%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO182+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 : n017.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 0.15s 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO182+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
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 13:01:55 UTC 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 0.15/0.46 % Refutation found
% 0.15/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.46 fof(f1,axiom,(
% 0.15/0.46 (! [X] : ~ distinct_points(X,X) )),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f4,axiom,(
% 0.15/0.46 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f7,axiom,(
% 0.15/0.46 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f8,axiom,(
% 0.15/0.46 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f11,axiom,(
% 0.15/0.46 (! [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) ) ) )),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f13,axiom,(
% 0.15/0.46 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f15,conjecture,(
% 0.15/0.46 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(Z,line_connecting(Y,X)) ) ) )),
% 0.15/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.46 fof(f16,negated_conjecture,(
% 0.15/0.46 ~((! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(Z,line_connecting(Y,X)) ) ) ))),
% 0.15/0.46 inference(negated_conjecture,[status(cth)],[f15])).
% 0.15/0.46 fof(f17,plain,(
% 0.15/0.46 ![X0]: (~distinct_points(X0,X0))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f1])).
% 0.15/0.46 fof(f20,plain,(
% 0.15/0.46 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.15/0.46 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.15/0.46 fof(f21,plain,(
% 0.15/0.46 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f20])).
% 0.15/0.46 fof(f22,plain,(
% 0.15/0.46 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f21])).
% 0.15/0.46 fof(f29,plain,(
% 0.15/0.46 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.15/0.46 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.15/0.46 fof(f30,plain,(
% 0.15/0.46 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f29])).
% 0.15/0.46 fof(f31,plain,(
% 0.15/0.46 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.15/0.46 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.15/0.46 fof(f32,plain,(
% 0.15/0.46 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f31])).
% 0.15/0.46 fof(f37,plain,(
% 0.15/0.46 ![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)))),
% 0.15/0.46 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.15/0.46 fof(f38,plain,(
% 0.15/0.46 ![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))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f37])).
% 0.15/0.46 fof(f42,plain,(
% 0.15/0.46 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.15/0.46 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.15/0.46 fof(f43,plain,(
% 0.15/0.46 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f42])).
% 0.15/0.46 fof(f44,plain,(
% 0.15/0.46 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f43])).
% 0.15/0.46 fof(f48,plain,(
% 0.15/0.46 (?[X,Y,Z]: (distinct_points(X,Y)&(apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(Z,line_connecting(Y,X)))))),
% 0.15/0.46 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.15/0.46 fof(f49,plain,(
% 0.15/0.46 ?[X,Y]: (distinct_points(X,Y)&(?[Z]: (apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(Z,line_connecting(Y,X)))))),
% 0.15/0.46 inference(miniscoping,[status(thm)],[f48])).
% 0.15/0.46 fof(f50,plain,(
% 0.15/0.46 (distinct_points(sK0_skl,sK1_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))))),
% 0.15/0.46 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)],[f49])).
% 0.15/0.46 fof(f51,plain,(
% 0.15/0.46 distinct_points(sK0_skl,sK1_skl)),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f50])).
% 0.15/0.46 fof(f52,plain,(
% 0.15/0.46 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f50])).
% 0.15/0.46 fof(f53,plain,(
% 0.15/0.46 ~apart_point_and_line(sK2_skl,line_connecting(sK1_skl,sK0_skl))),
% 0.15/0.46 inference(cnf_transformation,[status(thm)],[f50])).
% 0.15/0.46 fof(f54,plain,(
% 0.15/0.46 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.15/0.46 inference(resolution,[status(thm)],[f22,f51])).
% 0.15/0.46 fof(f55,plain,(
% 0.15/0.46 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.15/0.46 inference(resolution,[status(thm)],[f54,f22])).
% 0.15/0.46 fof(f60,plain,(
% 0.15/0.46 distinct_points(sK1_skl,sK0_skl)),
% 0.15/0.46 inference(resolution,[status(thm)],[f55,f17])).
% 0.15/0.46 fof(f75,definition,(
% 0.15/0.46 sQ2_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.15/0.46 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.15/0.46 fof(f77,plain,(
% 0.15/0.46 ~distinct_points(sK0_skl,sK1_skl)|sQ2_spl),
% 0.15/0.46 inference(component_clause,[status(thm)],[f75])).
% 0.15/0.46 fof(f130,plain,(
% 0.15/0.46 $false|sQ2_spl),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f77,f51])).
% 0.15/0.46 fof(f131,plain,(
% 0.15/0.46 sQ2_spl),
% 0.15/0.46 inference(contradiction_clause,[status(thm)],[f130])).
% 0.15/0.46 fof(f150,plain,(
% 0.15/0.46 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,X0))),
% 0.15/0.46 inference(resolution,[status(thm)],[f44,f52])).
% 0.15/0.46 fof(f249,plain,(
% 0.15/0.46 ![X0,X1,X2]: (apart_point_and_line(sK2_skl,X0)|~distinct_points(X1,X2)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,X0)|apart_point_and_line(X2,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X2,X0))),
% 0.15/0.46 inference(resolution,[status(thm)],[f150,f38])).
% 0.15/0.46 fof(f309,plain,(
% 0.15/0.46 ![X0]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,X0))),
% 0.15/0.46 inference(resolution,[status(thm)],[f249,f60])).
% 0.15/0.46 fof(f333,definition,(
% 0.15/0.46 sQ16_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.15/0.46 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.15/0.46 fof(f334,plain,(
% 0.15/0.46 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ16_spl),
% 0.15/0.46 inference(component_clause,[status(thm)],[f333])).
% 0.15/0.46 fof(f340,definition,(
% 0.15/0.46 sQ18_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.15/0.46 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.15/0.46 fof(f341,plain,(
% 0.15/0.46 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ18_spl),
% 0.15/0.46 inference(component_clause,[status(thm)],[f340])).
% 0.15/0.46 fof(f361,definition,(
% 0.15/0.46 ![X0]: (sQ23_spl <=> (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)))),
% 0.15/0.46 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.15/0.46 fof(f362,plain,(
% 0.15/0.46 ![X0]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|~sQ23_spl)),
% 0.15/0.46 inference(component_clause,[status(thm)],[f361])).
% 0.15/0.46 fof(f364,plain,(
% 0.15/0.46 sQ23_spl|sQ16_spl|sQ18_spl),
% 0.15/0.46 inference(split_clause,[status(thm)],[f309,f361,f333,f340])).
% 0.15/0.46 fof(f414,plain,(
% 0.15/0.46 ~distinct_points(sK0_skl,sK1_skl)|~sQ18_spl),
% 0.15/0.46 inference(resolution,[status(thm)],[f341,f30])).
% 0.15/0.46 fof(f417,plain,(
% 0.15/0.46 ~sQ2_spl|~sQ18_spl),
% 0.15/0.46 inference(split_clause,[status(thm)],[f414,f75,f340])).
% 0.15/0.46 fof(f419,plain,(
% 0.15/0.46 ~distinct_points(sK0_skl,sK1_skl)|~sQ16_spl),
% 0.15/0.46 inference(resolution,[status(thm)],[f334,f32])).
% 0.15/0.46 fof(f422,plain,(
% 0.15/0.46 ~sQ2_spl|~sQ16_spl),
% 0.15/0.46 inference(split_clause,[status(thm)],[f419,f75,f333])).
% 0.15/0.46 fof(f726,plain,(
% 0.15/0.46 apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))|~sQ23_spl),
% 0.15/0.46 inference(resolution,[status(thm)],[f362,f53])).
% 0.15/0.46 fof(f731,definition,(
% 0.15/0.46 sQ56_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.15/0.46 introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition])).
% 0.15/0.46 fof(f732,plain,(
% 0.15/0.46 apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|~sQ56_spl),
% 0.15/0.46 inference(component_clause,[status(thm)],[f731])).
% 0.15/0.46 fof(f734,definition,(
% 0.15/0.46 sQ57_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.15/0.46 introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 0.15/0.46 fof(f735,plain,(
% 0.15/0.46 apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))|~sQ57_spl),
% 0.15/0.46 inference(component_clause,[status(thm)],[f734])).
% 0.15/0.46 fof(f737,plain,(
% 0.15/0.46 sQ56_spl|sQ57_spl|~sQ23_spl),
% 0.15/0.46 inference(split_clause,[status(thm)],[f726,f731,f734,f361])).
% 0.15/0.46 fof(f738,plain,(
% 0.15/0.46 ~distinct_points(sK1_skl,sK0_skl)|~sQ56_spl),
% 0.15/0.46 inference(resolution,[status(thm)],[f732,f30])).
% 0.15/0.46 fof(f741,plain,(
% 0.15/0.46 $false|~sQ56_spl),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f738,f60])).
% 0.15/0.46 fof(f742,plain,(
% 0.15/0.46 ~sQ56_spl),
% 0.15/0.46 inference(contradiction_clause,[status(thm)],[f741])).
% 0.15/0.46 fof(f743,plain,(
% 0.15/0.46 ~distinct_points(sK1_skl,sK0_skl)|~sQ57_spl),
% 0.15/0.46 inference(resolution,[status(thm)],[f735,f32])).
% 0.15/0.46 fof(f746,plain,(
% 0.15/0.46 $false|~sQ57_spl),
% 0.15/0.46 inference(forward_subsumption_resolution,[status(thm)],[f743,f60])).
% 0.15/0.46 fof(f747,plain,(
% 0.15/0.46 ~sQ57_spl),
% 0.15/0.46 inference(contradiction_clause,[status(thm)],[f746])).
% 0.15/0.46 fof(f748,plain,(
% 0.15/0.46 $false),
% 0.15/0.46 inference(sat_refutation,[status(thm)],[f131,f364,f417,f422,f737,f742,f747])).
% 0.15/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.48 % Elapsed time: 0.107410 seconds
% 0.15/0.48 % CPU time: 0.537432 seconds
% 0.15/0.48 % Total memory used: 23.148 MB
% 0.15/0.48 % Net memory used: 21.661 MB
%------------------------------------------------------------------------------