%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO190+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 : 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 12:26:01 PM UTC 2026
% Result : Theorem 0.09s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO190+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
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:18:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.48 % Refutation found
% 0.09/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.48 fof(f1,axiom,(
% 0.09/0.48 (! [X] : ~ distinct_points(X,X) )),
% 0.09/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.48 fof(f4,axiom,(
% 0.09/0.48 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.09/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.48 fof(f7,axiom,(
% 0.09/0.48 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.09/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.48 fof(f8,axiom,(
% 0.09/0.48 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.09/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.48 fof(f11,axiom,(
% 0.09/0.48 (! [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) ) ) )),
% 0.09/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.48 fof(f13,axiom,(
% 0.09/0.48 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.09/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.48 fof(f15,conjecture,(
% 0.09/0.48 (! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& distinct_points(Y,Z)& ~ apart_point_and_line(Z,line_connecting(X,Y)) )=> ~ apart_point_and_line(Z,line_connecting(Y,X)) ) )),
% 0.09/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.48 fof(f16,negated_conjecture,(
% 0.09/0.48 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& distinct_points(Y,Z)& ~ apart_point_and_line(Z,line_connecting(X,Y)) )=> ~ apart_point_and_line(Z,line_connecting(Y,X)) ) ))),
% 0.09/0.48 inference(negated_conjecture,[status(cth)],[f15])).
% 0.09/0.48 fof(f17,plain,(
% 0.09/0.48 ![X0]: (~distinct_points(X0,X0))),
% 0.09/0.48 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.48 fof(f20,plain,(
% 0.09/0.48 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.09/0.48 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.09/0.48 fof(f21,plain,(
% 0.09/0.48 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.09/0.48 inference(miniscoping,[status(thm)],[f20])).
% 0.09/0.48 fof(f22,plain,(
% 0.09/0.48 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.09/0.48 inference(cnf_transformation,[status(thm)],[f21])).
% 0.09/0.48 fof(f29,plain,(
% 0.09/0.48 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.09/0.48 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.09/0.48 fof(f30,plain,(
% 0.09/0.48 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.09/0.48 inference(cnf_transformation,[status(thm)],[f29])).
% 0.09/0.48 fof(f31,plain,(
% 0.09/0.48 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.09/0.48 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.09/0.48 fof(f32,plain,(
% 0.09/0.48 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.09/0.48 inference(cnf_transformation,[status(thm)],[f31])).
% 0.09/0.48 fof(f37,plain,(
% 0.09/0.48 ![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)))),
% 0.09/0.48 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.09/0.48 fof(f38,plain,(
% 0.09/0.48 ![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))),
% 0.09/0.48 inference(cnf_transformation,[status(thm)],[f37])).
% 0.09/0.48 fof(f42,plain,(
% 0.09/0.48 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.09/0.48 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.09/0.48 fof(f43,plain,(
% 0.09/0.48 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.09/0.48 inference(miniscoping,[status(thm)],[f42])).
% 0.09/0.48 fof(f44,plain,(
% 0.09/0.48 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.09/0.48 inference(cnf_transformation,[status(thm)],[f43])).
% 0.09/0.48 fof(f48,plain,(
% 0.09/0.48 (?[X,Y,Z]: ((((distinct_points(X,Y)&distinct_points(X,Z))&distinct_points(Y,Z))&~apart_point_and_line(Z,line_connecting(X,Y)))&apart_point_and_line(Z,line_connecting(Y,X))))),
% 0.09/0.48 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.09/0.48 fof(f49,plain,(
% 0.09/0.48 ((((distinct_points(sK0_skl,sK1_skl)&distinct_points(sK0_skl,sK2_skl))&distinct_points(sK1_skl,sK2_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)))),
% 0.09/0.48 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)],[f48])).
% 0.09/0.48 fof(f50,plain,(
% 0.09/0.48 distinct_points(sK0_skl,sK1_skl)),
% 0.09/0.48 inference(cnf_transformation,[status(thm)],[f49])).
% 0.09/0.48 fof(f53,plain,(
% 0.09/0.48 ~apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.09/0.48 inference(cnf_transformation,[status(thm)],[f49])).
% 0.09/0.48 fof(f54,plain,(
% 0.09/0.48 apart_point_and_line(sK2_skl,line_connecting(sK1_skl,sK0_skl))),
% 0.09/0.48 inference(cnf_transformation,[status(thm)],[f49])).
% 0.09/0.48 fof(f57,plain,(
% 0.09/0.48 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.09/0.48 inference(resolution,[status(thm)],[f22,f50])).
% 0.09/0.48 fof(f65,plain,(
% 0.09/0.48 ![X0]: (distinct_lines(line_connecting(sK1_skl,sK0_skl),X0)|apart_point_and_line(sK2_skl,X0))),
% 0.09/0.48 inference(resolution,[status(thm)],[f44,f54])).
% 0.09/0.48 fof(f75,definition,(
% 0.09/0.48 sQ1_spl <=> (distinct_points(sK1_skl,sK0_skl))),
% 0.09/0.48 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.48 fof(f77,plain,(
% 0.09/0.48 ~distinct_points(sK1_skl,sK0_skl)|sQ1_spl),
% 0.09/0.48 inference(component_clause,[status(thm)],[f75])).
% 0.09/0.48 fof(f83,plain,(
% 0.09/0.48 ![X0,X1,X2]: (apart_point_and_line(sK2_skl,X0)|~distinct_points(X1,X2)|apart_point_and_line(X1,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(X1,X0)|apart_point_and_line(X2,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(X2,X0))),
% 0.09/0.48 inference(resolution,[status(thm)],[f65,f38])).
% 0.09/0.48 fof(f86,plain,(
% 0.09/0.48 distinct_points(sK0_skl,sK0_skl)|sQ1_spl),
% 0.09/0.48 inference(resolution,[status(thm)],[f77,f57])).
% 0.09/0.48 fof(f87,plain,(
% 0.09/0.48 $false|sQ1_spl),
% 0.09/0.48 inference(forward_subsumption_resolution,[status(thm)],[f86,f17])).
% 0.09/0.48 fof(f88,plain,(
% 0.09/0.48 sQ1_spl),
% 0.09/0.48 inference(contradiction_clause,[status(thm)],[f87])).
% 0.09/0.48 fof(f335,plain,(
% 0.09/0.48 ![X0]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(sK1_skl,X0))),
% 0.09/0.48 inference(resolution,[status(thm)],[f83,f50])).
% 0.09/0.48 fof(f373,definition,(
% 0.09/0.48 sQ18_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.09/0.48 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.09/0.48 fof(f374,plain,(
% 0.09/0.48 apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|~sQ18_spl),
% 0.09/0.48 inference(component_clause,[status(thm)],[f373])).
% 0.09/0.48 fof(f380,definition,(
% 0.09/0.48 sQ20_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.09/0.48 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.09/0.48 fof(f381,plain,(
% 0.09/0.48 apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))|~sQ20_spl),
% 0.09/0.48 inference(component_clause,[status(thm)],[f380])).
% 0.09/0.48 fof(f421,definition,(
% 0.09/0.48 ![X0]: (sQ30_spl <=> (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)))),
% 0.09/0.48 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.09/0.48 fof(f422,plain,(
% 0.09/0.48 ![X0]: (apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|~sQ30_spl)),
% 0.09/0.48 inference(component_clause,[status(thm)],[f421])).
% 0.09/0.48 fof(f448,plain,(
% 0.09/0.48 sQ30_spl|sQ20_spl|sQ18_spl),
% 0.09/0.48 inference(split_clause,[status(thm)],[f335,f421,f380,f373])).
% 0.09/0.48 fof(f538,plain,(
% 0.09/0.48 ~distinct_points(sK1_skl,sK0_skl)|~sQ18_spl),
% 0.09/0.48 inference(resolution,[status(thm)],[f374,f30])).
% 0.09/0.48 fof(f541,plain,(
% 0.09/0.48 ~sQ1_spl|~sQ18_spl),
% 0.09/0.48 inference(split_clause,[status(thm)],[f538,f75,f373])).
% 0.09/0.48 fof(f543,plain,(
% 0.09/0.48 ~distinct_points(sK1_skl,sK0_skl)|~sQ20_spl),
% 0.09/0.48 inference(resolution,[status(thm)],[f381,f32])).
% 0.09/0.48 fof(f546,plain,(
% 0.09/0.48 ~sQ1_spl|~sQ20_spl),
% 0.09/0.48 inference(split_clause,[status(thm)],[f543,f75,f380])).
% 0.09/0.48 fof(f1013,plain,(
% 0.09/0.48 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ30_spl),
% 0.09/0.48 inference(resolution,[status(thm)],[f422,f53])).
% 0.09/0.48 fof(f1018,definition,(
% 0.09/0.48 sQ80_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.09/0.48 introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition])).
% 0.09/0.48 fof(f1019,plain,(
% 0.09/0.48 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ80_spl),
% 0.09/0.48 inference(component_clause,[status(thm)],[f1018])).
% 0.09/0.48 fof(f1021,definition,(
% 0.09/0.48 sQ81_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.09/0.48 introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition])).
% 0.09/0.48 fof(f1022,plain,(
% 0.09/0.48 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ81_spl),
% 0.09/0.48 inference(component_clause,[status(thm)],[f1021])).
% 0.09/0.48 fof(f1024,plain,(
% 0.09/0.48 sQ80_spl|sQ81_spl|~sQ30_spl),
% 0.09/0.48 inference(split_clause,[status(thm)],[f1013,f1018,f1021,f421])).
% 0.09/0.48 fof(f1025,plain,(
% 0.09/0.48 ~distinct_points(sK0_skl,sK1_skl)|~sQ80_spl),
% 0.09/0.48 inference(resolution,[status(thm)],[f1019,f32])).
% 0.09/0.48 fof(f1028,plain,(
% 0.09/0.48 $false|~sQ80_spl),
% 0.09/0.48 inference(forward_subsumption_resolution,[status(thm)],[f1025,f50])).
% 0.09/0.48 fof(f1029,plain,(
% 0.09/0.48 ~sQ80_spl),
% 0.09/0.48 inference(contradiction_clause,[status(thm)],[f1028])).
% 0.09/0.48 fof(f1030,plain,(
% 0.09/0.48 ~distinct_points(sK0_skl,sK1_skl)|~sQ81_spl),
% 0.09/0.48 inference(resolution,[status(thm)],[f1022,f30])).
% 0.09/0.48 fof(f1033,plain,(
% 0.09/0.48 $false|~sQ81_spl),
% 0.09/0.48 inference(forward_subsumption_resolution,[status(thm)],[f1030,f50])).
% 0.09/0.48 fof(f1034,plain,(
% 0.09/0.48 ~sQ81_spl),
% 0.09/0.48 inference(contradiction_clause,[status(thm)],[f1033])).
% 0.09/0.48 fof(f1035,plain,(
% 0.09/0.48 $false),
% 0.09/0.48 inference(sat_refutation,[status(thm)],[f88,f448,f541,f546,f1024,f1029,f1034])).
% 0.09/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.49 % Elapsed time: 0.116526 seconds
% 0.09/0.49 % CPU time: 0.696807 seconds
% 0.09/0.49 % Total memory used: 25.843 MB
% 0.09/0.49 % Net memory used: 23.992 MB
%------------------------------------------------------------------------------