%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO180+2 : 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 : n014.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 0.13s 0.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO180+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 13:11:19 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.56 % Refutation found
% 0.13/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.56 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.56 fof(f1,axiom,(
% 0.13/0.56 (! [X] : ~ distinct_points(X,X) )),
% 0.13/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.56 fof(f4,axiom,(
% 0.13/0.56 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.13/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.56 fof(f7,axiom,(
% 0.13/0.56 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 0.13/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.56 fof(f9,axiom,(
% 0.13/0.56 (! [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) ) ) )),
% 0.13/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.56 fof(f11,axiom,(
% 0.13/0.56 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.13/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.56 fof(f13,conjecture,(
% 0.13/0.56 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(X,line_connecting(Z,Y)) ) ) )),
% 0.13/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.56 fof(f14,negated_conjecture,(
% 0.13/0.56 ~((! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(X,line_connecting(Z,Y)) ) ) ))),
% 0.13/0.56 inference(negated_conjecture,[status(cth)],[f13])).
% 0.13/0.56 fof(f15,plain,(
% 0.13/0.56 ![X0]: (~distinct_points(X0,X0))),
% 0.13/0.56 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.56 fof(f18,plain,(
% 0.13/0.56 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.13/0.56 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/0.56 fof(f19,plain,(
% 0.13/0.56 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.13/0.56 inference(miniscoping,[status(thm)],[f18])).
% 0.13/0.56 fof(f20,plain,(
% 0.13/0.56 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.13/0.56 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.56 fof(f27,plain,(
% 0.13/0.56 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 0.13/0.56 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.13/0.56 fof(f28,plain,(
% 0.13/0.56 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 0.13/0.56 inference(miniscoping,[status(thm)],[f27])).
% 0.13/0.56 fof(f29,plain,(
% 0.13/0.56 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 0.13/0.56 inference(cnf_transformation,[status(thm)],[f28])).
% 0.13/0.56 fof(f30,plain,(
% 0.13/0.56 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 0.13/0.56 inference(cnf_transformation,[status(thm)],[f28])).
% 0.13/0.56 fof(f35,plain,(
% 0.13/0.56 ![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)))),
% 0.13/0.56 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.13/0.56 fof(f36,plain,(
% 0.13/0.56 ![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))),
% 0.13/0.56 inference(cnf_transformation,[status(thm)],[f35])).
% 0.13/0.56 fof(f40,plain,(
% 0.13/0.56 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.13/0.56 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.13/0.56 fof(f41,plain,(
% 0.13/0.56 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.13/0.56 inference(miniscoping,[status(thm)],[f40])).
% 0.13/0.56 fof(f42,plain,(
% 0.13/0.56 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.13/0.56 inference(cnf_transformation,[status(thm)],[f41])).
% 0.13/0.56 fof(f45,plain,(
% 0.13/0.56 (?[X,Y,Z]: (distinct_points(X,Y)&(apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(X,line_connecting(Z,Y)))))),
% 0.13/0.56 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.13/0.56 fof(f46,plain,(
% 0.13/0.56 ?[X,Y]: (distinct_points(X,Y)&(?[Z]: (apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(X,line_connecting(Z,Y)))))),
% 0.13/0.56 inference(miniscoping,[status(thm)],[f45])).
% 0.13/0.56 fof(f47,plain,(
% 0.13/0.56 (distinct_points(sK0_skl,sK1_skl)&(apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))&~apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl))))),
% 0.13/0.56 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)],[f46])).
% 0.13/0.56 fof(f48,plain,(
% 0.13/0.56 distinct_points(sK0_skl,sK1_skl)),
% 0.13/0.56 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/0.56 fof(f49,plain,(
% 0.13/0.56 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.13/0.56 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/0.56 fof(f50,plain,(
% 0.13/0.56 ~apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl))),
% 0.13/0.56 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/0.56 fof(f51,plain,(
% 0.13/0.56 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.13/0.56 inference(resolution,[status(thm)],[f20,f48])).
% 0.13/0.56 fof(f53,plain,(
% 0.13/0.56 distinct_points(sK1_skl,sK0_skl)),
% 0.13/0.56 inference(resolution,[status(thm)],[f51,f15])).
% 0.13/0.56 fof(f66,definition,(
% 0.13/0.56 sQ0_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.13/0.56 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.56 fof(f68,plain,(
% 0.13/0.56 ~distinct_points(sK0_skl,sK1_skl)|sQ0_spl),
% 0.13/0.56 inference(component_clause,[status(thm)],[f66])).
% 0.13/0.56 fof(f90,plain,(
% 0.13/0.56 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK2_skl,sK1_skl)),
% 0.13/0.56 inference(resolution,[status(thm)],[f30,f49])).
% 0.13/0.56 fof(f91,definition,(
% 0.13/0.56 sQ5_spl <=> (distinct_points(sK2_skl,sK1_skl))),
% 0.13/0.56 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/0.56 fof(f94,plain,(
% 0.13/0.56 ~sQ0_spl|sQ5_spl),
% 0.13/0.56 inference(split_clause,[status(thm)],[f90,f66,f91])).
% 0.13/0.56 fof(f95,plain,(
% 0.13/0.56 $false|sQ0_spl),
% 0.13/0.56 inference(forward_subsumption_resolution,[status(thm)],[f68,f48])).
% 0.13/0.56 fof(f96,plain,(
% 0.13/0.56 sQ0_spl),
% 0.13/0.56 inference(contradiction_clause,[status(thm)],[f95])).
% 0.13/0.56 fof(f256,plain,(
% 0.13/0.56 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,X0))),
% 0.13/0.56 inference(resolution,[status(thm)],[f42,f49])).
% 0.13/0.56 fof(f334,plain,(
% 0.13/0.56 ![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))),
% 0.13/0.56 inference(resolution,[status(thm)],[f256,f36])).
% 0.13/0.56 fof(f482,plain,(
% 0.13/0.56 ![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))),
% 0.13/0.56 inference(resolution,[status(thm)],[f334,f53])).
% 0.13/0.56 fof(f580,definition,(
% 0.13/0.56 sQ20_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.13/0.56 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.13/0.56 fof(f581,plain,(
% 0.13/0.56 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ20_spl),
% 0.13/0.56 inference(component_clause,[status(thm)],[f580])).
% 0.13/0.56 fof(f587,definition,(
% 0.13/0.56 sQ22_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.13/0.56 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.13/0.56 fof(f588,plain,(
% 0.13/0.56 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ22_spl),
% 0.13/0.56 inference(component_clause,[status(thm)],[f587])).
% 0.13/0.56 fof(f642,definition,(
% 0.13/0.56 ![X0]: (sQ34_spl <=> (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)))),
% 0.13/0.56 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.13/0.56 fof(f643,plain,(
% 0.13/0.56 ![X0]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|~sQ34_spl)),
% 0.13/0.56 inference(component_clause,[status(thm)],[f642])).
% 0.13/0.56 fof(f645,plain,(
% 0.13/0.56 sQ34_spl|sQ22_spl|sQ20_spl),
% 0.13/0.56 inference(split_clause,[status(thm)],[f482,f642,f587,f580])).
% 0.13/0.56 fof(f831,plain,(
% 0.13/0.56 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ22_spl),
% 0.13/0.56 inference(resolution,[status(thm)],[f588,f30])).
% 0.13/0.57 fof(f835,definition,(
% 0.13/0.57 sQ66_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 0.13/0.57 introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition])).
% 0.13/0.57 fof(f836,plain,(
% 0.13/0.57 distinct_points(sK1_skl,sK1_skl)|~sQ66_spl),
% 0.13/0.57 inference(component_clause,[status(thm)],[f835])).
% 0.13/0.57 fof(f838,plain,(
% 0.13/0.57 ~sQ0_spl|sQ66_spl|~sQ22_spl),
% 0.13/0.57 inference(split_clause,[status(thm)],[f831,f66,f835,f587])).
% 0.13/0.57 fof(f840,plain,(
% 0.13/0.57 $false|~sQ66_spl),
% 0.13/0.57 inference(forward_subsumption_resolution,[status(thm)],[f836,f15])).
% 0.13/0.57 fof(f841,plain,(
% 0.13/0.57 ~sQ66_spl),
% 0.13/0.57 inference(contradiction_clause,[status(thm)],[f840])).
% 0.13/0.57 fof(f851,plain,(
% 0.13/0.57 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ20_spl),
% 0.13/0.57 inference(resolution,[status(thm)],[f581,f29])).
% 0.13/0.57 fof(f855,definition,(
% 0.13/0.57 sQ69_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 0.13/0.57 introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition])).
% 0.13/0.57 fof(f856,plain,(
% 0.13/0.57 distinct_points(sK0_skl,sK0_skl)|~sQ69_spl),
% 0.13/0.57 inference(component_clause,[status(thm)],[f855])).
% 0.13/0.57 fof(f858,plain,(
% 0.13/0.57 ~sQ0_spl|sQ69_spl|~sQ20_spl),
% 0.13/0.57 inference(split_clause,[status(thm)],[f851,f66,f855,f580])).
% 0.13/0.57 fof(f859,plain,(
% 0.13/0.57 $false|~sQ69_spl),
% 0.13/0.57 inference(forward_subsumption_resolution,[status(thm)],[f856,f15])).
% 0.13/0.57 fof(f860,plain,(
% 0.13/0.57 ~sQ69_spl),
% 0.13/0.57 inference(contradiction_clause,[status(thm)],[f859])).
% 0.13/0.57 fof(f1181,plain,(
% 0.13/0.57 apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl))|apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl))|~sQ34_spl),
% 0.13/0.57 inference(resolution,[status(thm)],[f643,f50])).
% 0.13/0.57 fof(f1187,definition,(
% 0.13/0.57 sQ90_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)))),
% 0.13/0.57 introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition])).
% 0.13/0.57 fof(f1188,plain,(
% 0.13/0.57 apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl))|~sQ90_spl),
% 0.13/0.57 inference(component_clause,[status(thm)],[f1187])).
% 0.13/0.57 fof(f1190,definition,(
% 0.13/0.57 sQ91_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl)))),
% 0.13/0.57 introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition])).
% 0.13/0.57 fof(f1191,plain,(
% 0.13/0.57 apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl))|~sQ91_spl),
% 0.13/0.57 inference(component_clause,[status(thm)],[f1190])).
% 0.13/0.57 fof(f1193,plain,(
% 0.13/0.57 sQ90_spl|sQ91_spl|~sQ34_spl),
% 0.13/0.57 inference(split_clause,[status(thm)],[f1181,f1187,f1190,f642])).
% 0.13/0.57 fof(f1195,plain,(
% 0.13/0.57 ~distinct_points(sK2_skl,sK1_skl)|distinct_points(sK2_skl,sK2_skl)|~sQ90_spl),
% 0.13/0.57 inference(resolution,[status(thm)],[f1188,f29])).
% 0.13/0.57 fof(f1199,definition,(
% 0.13/0.57 sQ92_spl <=> (distinct_points(sK2_skl,sK2_skl))),
% 0.13/0.57 introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition])).
% 0.13/0.57 fof(f1200,plain,(
% 0.13/0.57 distinct_points(sK2_skl,sK2_skl)|~sQ92_spl),
% 0.13/0.57 inference(component_clause,[status(thm)],[f1199])).
% 0.13/0.57 fof(f1202,plain,(
% 0.13/0.57 ~sQ5_spl|sQ92_spl|~sQ90_spl),
% 0.13/0.57 inference(split_clause,[status(thm)],[f1195,f91,f1199,f1187])).
% 0.13/0.57 fof(f1203,plain,(
% 0.13/0.57 $false|~sQ92_spl),
% 0.13/0.57 inference(forward_subsumption_resolution,[status(thm)],[f1200,f15])).
% 0.13/0.57 fof(f1204,plain,(
% 0.13/0.57 ~sQ92_spl),
% 0.13/0.57 inference(contradiction_clause,[status(thm)],[f1203])).
% 0.13/0.57 fof(f1311,plain,(
% 0.13/0.57 ~distinct_points(sK2_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ91_spl),
% 0.13/0.57 inference(resolution,[status(thm)],[f1191,f30])).
% 0.13/0.57 fof(f1315,plain,(
% 0.13/0.57 ~sQ5_spl|sQ66_spl|~sQ91_spl),
% 0.13/0.57 inference(split_clause,[status(thm)],[f1311,f91,f835,f1190])).
% 0.13/0.57 fof(f1317,plain,(
% 0.13/0.57 $false),
% 0.13/0.57 inference(sat_refutation,[status(thm)],[f94,f96,f645,f838,f841,f858,f860,f1193,f1202,f1204,f1315])).
% 0.13/0.57 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.57 % Elapsed time: 0.209073 seconds
% 0.13/0.57 % CPU time: 1.431844 seconds
% 0.13/0.57 % Total memory used: 33.899 MB
% 0.13/0.57 % Net memory used: 30.726 MB
%------------------------------------------------------------------------------