%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO201+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 : n020.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 0.12s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:22:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.51 % Refutation found
% 0.12/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.51 fof(f1,axiom,(
% 0.12/0.51 (! [X] : ~ distinct_points(X,X) )),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f3,axiom,(
% 0.12/0.51 (! [X] : ~ convergent_lines(X,X) )),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f4,axiom,(
% 0.12/0.51 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f6,axiom,(
% 0.12/0.51 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f8,axiom,(
% 0.12/0.51 (! [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)) ) ) )),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f9,axiom,(
% 0.12/0.51 (! [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) ) ) )),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f12,axiom,(
% 0.12/0.51 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f13,conjecture,(
% 0.12/0.51 (! [X,Y] :( convergent_lines(X,Y)=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ) )),
% 0.12/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.51 fof(f14,negated_conjecture,(
% 0.12/0.51 ~((! [X,Y] :( convergent_lines(X,Y)=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ) ))),
% 0.12/0.51 inference(negated_conjecture,[status(cth)],[f13])).
% 0.12/0.51 fof(f15,plain,(
% 0.12/0.51 ![X0]: (~distinct_points(X0,X0))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.51 fof(f17,plain,(
% 0.12/0.51 ![X0]: (~convergent_lines(X0,X0))),
% 0.12/0.51 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.51 fof(f18,plain,(
% 0.12/0.51 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.12/0.51 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.12/0.52 fof(f19,plain,(
% 0.12/0.52 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.12/0.52 inference(miniscoping,[status(thm)],[f18])).
% 0.12/0.52 fof(f20,plain,(
% 0.12/0.52 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f19])).
% 0.12/0.52 fof(f24,plain,(
% 0.12/0.52 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.12/0.52 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.12/0.52 fof(f25,plain,(
% 0.12/0.52 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.12/0.52 inference(miniscoping,[status(thm)],[f24])).
% 0.12/0.52 fof(f26,plain,(
% 0.12/0.52 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f25])).
% 0.12/0.52 fof(f31,plain,(
% 0.12/0.52 ![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))))),
% 0.12/0.52 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.12/0.52 fof(f32,plain,(
% 0.12/0.52 ![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)))))),
% 0.12/0.52 inference(miniscoping,[status(thm)],[f31])).
% 0.12/0.52 fof(f33,plain,(
% 0.12/0.52 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f32])).
% 0.12/0.52 fof(f34,plain,(
% 0.12/0.52 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f32])).
% 0.12/0.52 fof(f35,plain,(
% 0.12/0.52 ![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)))),
% 0.12/0.52 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.12/0.52 fof(f36,plain,(
% 0.12/0.52 ![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))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f35])).
% 0.12/0.52 fof(f43,plain,(
% 0.12/0.52 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 0.12/0.52 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.12/0.52 fof(f44,plain,(
% 0.12/0.52 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f43])).
% 0.12/0.52 fof(f45,plain,(
% 0.12/0.52 (?[X,Y]: (convergent_lines(X,Y)&distinct_points(intersection_point(X,Y),intersection_point(Y,X))))),
% 0.12/0.52 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.12/0.52 fof(f46,plain,(
% 0.12/0.52 (convergent_lines(sK0_skl,sK1_skl)&distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl)))),
% 0.12/0.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f45])).
% 0.12/0.52 fof(f47,plain,(
% 0.12/0.52 convergent_lines(sK0_skl,sK1_skl)),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f46])).
% 0.12/0.52 fof(f48,plain,(
% 0.12/0.52 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl))),
% 0.12/0.52 inference(cnf_transformation,[status(thm)],[f46])).
% 0.12/0.52 fof(f49,plain,(
% 0.12/0.52 ![X0]: (~apart_point_and_line(X0,sK0_skl)|distinct_points(X0,intersection_point(sK0_skl,sK1_skl)))),
% 0.12/0.52 inference(resolution,[status(thm)],[f33,f47])).
% 0.12/0.52 fof(f50,plain,(
% 0.12/0.52 ![X0]: (~apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK0_skl,sK1_skl)))),
% 0.12/0.52 inference(resolution,[status(thm)],[f34,f47])).
% 0.12/0.52 fof(f51,plain,(
% 0.12/0.52 distinct_lines(sK0_skl,sK1_skl)),
% 0.12/0.52 inference(resolution,[status(thm)],[f44,f47])).
% 0.12/0.52 fof(f52,plain,(
% 0.12/0.52 ![X0]: (distinct_points(intersection_point(sK0_skl,sK1_skl),X0)|distinct_points(intersection_point(sK1_skl,sK0_skl),X0))),
% 0.12/0.52 inference(resolution,[status(thm)],[f20,f48])).
% 0.12/0.52 fof(f53,plain,(
% 0.12/0.52 ![X0,X1]: (distinct_points(intersection_point(sK0_skl,sK1_skl),X0)|distinct_points(intersection_point(sK1_skl,sK0_skl),X1)|distinct_points(X0,X1))),
% 0.12/0.52 inference(resolution,[status(thm)],[f52,f20])).
% 0.12/0.52 fof(f62,plain,(
% 0.12/0.52 ![X0]: (distinct_points(intersection_point(sK0_skl,sK1_skl),X0)|distinct_points(X0,intersection_point(sK1_skl,sK0_skl)))),
% 0.12/0.52 inference(resolution,[status(thm)],[f53,f15])).
% 0.12/0.52 fof(f150,plain,(
% 0.12/0.52 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.12/0.52 inference(resolution,[status(thm)],[f26,f47])).
% 0.12/0.52 fof(f151,plain,(
% 0.12/0.52 ![X0,X1]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X1)|convergent_lines(X0,X1))),
% 0.12/0.52 inference(resolution,[status(thm)],[f150,f26])).
% 0.12/0.52 fof(f170,plain,(
% 0.12/0.52 convergent_lines(sK1_skl,sK0_skl)),
% 0.12/0.52 inference(resolution,[status(thm)],[f151,f17])).
% 0.12/0.52 fof(f459,plain,(
% 0.12/0.52 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X1,sK0_skl)|apart_point_and_line(X1,sK1_skl))),
% 0.12/0.52 inference(resolution,[status(thm)],[f36,f51])).
% 0.12/0.52 fof(f477,plain,(
% 0.12/0.52 ![X0]: (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK1_skl,sK0_skl)))),
% 0.12/0.52 inference(resolution,[status(thm)],[f459,f62])).
% 0.12/0.52 fof(f515,definition,(
% 0.12/0.52 sQ30_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.12/0.52 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.12/0.52 fof(f516,plain,(
% 0.12/0.52 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ30_spl),
% 0.12/0.52 inference(component_clause,[status(thm)],[f515])).
% 0.12/0.52 fof(f518,definition,(
% 0.12/0.52 sQ31_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 0.12/0.52 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.12/0.52 fof(f519,plain,(
% 0.12/0.52 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ31_spl),
% 0.12/0.52 inference(component_clause,[status(thm)],[f518])).
% 0.12/0.52 fof(f540,definition,(
% 0.12/0.52 ![X0]: (sQ36_spl <=> (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK1_skl,sK0_skl))))),
% 0.12/0.52 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.12/0.52 fof(f541,plain,(
% 0.12/0.52 ![X0]: (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK1_skl,sK0_skl))|~sQ36_spl)),
% 0.12/0.52 inference(component_clause,[status(thm)],[f540])).
% 0.12/0.52 fof(f543,plain,(
% 0.12/0.52 sQ30_spl|sQ31_spl|sQ36_spl),
% 0.12/0.52 inference(split_clause,[status(thm)],[f477,f515,f518,f540])).
% 0.12/0.52 fof(f727,plain,(
% 0.12/0.52 ![X0]: (~apart_point_and_line(X0,sK0_skl)|distinct_points(X0,intersection_point(sK1_skl,sK0_skl)))),
% 0.12/0.52 inference(resolution,[status(thm)],[f170,f34])).
% 0.12/0.52 fof(f728,plain,(
% 0.12/0.52 ![X0]: (~apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK1_skl,sK0_skl)))),
% 0.12/0.52 inference(resolution,[status(thm)],[f170,f33])).
% 0.12/0.52 fof(f729,plain,(
% 0.12/0.52 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ31_spl),
% 0.12/0.52 inference(resolution,[status(thm)],[f519,f50])).
% 0.12/0.52 fof(f740,plain,(
% 0.12/0.52 $false|~sQ31_spl),
% 0.12/0.52 inference(forward_subsumption_resolution,[status(thm)],[f729,f15])).
% 0.12/0.52 fof(f741,plain,(
% 0.12/0.52 ~sQ31_spl),
% 0.12/0.52 inference(contradiction_clause,[status(thm)],[f740])).
% 0.12/0.52 fof(f747,plain,(
% 0.12/0.52 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ30_spl),
% 0.12/0.52 inference(resolution,[status(thm)],[f516,f49])).
% 0.12/0.52 fof(f756,plain,(
% 0.12/0.52 $false|~sQ30_spl),
% 0.12/0.52 inference(forward_subsumption_resolution,[status(thm)],[f747,f15])).
% 0.12/0.52 fof(f757,plain,(
% 0.12/0.52 ~sQ30_spl),
% 0.12/0.52 inference(contradiction_clause,[status(thm)],[f756])).
% 0.12/0.52 fof(f758,plain,(
% 0.12/0.52 ![X0]: (distinct_points(X0,intersection_point(sK1_skl,sK0_skl))|~sQ36_spl)),
% 0.12/0.52 inference(backward_subsumption_resolution,[status(thm)],[f728,f759])).
% 0.12/0.52 fof(f759,plain,(
% 0.12/0.52 ![X0]: (apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK1_skl,sK0_skl))|~sQ36_spl)),
% 0.12/0.52 inference(forward_subsumption_resolution,[status(thm)],[f541,f727])).
% 0.12/0.52 fof(f762,plain,(
% 0.12/0.52 $false|~sQ36_spl),
% 0.12/0.52 inference(resolution,[status(thm)],[f758,f15])).
% 0.12/0.52 fof(f765,plain,(
% 0.12/0.52 ~sQ36_spl),
% 0.12/0.52 inference(contradiction_clause,[status(thm)],[f762])).
% 0.12/0.52 fof(f766,plain,(
% 0.12/0.52 $false),
% 0.12/0.52 inference(sat_refutation,[status(thm)],[f543,f741,f757,f765])).
% 0.12/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.31/0.53 % Elapsed time: 0.166758 seconds
% 0.31/0.53 % CPU time: 1.088114 seconds
% 0.31/0.53 % Total memory used: 29.763 MB
% 0.31/0.53 % Net memory used: 26.895 MB
%------------------------------------------------------------------------------