%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO172+1 : 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 : n026.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 12:25:56 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO172+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 12:59:37 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.41 fof(f1,axiom,(
% 0.13/0.41 (! [X] : ~ distinct_points(X,X) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f3,axiom,(
% 0.13/0.41 (! [X] : ~ convergent_lines(X,X) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f4,axiom,(
% 0.13/0.41 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f9,axiom,(
% 0.13/0.41 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f10,axiom,(
% 0.13/0.41 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f11,axiom,(
% 0.13/0.41 (! [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) ) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f14,axiom,(
% 0.13/0.41 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f15,conjecture,(
% 0.13/0.41 (! [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)) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f16,negated_conjecture,(
% 0.13/0.41 ~((! [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)) ) ))),
% 0.13/0.41 inference(negated_conjecture,[status(cth)],[f15])).
% 0.13/0.41 fof(f17,plain,(
% 0.13/0.41 ![X0]: (~distinct_points(X0,X0))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.41 fof(f19,plain,(
% 0.13/0.41 ![X0]: (~convergent_lines(X0,X0))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.41 fof(f20,plain,(
% 0.13/0.41 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/0.41 fof(f21,plain,(
% 0.13/0.41 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f20])).
% 0.13/0.41 fof(f22,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f21])).
% 0.13/0.41 fof(f33,plain,(
% 0.13/0.41 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.13/0.41 fof(f34,plain,(
% 0.13/0.41 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f33])).
% 0.13/0.41 fof(f35,plain,(
% 0.13/0.41 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.13/0.41 fof(f36,plain,(
% 0.13/0.41 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f35])).
% 0.13/0.41 fof(f37,plain,(
% 0.13/0.41 ![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)))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.13/0.41 fof(f38,plain,(
% 0.13/0.41 ![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))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f37])).
% 0.13/0.41 fof(f45,plain,(
% 0.13/0.41 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.13/0.41 fof(f46,plain,(
% 0.13/0.41 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f45])).
% 0.13/0.41 fof(f47,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f46])).
% 0.13/0.41 fof(f48,plain,(
% 0.13/0.41 (?[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))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.13/0.41 fof(f49,plain,(
% 0.13/0.41 (((convergent_lines(sK0_skl,sK1_skl)&~apart_point_and_line(sK2_skl,sK0_skl))&~apart_point_and_line(sK2_skl,sK1_skl))&distinct_points(sK2_skl,intersection_point(sK0_skl,sK1_skl)))),
% 0.13/0.41 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)],[f48])).
% 0.13/0.41 fof(f50,plain,(
% 0.13/0.41 convergent_lines(sK0_skl,sK1_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.41 fof(f51,plain,(
% 0.13/0.41 ~apart_point_and_line(sK2_skl,sK0_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.41 fof(f52,plain,(
% 0.13/0.41 ~apart_point_and_line(sK2_skl,sK1_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.41 fof(f53,plain,(
% 0.13/0.41 distinct_points(sK2_skl,intersection_point(sK0_skl,sK1_skl))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/0.41 fof(f54,plain,(
% 0.13/0.41 ![X0]: (distinct_points(sK2_skl,X0)|distinct_points(intersection_point(sK0_skl,sK1_skl),X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f22,f53])).
% 0.13/0.41 fof(f56,plain,(
% 0.13/0.41 ![X0,X1]: (distinct_points(sK2_skl,X0)|distinct_points(intersection_point(sK0_skl,sK1_skl),X1)|distinct_points(X0,X1))),
% 0.13/0.41 inference(resolution,[status(thm)],[f54,f22])).
% 0.13/0.41 fof(f61,plain,(
% 0.13/0.41 ![X0]: (distinct_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f47,f50])).
% 0.13/0.41 fof(f64,plain,(
% 0.13/0.41 distinct_lines(sK1_skl,sK0_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f61,f19])).
% 0.13/0.41 fof(f66,plain,(
% 0.13/0.41 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X1,sK1_skl)|apart_point_and_line(X1,sK0_skl))),
% 0.13/0.41 inference(resolution,[status(thm)],[f38,f64])).
% 0.13/0.41 fof(f69,plain,(
% 0.13/0.41 distinct_points(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f56,f17])).
% 0.13/0.41 fof(f287,plain,(
% 0.13/0.41 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(sK2_skl,sK1_skl)|apart_point_and_line(sK2_skl,sK0_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f66,f69])).
% 0.13/0.41 fof(f297,definition,(
% 0.13/0.41 sQ22_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f298,plain,(
% 0.13/0.41 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ22_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f297])).
% 0.13/0.41 fof(f300,definition,(
% 0.13/0.41 sQ23_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f301,plain,(
% 0.13/0.41 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ23_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f300])).
% 0.13/0.41 fof(f303,definition,(
% 0.13/0.41 sQ24_spl <=> (apart_point_and_line(sK2_skl,sK1_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f304,plain,(
% 0.13/0.41 apart_point_and_line(sK2_skl,sK1_skl)|~sQ24_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f303])).
% 0.13/0.41 fof(f306,definition,(
% 0.13/0.41 sQ25_spl <=> (apart_point_and_line(sK2_skl,sK0_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f307,plain,(
% 0.13/0.41 apart_point_and_line(sK2_skl,sK0_skl)|~sQ25_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f306])).
% 0.13/0.41 fof(f309,plain,(
% 0.13/0.41 sQ22_spl|sQ23_spl|sQ24_spl|sQ25_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f287,f297,f300,f303,f306])).
% 0.13/0.41 fof(f334,plain,(
% 0.13/0.41 $false|~sQ25_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f307,f51])).
% 0.13/0.41 fof(f335,plain,(
% 0.13/0.41 ~sQ25_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f334])).
% 0.13/0.41 fof(f336,plain,(
% 0.13/0.41 $false|~sQ24_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f304,f52])).
% 0.13/0.41 fof(f337,plain,(
% 0.13/0.41 ~sQ24_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f336])).
% 0.13/0.41 fof(f428,plain,(
% 0.13/0.41 ~convergent_lines(sK0_skl,sK1_skl)|~sQ22_spl),
% 0.13/0.41 inference(resolution,[status(thm)],[f298,f36])).
% 0.13/0.41 fof(f431,plain,(
% 0.13/0.41 $false|~sQ22_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f428,f50])).
% 0.13/0.41 fof(f432,plain,(
% 0.13/0.41 ~sQ22_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f431])).
% 0.13/0.41 fof(f455,plain,(
% 0.13/0.41 ~convergent_lines(sK0_skl,sK1_skl)|~sQ23_spl),
% 0.13/0.41 inference(resolution,[status(thm)],[f301,f34])).
% 0.13/0.41 fof(f458,plain,(
% 0.13/0.41 $false|~sQ23_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f455,f50])).
% 0.13/0.41 fof(f459,plain,(
% 0.13/0.41 ~sQ23_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f458])).
% 0.13/0.41 fof(f460,plain,(
% 0.13/0.41 $false),
% 0.13/0.41 inference(sat_refutation,[status(thm)],[f309,f335,f337,f432,f459])).
% 0.13/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.43 % Elapsed time: 0.070392 seconds
% 0.13/0.43 % CPU time: 0.321490 seconds
% 0.13/0.43 % Total memory used: 19.758 MB
% 0.13/0.43 % Net memory used: 18.883 MB
%------------------------------------------------------------------------------