%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO186+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 : n002.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 12:26:00 PM UTC 2026
% Result : Theorem 0.13s 5.67s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO186+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
% 0.09/5.37 % Computer : n002.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 13:10:07 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.13/5.67 % Refutation found
% 0.13/5.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.67 % SZS output start CNFRefutation for theBenchmark
% 0.13/5.67 fof(f1,axiom,(
% 0.13/5.67 (! [X] : ~ distinct_points(X,X) )),
% 0.13/5.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.67 fof(f4,axiom,(
% 0.13/5.67 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.13/5.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.67 fof(f8,axiom,(
% 0.13/5.67 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( ( apart_point_and_line(Z,X)| apart_point_and_line(Z,Y) )=> distinct_points(Z,intersection_point(X,Y)) ) ) )),
% 0.13/5.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.67 fof(f9,axiom,(
% 0.13/5.67 (! [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) ) ) )),
% 0.13/5.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.67 fof(f12,axiom,(
% 0.13/5.67 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 0.13/5.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.67 fof(f13,conjecture,(
% 0.13/5.67 (! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& ~ apart_point_and_line(X,U)& ~ apart_point_and_line(X,V) )=> ~ distinct_points(X,intersection_point(U,V)) ) )),
% 0.13/5.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/5.67 fof(f14,negated_conjecture,(
% 0.13/5.67 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& ~ apart_point_and_line(X,U)& ~ apart_point_and_line(X,V) )=> ~ distinct_points(X,intersection_point(U,V)) ) ))),
% 0.13/5.67 inference(negated_conjecture,[status(cth)],[f13])).
% 0.13/5.67 fof(f15,plain,(
% 0.13/5.67 ![X0]: (~distinct_points(X0,X0))),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/5.67 fof(f18,plain,(
% 0.13/5.67 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.13/5.67 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/5.67 fof(f19,plain,(
% 0.13/5.67 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.13/5.67 inference(miniscoping,[status(thm)],[f18])).
% 0.13/5.67 fof(f20,plain,(
% 0.13/5.67 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/5.67 fof(f31,plain,(
% 0.13/5.67 ![X,Y,Z]: (~convergent_lines(X,Y)|((~apart_point_and_line(Z,X)&~apart_point_and_line(Z,Y))|distinct_points(Z,intersection_point(X,Y))))),
% 0.13/5.67 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.13/5.67 fof(f32,plain,(
% 0.13/5.67 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: ((~apart_point_and_line(Z,X)&~apart_point_and_line(Z,Y))|distinct_points(Z,intersection_point(X,Y)))))),
% 0.13/5.67 inference(miniscoping,[status(thm)],[f31])).
% 0.13/5.67 fof(f33,plain,(
% 0.13/5.67 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f32])).
% 0.13/5.67 fof(f34,plain,(
% 0.13/5.67 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f32])).
% 0.13/5.67 fof(f35,plain,(
% 0.13/5.67 ![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)))),
% 0.13/5.67 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.13/5.67 fof(f36,plain,(
% 0.13/5.67 ![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))),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f35])).
% 0.13/5.67 fof(f43,plain,(
% 0.13/5.67 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 0.13/5.67 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.13/5.67 fof(f44,plain,(
% 0.13/5.67 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f43])).
% 0.13/5.67 fof(f45,plain,(
% 0.13/5.67 (?[X,Y,U,V]: ((((distinct_points(X,Y)&convergent_lines(U,V))&~apart_point_and_line(X,U))&~apart_point_and_line(X,V))&distinct_points(X,intersection_point(U,V))))),
% 0.13/5.67 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.13/5.67 fof(f46,plain,(
% 0.13/5.67 ?[X,U,V]: (((((?[Y]: distinct_points(X,Y))&convergent_lines(U,V))&~apart_point_and_line(X,U))&~apart_point_and_line(X,V))&distinct_points(X,intersection_point(U,V)))),
% 0.13/5.67 inference(miniscoping,[status(thm)],[f45])).
% 0.13/5.67 fof(f47,plain,(
% 0.13/5.67 ((((distinct_points(sK0_skl,sK3_skl)&convergent_lines(sK1_skl,sK2_skl))&~apart_point_and_line(sK0_skl,sK1_skl))&~apart_point_and_line(sK0_skl,sK2_skl))&distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl)))),
% 0.13/5.67 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(U,sK1_skl),skolemize(V,sK2_skl),skolemize(Y,sK3_skl)],[f46])).
% 0.13/5.67 fof(f49,plain,(
% 0.13/5.67 convergent_lines(sK1_skl,sK2_skl)),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/5.67 fof(f50,plain,(
% 0.13/5.67 ~apart_point_and_line(sK0_skl,sK1_skl)),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/5.67 fof(f51,plain,(
% 0.13/5.67 ~apart_point_and_line(sK0_skl,sK2_skl)),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/5.67 fof(f52,plain,(
% 0.13/5.67 distinct_points(sK0_skl,intersection_point(sK1_skl,sK2_skl))),
% 0.13/5.67 inference(cnf_transformation,[status(thm)],[f47])).
% 0.13/5.67 fof(f53,plain,(
% 0.13/5.67 ![X0]: (~apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK1_skl,sK2_skl)))),
% 0.13/5.67 inference(resolution,[status(thm)],[f33,f49])).
% 0.13/5.67 fof(f54,plain,(
% 0.13/5.67 ![X0]: (~apart_point_and_line(X0,sK2_skl)|distinct_points(X0,intersection_point(sK1_skl,sK2_skl)))),
% 0.13/5.67 inference(resolution,[status(thm)],[f34,f49])).
% 0.13/5.67 fof(f55,plain,(
% 0.13/5.67 distinct_lines(sK1_skl,sK2_skl)),
% 0.13/5.67 inference(resolution,[status(thm)],[f44,f49])).
% 0.13/5.67 fof(f56,plain,(
% 0.13/5.67 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(intersection_point(sK1_skl,sK2_skl),X0))),
% 0.13/5.67 inference(resolution,[status(thm)],[f20,f52])).
% 0.13/5.67 fof(f58,plain,(
% 0.13/5.67 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(intersection_point(sK1_skl,sK2_skl),X1)|distinct_points(X0,X1))),
% 0.13/5.67 inference(resolution,[status(thm)],[f56,f20])).
% 0.13/5.67 fof(f678,plain,(
% 0.13/5.67 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X1,sK1_skl)|apart_point_and_line(X1,sK2_skl))),
% 0.13/5.67 inference(resolution,[status(thm)],[f36,f55])).
% 0.13/5.67 fof(f739,plain,(
% 0.13/5.67 ![X0,X1]: (apart_point_and_line(sK0_skl,sK1_skl)|apart_point_and_line(sK0_skl,sK2_skl)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK2_skl)|distinct_points(intersection_point(sK1_skl,sK2_skl),X1)|distinct_points(X0,X1))),
% 0.13/5.67 inference(resolution,[status(thm)],[f678,f58])).
% 0.13/5.67 fof(f822,definition,(
% 0.13/5.67 sQ40_spl <=> (apart_point_and_line(sK0_skl,sK1_skl))),
% 0.13/5.67 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.13/5.67 fof(f823,plain,(
% 0.13/5.67 apart_point_and_line(sK0_skl,sK1_skl)|~sQ40_spl),
% 0.13/5.67 inference(component_clause,[status(thm)],[f822])).
% 0.13/5.67 fof(f825,definition,(
% 0.13/5.67 sQ41_spl <=> (apart_point_and_line(sK0_skl,sK2_skl))),
% 0.13/5.67 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.13/5.67 fof(f826,plain,(
% 0.13/5.67 apart_point_and_line(sK0_skl,sK2_skl)|~sQ41_spl),
% 0.13/5.67 inference(component_clause,[status(thm)],[f825])).
% 0.13/5.67 fof(f862,definition,(
% 0.13/5.67 ![X0,X1]: (sQ48_spl <=> (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK2_skl)|distinct_points(intersection_point(sK1_skl,sK2_skl),X1)|distinct_points(X0,X1)))),
% 0.13/5.67 introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition])).
% 0.13/5.67 fof(f863,plain,(
% 0.13/5.67 ![X0,X1]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK2_skl)|distinct_points(intersection_point(sK1_skl,sK2_skl),X1)|distinct_points(X0,X1)|~sQ48_spl)),
% 0.13/5.67 inference(component_clause,[status(thm)],[f862])).
% 0.13/5.67 fof(f865,plain,(
% 0.13/5.67 sQ40_spl|sQ41_spl|sQ48_spl),
% 0.13/5.67 inference(split_clause,[status(thm)],[f739,f822,f825,f862])).
% 0.13/5.67 fof(f957,plain,(
% 0.13/5.67 $false|~sQ41_spl),
% 0.13/5.67 inference(forward_subsumption_resolution,[status(thm)],[f826,f51])).
% 0.13/5.67 fof(f958,plain,(
% 0.13/5.67 ~sQ41_spl),
% 0.13/5.67 inference(contradiction_clause,[status(thm)],[f957])).
% 0.13/5.67 fof(f959,plain,(
% 0.13/5.67 $false|~sQ40_spl),
% 0.13/5.67 inference(forward_subsumption_resolution,[status(thm)],[f823,f50])).
% 0.13/5.67 fof(f960,plain,(
% 0.13/5.67 ~sQ40_spl),
% 0.13/5.67 inference(contradiction_clause,[status(thm)],[f959])).
% 0.13/5.67 fof(f1520,plain,(
% 0.13/5.67 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK2_skl)|distinct_points(X0,intersection_point(sK1_skl,sK2_skl))|~sQ48_spl)),
% 0.13/5.67 inference(resolution,[status(thm)],[f863,f15])).
% 0.13/5.67 fof(f1548,plain,(
% 0.13/5.67 ![X0]: (apart_point_and_line(X0,sK2_skl)|distinct_points(X0,intersection_point(sK1_skl,sK2_skl))|~sQ48_spl)),
% 0.13/5.67 inference(forward_subsumption_resolution,[status(thm)],[f1520,f53])).
% 0.13/5.67 fof(f1711,plain,(
% 0.13/5.67 ![X0]: (distinct_points(X0,intersection_point(sK1_skl,sK2_skl))|~sQ48_spl)),
% 0.13/5.67 inference(forward_subsumption_resolution,[status(thm)],[f1548,f54])).
% 0.13/5.67 fof(f1714,plain,(
% 0.13/5.67 $false|~sQ48_spl),
% 0.13/5.67 inference(resolution,[status(thm)],[f1711,f15])).
% 0.13/5.67 fof(f1717,plain,(
% 0.13/5.67 ~sQ48_spl),
% 0.13/5.67 inference(contradiction_clause,[status(thm)],[f1714])).
% 0.13/5.67 fof(f1718,plain,(
% 0.13/5.67 $false),
% 0.13/5.67 inference(sat_refutation,[status(thm)],[f865,f958,f960,f1717])).
% 0.13/5.67 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/5.67 % Elapsed time: 0.298264 seconds
% 0.13/5.67 % CPU time: 2.195216 seconds
% 0.13/5.67 % Total memory used: 39.312 MB
% 0.13/5.67 % Net memory used: 34.024 MB
%------------------------------------------------------------------------------