%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO200+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 : n005.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 12:26:04 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO200+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.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 13:20:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.38 fof(f1,axiom,(
% 0.09/0.38 (! [X] : ~ distinct_points(X,X) )),
% 0.09/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f4,axiom,(
% 0.09/0.38 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.09/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f7,axiom,(
% 0.09/0.38 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.09/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f8,axiom,(
% 0.09/0.38 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.09/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f11,axiom,(
% 0.09/0.38 (! [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) ) ) )),
% 0.09/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f32,axiom,(
% 0.09/0.38 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 0.09/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f36,conjecture,(
% 0.09/0.38 (! [X,Y] :( distinct_points(X,Y)=> equal_lines(line_connecting(X,Y),line_connecting(Y,X)) ) )),
% 0.09/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.38 fof(f37,negated_conjecture,(
% 0.09/0.38 ~((! [X,Y] :( distinct_points(X,Y)=> equal_lines(line_connecting(X,Y),line_connecting(Y,X)) ) ))),
% 0.09/0.38 inference(negated_conjecture,[status(cth)],[f36])).
% 0.09/0.38 fof(f38,plain,(
% 0.09/0.38 ![X0]: (~distinct_points(X0,X0))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.38 fof(f41,plain,(
% 0.09/0.38 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.09/0.38 fof(f42,plain,(
% 0.09/0.38 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.09/0.38 inference(miniscoping,[status(thm)],[f41])).
% 0.09/0.38 fof(f43,plain,(
% 0.09/0.38 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f42])).
% 0.09/0.38 fof(f50,plain,(
% 0.09/0.38 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.09/0.38 fof(f51,plain,(
% 0.09/0.38 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f50])).
% 0.09/0.38 fof(f52,plain,(
% 0.09/0.38 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.09/0.38 fof(f53,plain,(
% 0.09/0.38 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f52])).
% 0.09/0.38 fof(f58,plain,(
% 0.09/0.38 ![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)))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.09/0.38 fof(f59,plain,(
% 0.09/0.38 ![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))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f58])).
% 0.09/0.38 fof(f111,plain,(
% 0.09/0.38 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.09/0.38 inference(NNF_transformation,[status(thm)],[f32])).
% 0.09/0.38 fof(f112,plain,(
% 0.09/0.38 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.09/0.38 inference(miniscoping,[status(thm)],[f111])).
% 0.09/0.38 fof(f114,plain,(
% 0.09/0.38 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f112])).
% 0.09/0.38 fof(f127,plain,(
% 0.09/0.38 (?[X,Y]: (distinct_points(X,Y)&~equal_lines(line_connecting(X,Y),line_connecting(Y,X))))),
% 0.09/0.38 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.09/0.38 fof(f128,plain,(
% 0.09/0.38 (distinct_points(sK0_skl,sK1_skl)&~equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl)))),
% 0.09/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f127])).
% 0.09/0.38 fof(f129,plain,(
% 0.09/0.38 distinct_points(sK0_skl,sK1_skl)),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f128])).
% 0.09/0.38 fof(f130,plain,(
% 0.09/0.38 ~equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl))),
% 0.09/0.38 inference(cnf_transformation,[status(thm)],[f128])).
% 0.09/0.38 fof(f141,plain,(
% 0.09/0.38 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.09/0.38 inference(resolution,[status(thm)],[f43,f129])).
% 0.09/0.38 fof(f142,plain,(
% 0.09/0.38 distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK1_skl,sK0_skl))),
% 0.09/0.38 inference(resolution,[status(thm)],[f114,f130])).
% 0.09/0.38 fof(f144,plain,(
% 0.09/0.38 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.09/0.38 inference(resolution,[status(thm)],[f141,f43])).
% 0.09/0.38 fof(f150,plain,(
% 0.09/0.38 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X0,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,line_connecting(sK1_skl,sK0_skl)))),
% 0.09/0.38 inference(resolution,[status(thm)],[f142,f59])).
% 0.09/0.38 fof(f153,plain,(
% 0.09/0.38 distinct_points(sK1_skl,sK0_skl)),
% 0.09/0.38 inference(resolution,[status(thm)],[f144,f38])).
% 0.09/0.38 fof(f212,plain,(
% 0.09/0.38 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))),
% 0.09/0.38 inference(resolution,[status(thm)],[f150,f153])).
% 0.09/0.38 fof(f236,definition,(
% 0.09/0.38 sQ5_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.09/0.38 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.09/0.38 fof(f237,plain,(
% 0.09/0.38 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ5_spl),
% 0.09/0.38 inference(component_clause,[status(thm)],[f236])).
% 0.09/0.38 fof(f239,definition,(
% 0.09/0.38 sQ6_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.09/0.38 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.38 fof(f240,plain,(
% 0.09/0.38 apart_point_and_line(sK1_skl,line_connecting(sK1_skl,sK0_skl))|~sQ6_spl),
% 0.09/0.38 inference(component_clause,[status(thm)],[f239])).
% 0.09/0.38 fof(f242,definition,(
% 0.09/0.38 sQ7_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.09/0.38 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.38 fof(f243,plain,(
% 0.09/0.38 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ7_spl),
% 0.09/0.38 inference(component_clause,[status(thm)],[f242])).
% 0.09/0.38 fof(f245,definition,(
% 0.09/0.38 sQ8_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl)))),
% 0.09/0.38 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/0.38 fof(f246,plain,(
% 0.09/0.38 apart_point_and_line(sK0_skl,line_connecting(sK1_skl,sK0_skl))|~sQ8_spl),
% 0.09/0.38 inference(component_clause,[status(thm)],[f245])).
% 0.09/0.38 fof(f248,plain,(
% 0.09/0.38 sQ5_spl|sQ6_spl|sQ7_spl|sQ8_spl),
% 0.09/0.38 inference(split_clause,[status(thm)],[f212,f236,f239,f242,f245])).
% 0.09/0.38 fof(f354,plain,(
% 0.09/0.38 ~distinct_points(sK1_skl,sK0_skl)|~sQ6_spl),
% 0.09/0.38 inference(resolution,[status(thm)],[f240,f51])).
% 0.09/0.38 fof(f357,plain,(
% 0.09/0.38 $false|~sQ6_spl),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f354,f153])).
% 0.09/0.38 fof(f358,plain,(
% 0.09/0.38 ~sQ6_spl),
% 0.09/0.38 inference(contradiction_clause,[status(thm)],[f357])).
% 0.09/0.38 fof(f359,plain,(
% 0.09/0.38 ~distinct_points(sK1_skl,sK0_skl)|~sQ8_spl),
% 0.09/0.38 inference(resolution,[status(thm)],[f246,f53])).
% 0.09/0.38 fof(f362,plain,(
% 0.09/0.38 $false|~sQ8_spl),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f359,f153])).
% 0.09/0.38 fof(f363,plain,(
% 0.09/0.38 ~sQ8_spl),
% 0.09/0.38 inference(contradiction_clause,[status(thm)],[f362])).
% 0.09/0.38 fof(f422,plain,(
% 0.09/0.38 ~distinct_points(sK0_skl,sK1_skl)|~sQ5_spl),
% 0.09/0.38 inference(resolution,[status(thm)],[f237,f53])).
% 0.09/0.38 fof(f425,plain,(
% 0.09/0.38 $false|~sQ5_spl),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f422,f129])).
% 0.09/0.38 fof(f426,plain,(
% 0.09/0.38 ~sQ5_spl),
% 0.09/0.38 inference(contradiction_clause,[status(thm)],[f425])).
% 0.09/0.38 fof(f427,plain,(
% 0.09/0.38 ~distinct_points(sK0_skl,sK1_skl)|~sQ7_spl),
% 0.09/0.38 inference(resolution,[status(thm)],[f243,f51])).
% 0.09/0.38 fof(f430,plain,(
% 0.09/0.38 $false|~sQ7_spl),
% 0.09/0.38 inference(forward_subsumption_resolution,[status(thm)],[f427,f129])).
% 0.09/0.38 fof(f431,plain,(
% 0.09/0.38 ~sQ7_spl),
% 0.09/0.38 inference(contradiction_clause,[status(thm)],[f430])).
% 0.09/0.38 fof(f432,plain,(
% 0.09/0.38 $false),
% 0.09/0.38 inference(sat_refutation,[status(thm)],[f248,f358,f363,f426,f431])).
% 0.09/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.40 % Elapsed time: 0.030159 seconds
% 0.09/0.40 % CPU time: 0.058367 seconds
% 0.09/0.40 % Total memory used: 4.320 MB
% 0.09/0.40 % Net memory used: 4.271 MB
%------------------------------------------------------------------------------