64])).
% 0.10/0.40 fof(f69,plain,(
% 0.10/0.40 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,line_connecting(sK0_skl,sK2_skl))|~sQ1_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f57,f38])).
% 0.10/0.40 fof(f74,plain,(
% 0.10/0.40 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))|~sQ1_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f69,f50])).
% 0.10/0.40 fof(f78,definition,(
% 0.10/0.40 sQ3_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f79,plain,(
% 0.10/0.40 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl))|~sQ3_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f78])).
% 0.10/0.40 fof(f80,plain,(
% 0.10/0.40 ~apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl))|sQ3_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f78])).
% 0.10/0.40 fof(f85,definition,(
% 0.10/0.40 sQ5_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f86,plain,(
% 0.10/0.40 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ5_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f85])).
% 0.10/0.40 fof(f88,definition,(
% 0.10/0.40 sQ6_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f89,plain,(
% 0.10/0.40 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))|~sQ6_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f88])).
% 0.10/0.40 fof(f92,definition,(
% 0.10/0.40 sQ7_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f93,plain,(
% 0.10/0.40 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ7_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f92])).
% 0.10/0.40 fof(f95,definition,(
% 0.10/0.40 sQ8_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f96,plain,(
% 0.10/0.40 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|~sQ8_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f95])).
% 0.10/0.41 fof(f99,plain,(
% 0.10/0.41 sQ7_spl|sQ8_spl|sQ5_spl|sQ6_spl|~sQ1_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f74,f92,f95,f85,f88,f56])).
% 0.10/0.41 fof(f104,plain,(
% 0.10/0.41 ![X0]: (distinct_points(sK1_skl,X0)|apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))|~sQ6_spl)),
% 0.10/0.41 inference(resolution,[status(thm)],[f89,f41])).
% 0.10/0.41 fof(f105,plain,(
% 0.10/0.41 ~distinct_points(sK0_skl,sK1_skl)|~sQ5_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f86,f32])).
% 0.10/0.41 fof(f108,plain,(
% 0.10/0.41 $false|~sQ5_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f105,f50])).
% 0.10/0.41 fof(f109,plain,(
% 0.10/0.41 ~sQ5_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f108])).
% 0.10/0.41 fof(f110,plain,(
% 0.10/0.41 ~distinct_points(sK0_skl,sK2_skl)|~sQ8_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f96,f30])).
% 0.10/0.41 fof(f113,plain,(
% 0.10/0.41 ~sQ0_spl|~sQ8_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f110,f53,f95])).
% 0.10/0.41 fof(f170,plain,(
% 0.10/0.41 ~distinct_points(sK0_skl,sK1_skl)|~sQ7_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f93,f30])).
% 0.10/0.41 fof(f173,plain,(
% 0.10/0.41 $false|~sQ7_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f170,f50])).
% 0.10/0.41 fof(f174,plain,(
% 0.10/0.41 ~sQ7_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f173])).
% 0.10/0.41 fof(f291,plain,(
% 0.10/0.41 ~distinct_points(sK0_skl,sK2_skl)|~sQ3_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f79,f32])).
% 0.10/0.41 fof(f294,plain,(
% 0.10/0.41 ~sQ0_spl|~sQ3_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f291,f53,f78])).
% 0.10/0.41 fof(f362,plain,(
% 0.10/0.41 distinct_points(sK1_skl,sK2_skl)|~sQ6_spl|sQ3_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f104,f80])).
% 0.10/0.41 fof(f370,plain,(
% 0.10/0.41 $false|~sQ6_spl|sQ3_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f362,f51])).
% 0.10/0.41 fof(f371,plain,(
% 0.10/0.41 ~sQ6_spl|sQ3_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f370])).
% 0.10/0.41 fof(f372,plain,(
% 0.10/0.41 $false),
% 0.10/0.41 inference(sat_refutation,[status(thm)],[f59,f65,f99,f109,f113,f174,f294,f371])).
% 0.10/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.43 % Elapsed time: 0.050853 seconds
% 0.10/0.43 % CPU time: 0.163430 seconds
% 0.10/0.43 % Total memory used: 18.021 MB
% 0.10/0.43 % Net memory used: 17.553 MB
%------------------------------------------------------------------------------