%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO204+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 : n011.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 12:26:05 PM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+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
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 13:22:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.42 fof(f1,axiom,(
% 0.09/0.42 (! [X] : ~ distinct_points(X,X) )),
% 0.09/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.42 fof(f4,axiom,(
% 0.09/0.42 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.09/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.42 fof(f7,axiom,(
% 0.09/0.42 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.09/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.42 fof(f8,axiom,(
% 0.09/0.42 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.09/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.42 fof(f11,axiom,(
% 0.09/0.42 (! [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) ) ) )),
% 0.09/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.42 fof(f12,axiom,(
% 0.09/0.42 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 0.09/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.42 fof(f31,axiom,(
% 0.09/0.42 (! [X,Y] :( equal_points(X,Y)<=> ~ distinct_points(X,Y) ) )),
% 0.09/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.42 fof(f32,axiom,(
% 0.09/0.42 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 0.09/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.42 fof(f36,conjecture,(
% 0.09/0.42 (! [X,Y,Z] :( ( distinct_points(X,Y)& equal_points(Y,Z) )=> ( distinct_points(X,Z)& equal_lines(line_connecting(X,Y),line_connecting(X,Z)) ) ) )),
% 0.09/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.42 fof(f37,negated_conjecture,(
% 0.09/0.42 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& equal_points(Y,Z) )=> ( distinct_points(X,Z)& equal_lines(line_connecting(X,Y),line_connecting(X,Z)) ) ) ))),
% 0.09/0.42 inference(negated_conjecture,[status(cth)],[f36])).
% 0.09/0.42 fof(f38,plain,(
% 0.09/0.42 ![X0]: (~distinct_points(X0,X0))),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.42 fof(f41,plain,(
% 0.09/0.42 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.09/0.42 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.09/0.42 fof(f42,plain,(
% 0.09/0.42 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.09/0.42 inference(miniscoping,[status(thm)],[f41])).
% 0.09/0.42 fof(f43,plain,(
% 0.09/0.42 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f42])).
% 0.09/0.42 fof(f50,plain,(
% 0.09/0.42 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.09/0.42 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.09/0.42 fof(f51,plain,(
% 0.09/0.42 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f50])).
% 0.09/0.42 fof(f52,plain,(
% 0.09/0.42 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.09/0.42 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.09/0.42 fof(f53,plain,(
% 0.09/0.42 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f52])).
% 0.09/0.42 fof(f58,plain,(
% 0.09/0.42 ![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)))),
% 0.09/0.42 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.09/0.42 fof(f59,plain,(
% 0.09/0.42 ![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))),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f58])).
% 0.09/0.42 fof(f60,plain,(
% 0.09/0.42 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 0.09/0.42 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.09/0.42 fof(f61,plain,(
% 0.09/0.42 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 0.09/0.42 inference(miniscoping,[status(thm)],[f60])).
% 0.09/0.42 fof(f62,plain,(
% 0.09/0.42 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f61])).
% 0.09/0.42 fof(f107,plain,(
% 0.09/0.42 ![X,Y]: ((~equal_points(X,Y)|~distinct_points(X,Y))&(equal_points(X,Y)|distinct_points(X,Y)))),
% 0.09/0.42 inference(NNF_transformation,[status(thm)],[f31])).
% 0.09/0.42 fof(f108,plain,(
% 0.09/0.42 (![X,Y]: (~equal_points(X,Y)|~distinct_points(X,Y)))&(![X,Y]: (equal_points(X,Y)|distinct_points(X,Y)))),
% 0.09/0.42 inference(miniscoping,[status(thm)],[f107])).
% 0.09/0.42 fof(f109,plain,(
% 0.09/0.42 ![X0,X1]: (~equal_points(X0,X1)|~distinct_points(X0,X1))),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f108])).
% 0.09/0.42 fof(f111,plain,(
% 0.09/0.42 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.09/0.42 inference(NNF_transformation,[status(thm)],[f32])).
% 0.09/0.42 fof(f112,plain,(
% 0.09/0.42 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.09/0.42 inference(miniscoping,[status(thm)],[f111])).
% 0.09/0.42 fof(f114,plain,(
% 0.09/0.42 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f112])).
% 0.09/0.42 fof(f127,plain,(
% 0.09/0.42 (?[X,Y,Z]: ((distinct_points(X,Y)&equal_points(Y,Z))&(~distinct_points(X,Z)|~equal_lines(line_connecting(X,Y),line_connecting(X,Z)))))),
% 0.09/0.42 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.09/0.42 fof(f128,plain,(
% 0.09/0.42 ((distinct_points(sK0_skl,sK1_skl)&equal_points(sK1_skl,sK2_skl))&(~distinct_points(sK0_skl,sK2_skl)|~equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))))),
% 0.09/0.42 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])).
% 0.09/0.42 fof(f129,plain,(
% 0.09/0.42 distinct_points(sK0_skl,sK1_skl)),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f128])).
% 0.09/0.42 fof(f130,plain,(
% 0.09/0.42 equal_points(sK1_skl,sK2_skl)),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f128])).
% 0.09/0.42 fof(f131,plain,(
% 0.09/0.42 ~distinct_points(sK0_skl,sK2_skl)|~equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))),
% 0.09/0.42 inference(cnf_transformation,[status(thm)],[f128])).
% 0.09/0.42 fof(f142,definition,(
% 0.09/0.42 sQ0_spl <=> (distinct_points(sK0_skl,sK2_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f144,plain,(
% 0.09/0.42 ~distinct_points(sK0_skl,sK2_skl)|sQ0_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f142])).
% 0.09/0.42 fof(f145,definition,(
% 0.09/0.42 sQ1_spl <=> (equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f147,plain,(
% 0.09/0.42 ~equal_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))|sQ1_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f145])).
% 0.09/0.42 fof(f148,plain,(
% 0.09/0.42 ~sQ0_spl|~sQ1_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f131,f142,f145])).
% 0.09/0.42 fof(f149,plain,(
% 0.09/0.42 ~distinct_points(sK1_skl,sK2_skl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f109,f130])).
% 0.09/0.42 fof(f152,plain,(
% 0.09/0.42 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.09/0.42 inference(resolution,[status(thm)],[f43,f129])).
% 0.09/0.42 fof(f155,plain,(
% 0.09/0.42 distinct_points(sK0_skl,sK2_skl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f152,f149])).
% 0.09/0.42 fof(f158,plain,(
% 0.09/0.42 $false|sQ0_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f155,f144])).
% 0.09/0.42 fof(f159,plain,(
% 0.09/0.42 sQ0_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f158])).
% 0.09/0.42 fof(f161,plain,(
% 0.09/0.42 distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))|sQ1_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f147,f114])).
% 0.09/0.42 fof(f191,definition,(
% 0.09/0.42 sQ6_spl <=> (distinct_points(sK1_skl,sK2_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f192,plain,(
% 0.09/0.42 distinct_points(sK1_skl,sK2_skl)|~sQ6_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f191])).
% 0.09/0.42 fof(f206,plain,(
% 0.09/0.42 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,line_connecting(sK0_skl,sK2_skl))|sQ1_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f59,f161])).
% 0.09/0.42 fof(f319,definition,(
% 0.09/0.42 sQ11_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f320,plain,(
% 0.09/0.42 distinct_points(sK1_skl,sK1_skl)|~sQ11_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f319])).
% 0.09/0.42 fof(f346,plain,(
% 0.09/0.42 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))|sQ1_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f206,f129])).
% 0.09/0.42 fof(f383,definition,(
% 0.09/0.42 sQ14_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f384,plain,(
% 0.09/0.42 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ14_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f383])).
% 0.09/0.42 fof(f386,definition,(
% 0.09/0.42 sQ15_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f387,plain,(
% 0.09/0.42 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|~sQ15_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f386])).
% 0.09/0.42 fof(f403,definition,(
% 0.09/0.42 sQ19_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f404,plain,(
% 0.09/0.42 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ19_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f403])).
% 0.09/0.42 fof(f406,definition,(
% 0.09/0.42 sQ20_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.09/0.42 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.09/0.42 fof(f407,plain,(
% 0.09/0.42 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))|~sQ20_spl),
% 0.09/0.42 inference(component_clause,[status(thm)],[f406])).
% 0.09/0.42 fof(f409,plain,(
% 0.09/0.42 sQ14_spl|sQ15_spl|sQ19_spl|sQ20_spl|sQ1_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f346,f383,f386,f403,f406,f145])).
% 0.09/0.42 fof(f522,plain,(
% 0.09/0.42 ~distinct_points(sK0_skl,sK2_skl)|~sQ15_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f387,f51])).
% 0.09/0.42 fof(f525,plain,(
% 0.09/0.42 ~sQ0_spl|~sQ15_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f522,f142,f386])).
% 0.09/0.42 fof(f526,plain,(
% 0.09/0.42 $false|~sQ6_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f192,f149])).
% 0.09/0.42 fof(f527,plain,(
% 0.09/0.42 ~sQ6_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f526])).
% 0.09/0.42 fof(f528,plain,(
% 0.09/0.42 ~distinct_points(sK0_skl,sK1_skl)|~sQ14_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f384,f51])).
% 0.09/0.42 fof(f531,plain,(
% 0.09/0.42 $false|~sQ14_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f528,f129])).
% 0.09/0.42 fof(f532,plain,(
% 0.09/0.42 ~sQ14_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f531])).
% 0.09/0.42 fof(f533,plain,(
% 0.09/0.42 ~distinct_points(sK0_skl,sK1_skl)|~sQ19_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f404,f53])).
% 0.09/0.42 fof(f536,plain,(
% 0.09/0.42 $false|~sQ19_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f533,f129])).
% 0.09/0.42 fof(f537,plain,(
% 0.09/0.42 ~sQ19_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f536])).
% 0.09/0.42 fof(f541,plain,(
% 0.09/0.42 ![X0]: (distinct_points(sK1_skl,X0)|apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))|~sQ20_spl)),
% 0.09/0.42 inference(resolution,[status(thm)],[f407,f62])).
% 0.09/0.42 fof(f752,plain,(
% 0.09/0.42 $false|~sQ11_spl),
% 0.09/0.42 inference(forward_subsumption_resolution,[status(thm)],[f320,f38])).
% 0.09/0.42 fof(f753,plain,(
% 0.09/0.42 ~sQ11_spl),
% 0.09/0.42 inference(contradiction_clause,[status(thm)],[f752])).
% 0.09/0.42 fof(f1106,plain,(
% 0.09/0.42 distinct_points(sK1_skl,sK2_skl)|~distinct_points(sK0_skl,sK2_skl)|~sQ20_spl),
% 0.09/0.42 inference(resolution,[status(thm)],[f541,f53])).
% 0.09/0.42 fof(f1111,plain,(
% 0.09/0.42 sQ6_spl|~sQ0_spl|~sQ20_spl),
% 0.09/0.42 inference(split_clause,[status(thm)],[f1106,f191,f142,f406])).
% 0.09/0.42 fof(f1113,plain,(
% 0.09/0.42 $false),
% 0.09/0.42 inference(sat_refutation,[status(thm)],[f148,f159,f409,f525,f527,f532,f537,f753,f1111])).
% 0.09/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.44 % Elapsed time: 0.060856 seconds
% 0.09/0.44 % CPU time: 0.212777 seconds
% 0.09/0.44 % Total memory used: 19.802 MB
% 0.09/0.44 % Net memory used: 19.479 MB
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