%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO170+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 : n015.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 12:25:55 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO170+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 12:56:04 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.47 fof(f1,axiom,(
% 0.18/0.47 (! [X] : ~ distinct_points(X,X) )),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f4,axiom,(
% 0.18/0.47 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f7,axiom,(
% 0.18/0.47 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f8,axiom,(
% 0.18/0.47 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f11,axiom,(
% 0.18/0.47 (! [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) ) ) )),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f32,axiom,(
% 0.18/0.47 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f34,axiom,(
% 0.18/0.47 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f36,conjecture,(
% 0.18/0.47 (! [X,Y,Z] :( ( distinct_points(X,Y)& incident_point_and_line(X,Z)& incident_point_and_line(Y,Z) )=> equal_lines(Z,line_connecting(X,Y)) ) )),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f37,negated_conjecture,(
% 0.18/0.47 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& incident_point_and_line(X,Z)& incident_point_and_line(Y,Z) )=> equal_lines(Z,line_connecting(X,Y)) ) ))),
% 0.18/0.47 inference(negated_conjecture,[status(cth)],[f36])).
% 0.18/0.47 fof(f38,plain,(
% 0.18/0.47 ![X0]: (~distinct_points(X0,X0))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f1])).
% 0.18/0.47 fof(f41,plain,(
% 0.18/0.47 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.18/0.47 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.18/0.47 fof(f42,plain,(
% 0.18/0.47 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.18/0.47 inference(miniscoping,[status(thm)],[f41])).
% 0.18/0.47 fof(f43,plain,(
% 0.18/0.47 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f42])).
% 0.18/0.47 fof(f50,plain,(
% 0.18/0.47 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.18/0.47 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.18/0.47 fof(f51,plain,(
% 0.18/0.47 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f50])).
% 0.18/0.47 fof(f52,plain,(
% 0.18/0.47 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.18/0.47 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.18/0.47 fof(f53,plain,(
% 0.18/0.47 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f52])).
% 0.18/0.47 fof(f58,plain,(
% 0.18/0.47 ![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)))),
% 0.18/0.48 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.18/0.48 fof(f59,plain,(
% 0.18/0.48 ![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))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f58])).
% 0.18/0.48 fof(f111,plain,(
% 0.18/0.48 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.18/0.48 inference(NNF_transformation,[status(thm)],[f32])).
% 0.18/0.48 fof(f112,plain,(
% 0.18/0.48 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f111])).
% 0.18/0.48 fof(f114,plain,(
% 0.18/0.48 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f112])).
% 0.18/0.48 fof(f119,plain,(
% 0.18/0.48 ![X,Y]: ((~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y))&(incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 0.18/0.48 inference(NNF_transformation,[status(thm)],[f34])).
% 0.18/0.48 fof(f120,plain,(
% 0.18/0.48 (![X,Y]: (~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y)))&(![X,Y]: (incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 0.18/0.48 inference(miniscoping,[status(thm)],[f119])).
% 0.18/0.48 fof(f121,plain,(
% 0.18/0.48 ![X0,X1]: (~incident_point_and_line(X0,X1)|~apart_point_and_line(X0,X1))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f120])).
% 0.18/0.48 fof(f127,plain,(
% 0.18/0.48 (?[X,Y,Z]: (((distinct_points(X,Y)&incident_point_and_line(X,Z))&incident_point_and_line(Y,Z))&~equal_lines(Z,line_connecting(X,Y))))),
% 0.18/0.48 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.18/0.48 fof(f128,plain,(
% 0.18/0.48 (((distinct_points(sK0_skl,sK1_skl)&incident_point_and_line(sK0_skl,sK2_skl))&incident_point_and_line(sK1_skl,sK2_skl))&~equal_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.18/0.48 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])).
% 0.18/0.48 fof(f129,plain,(
% 0.18/0.48 distinct_points(sK0_skl,sK1_skl)),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f128])).
% 0.18/0.48 fof(f130,plain,(
% 0.18/0.48 incident_point_and_line(sK0_skl,sK2_skl)),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f128])).
% 0.18/0.48 fof(f131,plain,(
% 0.18/0.48 incident_point_and_line(sK1_skl,sK2_skl)),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f128])).
% 0.18/0.48 fof(f132,plain,(
% 0.18/0.48 ~equal_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.18/0.48 inference(cnf_transformation,[status(thm)],[f128])).
% 0.18/0.48 fof(f143,plain,(
% 0.18/0.48 distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.18/0.48 inference(resolution,[status(thm)],[f114,f132])).
% 0.18/0.48 fof(f145,plain,(
% 0.18/0.48 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.18/0.48 inference(resolution,[status(thm)],[f43,f129])).
% 0.18/0.48 fof(f150,plain,(
% 0.18/0.48 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.18/0.48 inference(resolution,[status(thm)],[f145,f43])).
% 0.18/0.48 fof(f158,plain,(
% 0.18/0.48 distinct_points(sK1_skl,sK0_skl)),
% 0.18/0.48 inference(resolution,[status(thm)],[f150,f38])).
% 0.18/0.48 fof(f190,plain,(
% 0.18/0.48 ![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)))),
% 0.18/0.48 inference(resolution,[status(thm)],[f59,f143])).
% 0.18/0.48 fof(f221,plain,(
% 0.18/0.48 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))),
% 0.18/0.48 inference(resolution,[status(thm)],[f190,f158])).
% 0.18/0.48 fof(f245,definition,(
% 0.18/0.48 sQ5_spl <=> (apart_point_and_line(sK1_skl,sK2_skl))),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.18/0.48 fof(f246,plain,(
% 0.18/0.48 apart_point_and_line(sK1_skl,sK2_skl)|~sQ5_spl),
% 0.18/0.48 inference(component_clause,[status(thm)],[f245])).
% 0.18/0.48 fof(f248,definition,(
% 0.18/0.48 sQ6_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.18/0.48 fof(f249,plain,(
% 0.18/0.48 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ6_spl),
% 0.18/0.48 inference(component_clause,[status(thm)],[f248])).
% 0.18/0.48 fof(f251,definition,(
% 0.18/0.48 sQ7_spl <=> (apart_point_and_line(sK0_skl,sK2_skl))),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.18/0.48 fof(f252,plain,(
% 0.18/0.48 apart_point_and_line(sK0_skl,sK2_skl)|~sQ7_spl),
% 0.18/0.48 inference(component_clause,[status(thm)],[f251])).
% 0.18/0.48 fof(f254,definition,(
% 0.18/0.48 sQ8_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.18/0.48 fof(f255,plain,(
% 0.18/0.48 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ8_spl),
% 0.18/0.48 inference(component_clause,[status(thm)],[f254])).
% 0.18/0.48 fof(f257,plain,(
% 0.18/0.48 sQ5_spl|sQ6_spl|sQ7_spl|sQ8_spl),
% 0.18/0.48 inference(split_clause,[status(thm)],[f221,f245,f248,f251,f254])).
% 0.18/0.48 fof(f313,plain,(
% 0.18/0.48 ~incident_point_and_line(sK1_skl,sK2_skl)|~sQ5_spl),
% 0.18/0.48 inference(resolution,[status(thm)],[f246,f121])).
% 0.18/0.48 fof(f314,plain,(
% 0.18/0.48 $false|~sQ5_spl),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f313,f131])).
% 0.18/0.48 fof(f315,plain,(
% 0.18/0.48 ~sQ5_spl),
% 0.18/0.48 inference(contradiction_clause,[status(thm)],[f314])).
% 0.18/0.48 fof(f324,plain,(
% 0.18/0.48 ~distinct_points(sK0_skl,sK1_skl)|~sQ6_spl),
% 0.18/0.48 inference(resolution,[status(thm)],[f249,f53])).
% 0.18/0.48 fof(f328,plain,(
% 0.18/0.48 $false|~sQ6_spl),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f324,f129])).
% 0.18/0.48 fof(f329,plain,(
% 0.18/0.48 ~sQ6_spl),
% 0.18/0.48 inference(contradiction_clause,[status(thm)],[f328])).
% 0.18/0.48 fof(f332,plain,(
% 0.18/0.48 ~incident_point_and_line(sK0_skl,sK2_skl)|~sQ7_spl),
% 0.18/0.48 inference(resolution,[status(thm)],[f252,f121])).
% 0.18/0.48 fof(f333,plain,(
% 0.18/0.48 $false|~sQ7_spl),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f332,f130])).
% 0.18/0.48 fof(f334,plain,(
% 0.18/0.48 ~sQ7_spl),
% 0.18/0.48 inference(contradiction_clause,[status(thm)],[f333])).
% 0.18/0.48 fof(f423,plain,(
% 0.18/0.48 ~distinct_points(sK0_skl,sK1_skl)|~sQ8_spl),
% 0.18/0.48 inference(resolution,[status(thm)],[f255,f51])).
% 0.18/0.48 fof(f427,plain,(
% 0.18/0.48 $false|~sQ8_spl),
% 0.18/0.48 inference(forward_subsumption_resolution,[status(thm)],[f423,f129])).
% 0.18/0.48 fof(f428,plain,(
% 0.18/0.48 ~sQ8_spl),
% 0.18/0.48 inference(contradiction_clause,[status(thm)],[f427])).
% 0.18/0.48 fof(f429,plain,(
% 0.18/0.48 $false),
% 0.18/0.48 inference(sat_refutation,[status(thm)],[f257,f315,f329,f334,f428])).
% 0.18/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.53 % Elapsed time: 0.074696 seconds
% 0.18/0.53 % CPU time: 0.077475 seconds
% 0.18/0.53 % Total memory used: 1.944 MB
% 0.18/0.53 % Net memory used: 1.908 MB
%------------------------------------------------------------------------------