%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO173+1 : 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 : n001.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 12:25:56 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO173+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 13:02:12 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.40 fof(f1,axiom,(
% 0.14/0.40 (! [X] : ~ distinct_points(X,X) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f4,axiom,(
% 0.14/0.40 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f7,axiom,(
% 0.14/0.40 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f8,axiom,(
% 0.14/0.40 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f11,axiom,(
% 0.14/0.40 (! [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) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f15,conjecture,(
% 0.14/0.40 (! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& distinct_lines(U,line_connecting(X,Y)) )=> ( apart_point_and_line(X,U)| apart_point_and_line(Y,U) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f16,negated_conjecture,(
% 0.14/0.40 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& distinct_lines(U,line_connecting(X,Y)) )=> ( apart_point_and_line(X,U)| apart_point_and_line(Y,U) ) ) ))),
% 0.14/0.40 inference(negated_conjecture,[status(cth)],[f15])).
% 0.14/0.40 fof(f17,plain,(
% 0.14/0.40 ![X0]: (~distinct_points(X0,X0))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.40 fof(f20,plain,(
% 0.14/0.40 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.14/0.40 fof(f21,plain,(
% 0.14/0.40 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f20])).
% 0.14/0.40 fof(f22,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/0.40 fof(f29,plain,(
% 0.14/0.40 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.14/0.40 fof(f30,plain,(
% 0.14/0.40 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f29])).
% 0.14/0.40 fof(f31,plain,(
% 0.14/0.40 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.14/0.40 fof(f32,plain,(
% 0.14/0.40 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f31])).
% 0.14/0.40 fof(f37,plain,(
% 0.14/0.40 ![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)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.14/0.40 fof(f38,plain,(
% 0.14/0.40 ![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))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f37])).
% 0.14/0.40 fof(f48,plain,(
% 0.14/0.40 (?[X,Y,U,V]: (((distinct_points(X,Y)&convergent_lines(U,V))&distinct_lines(U,line_connecting(X,Y)))&(~apart_point_and_line(X,U)&~apart_point_and_line(Y,U))))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.14/0.40 fof(f49,plain,(
% 0.14/0.40 ?[X,Y,U]: (((distinct_points(X,Y)&(?[V]: convergent_lines(U,V)))&distinct_lines(U,line_connecting(X,Y)))&(~apart_point_and_line(X,U)&~apart_point_and_line(Y,U)))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f48])).
% 0.14/0.40 fof(f50,plain,(
% 0.14/0.40 (((distinct_points(sK0_skl,sK1_skl)&convergent_lines(sK2_skl,sK3_skl))&distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)))&(~apart_point_and_line(sK0_skl,sK2_skl)&~apart_point_and_line(sK1_skl,sK2_skl)))),
% 0.14/0.40 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)],[f49])).
% 0.14/0.40 fof(f51,plain,(
% 0.14/0.40 distinct_points(sK0_skl,sK1_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f50])).
% 0.14/0.40 fof(f53,plain,(
% 0.14/0.40 distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f50])).
% 0.14/0.40 fof(f54,plain,(
% 0.14/0.40 ~apart_point_and_line(sK0_skl,sK2_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f50])).
% 0.14/0.40 fof(f55,plain,(
% 0.14/0.40 ~apart_point_and_line(sK1_skl,sK2_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f50])).
% 0.14/0.40 fof(f56,plain,(
% 0.14/0.40 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.14/0.40 inference(resolution,[status(thm)],[f22,f51])).
% 0.14/0.40 fof(f59,plain,(
% 0.14/0.40 distinct_points(sK1_skl,sK0_skl)),
% 0.14/0.40 inference(resolution,[status(thm)],[f56,f17])).
% 0.14/0.40 fof(f65,plain,(
% 0.14/0.40 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,sK2_skl)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/0.40 inference(resolution,[status(thm)],[f38,f53])).
% 0.14/0.40 fof(f102,plain,(
% 0.14/0.40 apart_point_and_line(sK1_skl,sK2_skl)|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,sK2_skl)|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.14/0.40 inference(resolution,[status(thm)],[f65,f59])).
% 0.14/0.40 fof(f111,definition,(
% 0.14/0.40 sQ4_spl <=> (apart_point_and_line(sK1_skl,sK2_skl))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f112,plain,(
% 0.14/0.40 apart_point_and_line(sK1_skl,sK2_skl)|~sQ4_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f111])).
% 0.14/0.40 fof(f114,definition,(
% 0.14/0.40 sQ5_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f115,plain,(
% 0.14/0.40 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ5_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f114])).
% 0.14/0.40 fof(f117,definition,(
% 0.14/0.40 sQ6_spl <=> (apart_point_and_line(sK0_skl,sK2_skl))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f118,plain,(
% 0.14/0.40 apart_point_and_line(sK0_skl,sK2_skl)|~sQ6_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f117])).
% 0.14/0.40 fof(f120,definition,(
% 0.14/0.40 sQ7_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f121,plain,(
% 0.14/0.40 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ7_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f120])).
% 0.14/0.40 fof(f123,plain,(
% 0.14/0.40 sQ4_spl|sQ5_spl|sQ6_spl|sQ7_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f102,f111,f114,f117,f120])).
% 0.14/0.40 fof(f147,plain,(
% 0.14/0.40 $false|~sQ6_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f118,f54])).
% 0.14/0.40 fof(f148,plain,(
% 0.14/0.40 ~sQ6_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f147])).
% 0.14/0.40 fof(f160,plain,(
% 0.14/0.40 ~distinct_points(sK0_skl,sK1_skl)|~sQ7_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f121,f30])).
% 0.14/0.40 fof(f163,plain,(
% 0.14/0.40 $false|~sQ7_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f160,f51])).
% 0.14/0.40 fof(f164,plain,(
% 0.14/0.40 ~sQ7_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f163])).
% 0.14/0.40 fof(f165,plain,(
% 0.14/0.40 $false|~sQ4_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f112,f55])).
% 0.14/0.40 fof(f166,plain,(
% 0.14/0.40 ~sQ4_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f165])).
% 0.14/0.40 fof(f167,plain,(
% 0.14/0.40 ~distinct_points(sK0_skl,sK1_skl)|~sQ5_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f115,f32])).
% 0.14/0.40 fof(f170,plain,(
% 0.14/0.40 $false|~sQ5_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f167,f51])).
% 0.14/0.40 fof(f171,plain,(
% 0.14/0.40 ~sQ5_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f170])).
% 0.14/0.40 fof(f172,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(sat_refutation,[status(thm)],[f123,f148,f164,f166,f171])).
% 0.14/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.42 % Elapsed time: 0.040159 seconds
% 0.14/0.42 % CPU time: 0.117253 seconds
% 0.14/0.42 % Total memory used: 16.716 MB
% 0.14/0.42 % Net memory used: 16.338 MB
%------------------------------------------------------------------------------