%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO172+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 : n007.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 0.19s 0.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO172+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n007.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 20 12:55:34 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.19/0.61 % Refutation found
% 0.19/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.61 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.61 fof(f1,axiom,(
% 0.19/0.61 (! [X] : ~ distinct_points(X,X) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f8,axiom,(
% 0.19/0.61 (! [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)) ) ) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f9,axiom,(
% 0.19/0.61 (! [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) ) ) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f12,axiom,(
% 0.19/0.61 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f13,conjecture,(
% 0.19/0.61 (! [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)) ) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f14,negated_conjecture,(
% 0.19/0.61 ~((! [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)) ) ))),
% 0.19/0.61 inference(negated_conjecture,[status(cth)],[f13])).
% 0.19/0.61 fof(f15,plain,(
% 0.19/0.61 ![X0]: (~distinct_points(X0,X0))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f1])).
% 0.19/0.61 fof(f31,plain,(
% 0.19/0.61 ![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))))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.19/0.61 fof(f32,plain,(
% 0.19/0.61 ![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)))))),
% 0.19/0.61 inference(miniscoping,[status(thm)],[f31])).
% 0.19/0.61 fof(f33,plain,(
% 0.19/0.61 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f32])).
% 0.19/0.61 fof(f34,plain,(
% 0.19/0.61 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f32])).
% 0.19/0.61 fof(f35,plain,(
% 0.19/0.61 ![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)))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.19/0.61 fof(f36,plain,(
% 0.19/0.61 ![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))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f35])).
% 0.19/0.61 fof(f43,plain,(
% 0.19/0.61 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.19/0.61 fof(f44,plain,(
% 0.19/0.61 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f43])).
% 0.19/0.61 fof(f45,plain,(
% 0.19/0.61 (?[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))))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.19/0.61 fof(f46,plain,(
% 0.19/0.61 (((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)))),
% 0.19/0.61 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)],[f45])).
% 0.19/0.61 fof(f47,plain,(
% 0.19/0.61 convergent_lines(sK0_skl,sK1_skl)),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f46])).
% 0.19/0.61 fof(f48,plain,(
% 0.19/0.61 ~apart_point_and_line(sK2_skl,sK0_skl)),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f46])).
% 0.19/0.61 fof(f49,plain,(
% 0.19/0.61 ~apart_point_and_line(sK2_skl,sK1_skl)),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f46])).
% 0.19/0.61 fof(f50,plain,(
% 0.19/0.61 distinct_points(sK2_skl,intersection_point(sK0_skl,sK1_skl))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f46])).
% 0.19/0.61 fof(f52,plain,(
% 0.19/0.61 distinct_lines(sK0_skl,sK1_skl)),
% 0.19/0.62 inference(resolution,[status(thm)],[f44,f47])).
% 0.19/0.62 fof(f61,plain,(
% 0.19/0.62 ![X0]: (~apart_point_and_line(X0,sK0_skl)|distinct_points(X0,intersection_point(sK0_skl,sK1_skl)))),
% 0.19/0.62 inference(resolution,[status(thm)],[f33,f47])).
% 0.19/0.62 fof(f63,plain,(
% 0.19/0.62 ![X0]: (~apart_point_and_line(X0,sK1_skl)|distinct_points(X0,intersection_point(sK0_skl,sK1_skl)))),
% 0.19/0.62 inference(resolution,[status(thm)],[f34,f47])).
% 0.19/0.62 fof(f68,plain,(
% 0.19/0.62 ![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))),
% 0.19/0.62 inference(resolution,[status(thm)],[f36,f52])).
% 0.19/0.62 fof(f159,plain,(
% 0.19/0.62 apart_point_and_line(sK2_skl,sK0_skl)|apart_point_and_line(sK2_skl,sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)),
% 0.19/0.62 inference(resolution,[status(thm)],[f68,f50])).
% 0.19/0.62 fof(f160,definition,(
% 0.19/0.62 sQ10_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.19/0.62 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.19/0.62 fof(f161,plain,(
% 0.19/0.62 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ10_spl),
% 0.19/0.62 inference(component_clause,[status(thm)],[f160])).
% 0.19/0.62 fof(f163,definition,(
% 0.19/0.62 sQ11_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 0.19/0.62 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.19/0.62 fof(f164,plain,(
% 0.19/0.62 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ11_spl),
% 0.19/0.62 inference(component_clause,[status(thm)],[f163])).
% 0.19/0.62 fof(f170,definition,(
% 0.19/0.62 sQ13_spl <=> (apart_point_and_line(sK2_skl,sK0_skl))),
% 0.19/0.62 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.19/0.62 fof(f171,plain,(
% 0.19/0.62 apart_point_and_line(sK2_skl,sK0_skl)|~sQ13_spl),
% 0.19/0.62 inference(component_clause,[status(thm)],[f170])).
% 0.19/0.62 fof(f173,definition,(
% 0.19/0.62 sQ14_spl <=> (apart_point_and_line(sK2_skl,sK1_skl))),
% 0.19/0.62 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.19/0.62 fof(f174,plain,(
% 0.19/0.62 apart_point_and_line(sK2_skl,sK1_skl)|~sQ14_spl),
% 0.19/0.62 inference(component_clause,[status(thm)],[f173])).
% 0.19/0.62 fof(f176,plain,(
% 0.19/0.62 sQ13_spl|sQ14_spl|sQ10_spl|sQ11_spl),
% 0.19/0.62 inference(split_clause,[status(thm)],[f159,f170,f173,f160,f163])).
% 0.19/0.62 fof(f228,plain,(
% 0.19/0.62 $false|~sQ14_spl),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f174,f49])).
% 0.19/0.62 fof(f229,plain,(
% 0.19/0.62 ~sQ14_spl),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f228])).
% 0.19/0.62 fof(f230,plain,(
% 0.19/0.62 $false|~sQ13_spl),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f171,f48])).
% 0.19/0.62 fof(f231,plain,(
% 0.19/0.62 ~sQ13_spl),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f230])).
% 0.19/0.62 fof(f287,plain,(
% 0.19/0.62 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ10_spl),
% 0.19/0.62 inference(resolution,[status(thm)],[f161,f61])).
% 0.19/0.62 fof(f291,plain,(
% 0.19/0.62 $false|~sQ10_spl),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f287,f15])).
% 0.19/0.62 fof(f292,plain,(
% 0.19/0.62 ~sQ10_spl),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f291])).
% 0.19/0.62 fof(f370,plain,(
% 0.19/0.62 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK1_skl))|~sQ11_spl),
% 0.19/0.62 inference(resolution,[status(thm)],[f164,f63])).
% 0.19/0.62 fof(f374,plain,(
% 0.19/0.62 $false|~sQ11_spl),
% 0.19/0.62 inference(forward_subsumption_resolution,[status(thm)],[f370,f15])).
% 0.19/0.62 fof(f375,plain,(
% 0.19/0.62 ~sQ11_spl),
% 0.19/0.62 inference(contradiction_clause,[status(thm)],[f374])).
% 0.19/0.62 fof(f376,plain,(
% 0.19/0.62 $false),
% 0.19/0.62 inference(sat_refutation,[status(thm)],[f176,f229,f231,f292,f375])).
% 0.19/0.62 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.62 % Elapsed time: 0.148293 seconds
% 0.19/0.62 % CPU time: 0.893627 seconds
% 0.19/0.62 % Total memory used: 24.774 MB
% 0.19/0.62 % Net memory used: 23.051 MB
%------------------------------------------------------------------------------