%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO184+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:25:59 PM UTC 2026
% Result : Theorem 0.03s 5.32s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO184+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/5.30 % Computer : n012.cluster.edu
% 0.03/5.30 % Model : x86_64 x86_64
% 0.03/5.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.30 % Memory : 8046.5625MB
% 0.03/5.30 % OS : Linux 6.8.0-71-generic
% 0.03/5.31 % CPULimit : 300
% 0.03/5.31 % WCLimit : 300
% 0.03/5.31 % DateTime : Sun Sep 20 13:08:13 UTC 2026
% 0.03/5.31 % CPUTime :
% 0.03/5.31 % Drodi V4.1.1
% 0.03/5.32 % Refutation found
% 0.03/5.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/5.32 % SZS output start CNFRefutation for theBenchmark
% 0.03/5.32 fof(f1,axiom,(
% 0.03/5.32 (! [X] : ~ distinct_points(X,X) )),
% 0.03/5.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/5.32 fof(f4,axiom,(
% 0.03/5.32 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.03/5.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/5.32 fof(f7,axiom,(
% 0.03/5.32 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 0.03/5.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/5.32 fof(f9,axiom,(
% 0.03/5.32 (! [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) ) ) )),
% 0.03/5.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/5.32 fof(f13,conjecture,(
% 0.03/5.32 (! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& ~ apart_point_and_line(X,U)& ~ apart_point_and_line(Y,U) )=> ~ distinct_lines(U,line_connecting(X,Y)) ) )),
% 0.03/5.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.03/5.32 fof(f14,negated_conjecture,(
% 0.03/5.32 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& ~ apart_point_and_line(X,U)& ~ apart_point_and_line(Y,U) )=> ~ distinct_lines(U,line_connecting(X,Y)) ) ))),
% 0.03/5.32 inference(negated_conjecture,[status(cth)],[f13])).
% 0.03/5.32 fof(f15,plain,(
% 0.03/5.32 ![X0]: (~distinct_points(X0,X0))),
% 0.03/5.32 inference(cnf_transformation,[status(thm)],[f1])).
% 0.03/5.32 fof(f18,plain,(
% 0.03/5.32 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.03/5.32 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.03/5.32 fof(f19,plain,(
% 0.03/5.32 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.03/5.32 inference(miniscoping,[status(thm)],[f18])).
% 0.03/5.32 fof(f20,plain,(
% 0.03/5.32 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.03/5.32 inference(cnf_transformation,[status(thm)],[f19])).
% 0.03/5.32 fof(f27,plain,(
% 0.03/5.32 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 0.03/5.32 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.03/5.32 fof(f28,plain,(
% 0.03/5.32 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 0.03/5.32 inference(miniscoping,[status(thm)],[f27])).
% 0.03/5.32 fof(f29,plain,(
% 0.03/5.32 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 0.03/5.32 inference(cnf_transformation,[status(thm)],[f28])).
% 0.03/5.32 fof(f30,plain,(
% 0.03/5.32 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 0.03/5.32 inference(cnf_transformation,[status(thm)],[f28])).
% 0.03/5.32 fof(f35,plain,(
% 0.03/5.32 ![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)))),
% 0.03/5.32 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.03/5.32 fof(f36,plain,(
% 0.03/5.32 ![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))),
% 0.03/5.32 inference(cnf_transformation,[status(thm)],[f35])).
% 0.03/5.32 fof(f45,plain,(
% 0.03/5.32 (?[X,Y,U,V]: ((((distinct_points(X,Y)&convergent_lines(U,V))&~apart_point_and_line(X,U))&~apart_point_and_line(Y,U))&distinct_lines(U,line_connecting(X,Y))))),
% 0.03/5.32 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.03/5.32 fof(f46,plain,(
% 0.03/5.32 ?[X,Y,U]: ((((distinct_points(X,Y)&(?[V]: convergent_lines(U,V)))&~apart_point_and_line(X,U))&~apart_point_and_line(Y,U))&distinct_lines(U,line_connecting(X,Y)))),
% 0.03/5.32 inference(miniscoping,[status(thm)],[f45])).
% 0.03/5.32 fof(f47,plain,(
% 0.03/5.32 ((((distinct_points(sK0_skl,sK1_skl)&convergent_lines(sK2_skl,sK3_skl))&~apart_point_and_line(sK0_skl,sK2_skl))&~apart_point_and_line(sK1_skl,sK2_skl))&distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.03/5.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(U,sK2_skl),skolemize(V,sK3_skl)],[f46])).
% 0.03/5.32 fof(f48,plain,(
% 0.03/5.32 distinct_points(sK0_skl,sK1_skl)),
% 0.03/5.32 inference(cnf_transformation,[status(thm)],[f47])).
% 0.03/5.32 fof(f50,plain,(
% 0.03/5.32 ~apart_point_and_line(sK0_skl,sK2_skl)),
% 0.03/5.32 inference(cnf_transformation,[status(thm)],[f47])).
% 0.03/5.32 fof(f51,plain,(
% 0.03/5.32 ~apart_point_and_line(sK1_skl,sK2_skl)),
% 0.03/5.32 inference(cnf_transformation,[status(thm)],[f47])).
% 0.03/5.32 fof(f52,plain,(
% 0.03/5.32 distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.03/5.32 inference(cnf_transformation,[status(thm)],[f47])).
% 0.03/5.32 fof(f54,plain,(
% 0.03/5.32 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.03/5.32 inference(resolution,[status(thm)],[f20,f48])).
% 0.03/5.32 fof(f57,plain,(
% 0.03/5.32 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.03/5.32 inference(resolution,[status(thm)],[f54,f20])).
% 0.03/5.32 fof(f73,plain,(
% 0.03/5.32 distinct_points(sK1_skl,sK0_skl)),
% 0.03/5.32 inference(resolution,[status(thm)],[f57,f15])).
% 0.03/5.32 fof(f88,definition,(
% 0.03/5.32 sQ2_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.03/5.32 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.03/5.32 fof(f90,plain,(
% 0.03/5.32 ~distinct_points(sK0_skl,sK1_skl)|sQ2_spl),
% 0.03/5.32 inference(component_clause,[status(thm)],[f88])).
% 0.03/5.32 fof(f154,plain,(
% 0.03/5.32 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,sK2_skl)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl)))),
% 0.03/5.32 inference(resolution,[status(thm)],[f36,f52])).
% 0.03/5.32 fof(f156,plain,(
% 0.03/5.32 apart_point_and_line(sK1_skl,sK2_skl)|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,sK2_skl)|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.03/5.32 inference(resolution,[status(thm)],[f154,f73])).
% 0.03/5.32 fof(f167,definition,(
% 0.03/5.32 sQ10_spl <=> (apart_point_and_line(sK1_skl,sK2_skl))),
% 0.03/5.32 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.03/5.32 fof(f168,plain,(
% 0.03/5.32 apart_point_and_line(sK1_skl,sK2_skl)|~sQ10_spl),
% 0.03/5.32 inference(component_clause,[status(thm)],[f167])).
% 0.03/5.32 fof(f170,definition,(
% 0.03/5.32 sQ11_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.03/5.32 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.03/5.32 fof(f171,plain,(
% 0.03/5.32 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ11_spl),
% 0.03/5.32 inference(component_clause,[status(thm)],[f170])).
% 0.03/5.32 fof(f173,definition,(
% 0.03/5.32 sQ12_spl <=> (apart_point_and_line(sK0_skl,sK2_skl))),
% 0.03/5.32 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.03/5.32 fof(f174,plain,(
% 0.03/5.32 apart_point_and_line(sK0_skl,sK2_skl)|~sQ12_spl),
% 0.03/5.32 inference(component_clause,[status(thm)],[f173])).
% 0.03/5.32 fof(f176,definition,(
% 0.03/5.32 sQ13_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.03/5.32 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.03/5.32 fof(f177,plain,(
% 0.03/5.32 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ13_spl),
% 0.03/5.32 inference(component_clause,[status(thm)],[f176])).
% 0.03/5.32 fof(f179,plain,(
% 0.03/5.32 sQ10_spl|sQ11_spl|sQ12_spl|sQ13_spl),
% 0.03/5.32 inference(split_clause,[status(thm)],[f156,f167,f170,f173,f176])).
% 0.03/5.32 fof(f208,plain,(
% 0.03/5.32 $false|~sQ12_spl),
% 0.03/5.32 inference(forward_subsumption_resolution,[status(thm)],[f174,f50])).
% 0.03/5.32 fof(f209,plain,(
% 0.03/5.32 ~sQ12_spl),
% 0.03/5.32 inference(contradiction_clause,[status(thm)],[f208])).
% 0.03/5.32 fof(f217,plain,(
% 0.03/5.32 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ13_spl),
% 0.03/5.32 inference(resolution,[status(thm)],[f177,f29])).
% 0.03/5.32 fof(f222,definition,(
% 0.03/5.32 sQ20_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 0.03/5.32 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.03/5.32 fof(f223,plain,(
% 0.03/5.32 distinct_points(sK0_skl,sK0_skl)|~sQ20_spl),
% 0.03/5.32 inference(component_clause,[status(thm)],[f222])).
% 0.03/5.32 fof(f225,plain,(
% 0.03/5.32 ~sQ2_spl|sQ20_spl|~sQ13_spl),
% 0.03/5.32 inference(split_clause,[status(thm)],[f217,f88,f222,f176])).
% 0.03/5.32 fof(f226,plain,(
% 0.03/5.32 $false|sQ2_spl),
% 0.03/5.32 inference(forward_subsumption_resolution,[status(thm)],[f90,f48])).
% 0.03/5.32 fof(f227,plain,(
% 0.03/5.32 sQ2_spl),
% 0.03/5.32 inference(contradiction_clause,[status(thm)],[f226])).
% 0.03/5.32 fof(f228,plain,(
% 0.03/5.32 $false|~sQ20_spl),
% 0.03/5.32 inference(forward_subsumption_resolution,[status(thm)],[f223,f15])).
% 0.03/5.33 fof(f229,plain,(
% 0.03/5.33 ~sQ20_spl),
% 0.03/5.33 inference(contradiction_clause,[status(thm)],[f228])).
% 0.03/5.33 fof(f230,plain,(
% 0.03/5.33 $false|~sQ10_spl),
% 0.03/5.33 inference(forward_subsumption_resolution,[status(thm)],[f168,f51])).
% 0.03/5.33 fof(f231,plain,(
% 0.03/5.33 ~sQ10_spl),
% 0.03/5.33 inference(contradiction_clause,[status(thm)],[f230])).
% 0.03/5.33 fof(f232,plain,(
% 0.03/5.33 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ11_spl),
% 0.03/5.33 inference(resolution,[status(thm)],[f171,f30])).
% 0.03/5.33 fof(f237,definition,(
% 0.03/5.33 sQ21_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 0.03/5.33 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.03/5.33 fof(f238,plain,(
% 0.03/5.33 distinct_points(sK1_skl,sK1_skl)|~sQ21_spl),
% 0.03/5.33 inference(component_clause,[status(thm)],[f237])).
% 0.03/5.33 fof(f240,plain,(
% 0.03/5.33 ~sQ2_spl|sQ21_spl|~sQ11_spl),
% 0.03/5.33 inference(split_clause,[status(thm)],[f232,f88,f237,f170])).
% 0.03/5.33 fof(f242,plain,(
% 0.03/5.33 $false|~sQ21_spl),
% 0.03/5.33 inference(forward_subsumption_resolution,[status(thm)],[f238,f15])).
% 0.03/5.33 fof(f243,plain,(
% 0.03/5.33 ~sQ21_spl),
% 0.03/5.33 inference(contradiction_clause,[status(thm)],[f242])).
% 0.03/5.33 fof(f244,plain,(
% 0.03/5.33 $false),
% 0.03/5.33 inference(sat_refutation,[status(thm)],[f179,f209,f225,f227,f229,f231,f240,f243])).
% 0.03/5.33 % SZS output end CNFRefutation for theBenchmark.p
% 0.03/5.34 % Elapsed time: 0.028243 seconds
% 0.03/5.34 % CPU time: 0.072309 seconds
% 0.03/5.34 % Total memory used: 13.236 MB
% 0.03/5.34 % Net memory used: 12.927 MB
%------------------------------------------------------------------------------