%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO194+1 : 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 12:26:02 PM UTC 2026
% Result : Theorem 5.42s 16.10s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO194+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/15.33 % Computer : n012.cluster.edu
% 0.06/15.33 % Model : x86_64 x86_64
% 0.06/15.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/15.33 % Memory : 8046.5625MB
% 0.06/15.33 % OS : Linux 6.8.0-71-generic
% 0.06/15.33 % CPULimit : 300
% 0.06/15.33 % WCLimit : 300
% 0.06/15.33 % DateTime : Sun Sep 20 13:17:23 UTC 2026
% 0.06/15.33 % CPUTime :
% 0.06/15.34 % Drodi V4.1.1
% 5.42/16.10 % Refutation found
% 5.42/16.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.42/16.10 % SZS output start CNFRefutation for theBenchmark
% 5.42/16.10 fof(f2,axiom,(
% 5.42/16.10 (! [X] : ~ distinct_lines(X,X) )),
% 5.42/16.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.42/16.10 fof(f3,axiom,(
% 5.42/16.10 (! [X] : ~ convergent_lines(X,X) )),
% 5.42/16.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.42/16.10 fof(f9,axiom,(
% 5.42/16.10 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 5.42/16.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.42/16.10 fof(f10,axiom,(
% 5.42/16.10 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 5.42/16.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.42/16.10 fof(f11,axiom,(
% 5.42/16.10 (! [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) ) ) )),
% 5.42/16.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.42/16.10 fof(f12,axiom,(
% 5.42/16.10 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 5.42/16.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.42/16.10 fof(f13,axiom,(
% 5.42/16.10 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 5.42/16.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.42/16.10 fof(f14,axiom,(
% 5.42/16.10 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 5.42/16.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.42/16.10 fof(f15,conjecture,(
% 5.42/16.10 (! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(Z,Y)& convergent_lines(X,Z) )=> ( apart_point_and_line(intersection_point(X,Y),Z)=> apart_point_and_line(intersection_point(X,Z),Y) ) ) )),
% 5.42/16.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.42/16.10 fof(f16,negated_conjecture,(
% 5.42/16.10 ~((! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(Z,Y)& convergent_lines(X,Z) )=> ( apart_point_and_line(intersection_point(X,Y),Z)=> apart_point_and_line(intersection_point(X,Z),Y) ) ) ))),
% 5.42/16.10 inference(negated_conjecture,[status(cth)],[f15])).
% 5.42/16.10 fof(f18,plain,(
% 5.42/16.10 ![X0]: (~distinct_lines(X0,X0))),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f2])).
% 5.42/16.10 fof(f19,plain,(
% 5.42/16.10 ![X0]: (~convergent_lines(X0,X0))),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f3])).
% 5.42/16.10 fof(f33,plain,(
% 5.42/16.10 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 5.42/16.10 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 5.42/16.10 fof(f34,plain,(
% 5.42/16.10 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f33])).
% 5.42/16.10 fof(f35,plain,(
% 5.42/16.10 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 5.42/16.10 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 5.42/16.10 fof(f36,plain,(
% 5.42/16.10 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f35])).
% 5.42/16.10 fof(f37,plain,(
% 5.42/16.10 ![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)))),
% 5.42/16.10 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 5.42/16.10 fof(f38,plain,(
% 5.42/16.10 ![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))),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f37])).
% 5.42/16.10 fof(f39,plain,(
% 5.42/16.10 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 5.42/16.10 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 5.42/16.10 fof(f40,plain,(
% 5.42/16.10 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 5.42/16.10 inference(miniscoping,[status(thm)],[f39])).
% 5.42/16.10 fof(f41,plain,(
% 5.42/16.10 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f40])).
% 5.42/16.10 fof(f42,plain,(
% 5.42/16.10 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 5.42/16.10 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 5.42/16.10 fof(f43,plain,(
% 5.42/16.10 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 5.42/16.10 inference(miniscoping,[status(thm)],[f42])).
% 5.42/16.10 fof(f44,plain,(
% 5.42/16.10 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f43])).
% 5.42/16.10 fof(f45,plain,(
% 5.42/16.10 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 5.42/16.10 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 5.42/16.10 fof(f46,plain,(
% 5.42/16.10 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 5.42/16.10 inference(miniscoping,[status(thm)],[f45])).
% 5.42/16.10 fof(f47,plain,(
% 5.42/16.10 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f46])).
% 5.42/16.10 fof(f48,plain,(
% 5.42/16.10 (?[X,Y,Z]: (((convergent_lines(X,Y)&convergent_lines(Z,Y))&convergent_lines(X,Z))&(apart_point_and_line(intersection_point(X,Y),Z)&~apart_point_and_line(intersection_point(X,Z),Y))))),
% 5.42/16.10 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 5.42/16.10 fof(f49,plain,(
% 5.42/16.10 (((convergent_lines(sK0_skl,sK1_skl)&convergent_lines(sK2_skl,sK1_skl))&convergent_lines(sK0_skl,sK2_skl))&(apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)&~apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)))),
% 5.42/16.10 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])).
% 5.42/16.10 fof(f50,plain,(
% 5.42/16.10 convergent_lines(sK0_skl,sK1_skl)),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f49])).
% 5.42/16.10 fof(f52,plain,(
% 5.42/16.10 convergent_lines(sK0_skl,sK2_skl)),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f49])).
% 5.42/16.10 fof(f53,plain,(
% 5.42/16.10 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f49])).
% 5.42/16.10 fof(f54,plain,(
% 5.42/16.10 ~apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)),
% 5.42/16.10 inference(cnf_transformation,[status(thm)],[f49])).
% 5.42/16.10 fof(f446,plain,(
% 5.42/16.10 ![X0]: (distinct_lines(sK2_skl,X0)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0))),
% 5.42/16.10 inference(resolution,[status(thm)],[f44,f53])).
% 5.42/16.10 fof(f488,plain,(
% 5.42/16.10 ![X0]: (distinct_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 5.42/16.10 inference(resolution,[status(thm)],[f47,f50])).
% 5.42/16.10 fof(f609,plain,(
% 5.42/16.10 distinct_lines(sK1_skl,sK0_skl)),
% 5.42/16.10 inference(resolution,[status(thm)],[f488,f19])).
% 5.42/16.10 fof(f617,plain,(
% 5.42/16.10 ![X0,X1]: (distinct_lines(sK2_skl,X0)|distinct_points(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(X1,X0))),
% 5.42/16.10 inference(resolution,[status(thm)],[f446,f41])).
% 5.42/16.10 fof(f781,plain,(
% 5.42/16.10 ![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))),
% 5.42/16.10 inference(resolution,[status(thm)],[f609,f38])).
% 5.42/16.10 fof(f861,plain,(
% 5.42/16.10 ![X0,X1]: (distinct_lines(sK2_skl,X0)|distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(X1,X0))|~convergent_lines(X1,X0))),
% 5.42/16.10 inference(resolution,[status(thm)],[f617,f36])).
% 5.42/16.10 fof(f871,definition,(
% 5.42/16.10 sQ43_spl <=> (distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))),
% 5.42/16.10 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 5.42/16.10 fof(f872,plain,(
% 5.42/16.10 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))|~sQ43_spl),
% 5.42/16.10 inference(component_clause,[status(thm)],[f871])).
% 5.42/16.10 fof(f1310,definition,(
% 5.42/16.10 sQ53_spl <=> (distinct_lines(sK2_skl,sK2_skl))),
% 5.42/16.10 introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition])).
% 5.42/16.10 fof(f1311,plain,(
% 5.42/16.10 distinct_lines(sK2_skl,sK2_skl)|~sQ53_spl),
% 5.42/16.10 inference(component_clause,[status(thm)],[f1310])).
% 5.42/16.10 fof(f1716,definition,(
% 5.42/16.10 sQ65_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 5.42/16.10 introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition])).
% 5.42/16.10 fof(f1717,plain,(
% 5.42/16.10 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ65_spl),
% 5.42/16.10 inference(component_clause,[status(thm)],[f1716])).
% 5.42/16.10 fof(f2249,plain,(
% 5.42/16.10 ~convergent_lines(sK0_skl,sK1_skl)|~sQ65_spl),
% 5.42/16.10 inference(resolution,[status(thm)],[f1717,f36])).
% 5.42/16.10 fof(f2252,plain,(
% 5.42/16.10 $false|~sQ65_spl),
% 5.42/16.10 inference(forward_subsumption_resolution,[status(thm)],[f2249,f50])).
% 5.42/16.10 fof(f2253,plain,(
% 5.42/16.10 ~sQ65_spl),
% 5.42/16.10 inference(contradiction_clause,[status(thm)],[f2252])).
% 5.42/16.10 fof(f4175,plain,(
% 5.42/16.10 $false|~sQ53_spl),
% 5.42/16.10 inference(forward_subsumption_resolution,[status(thm)],[f1311,f18])).
% 5.42/16.10 fof(f4176,plain,(
% 5.42/16.10 ~sQ53_spl),
% 5.42/16.10 inference(contradiction_clause,[status(thm)],[f4175])).
% 5.42/16.10 fof(f5331,definition,(
% 5.42/16.10 sQ268_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 5.42/16.10 introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition])).
% 5.42/16.10 fof(f5332,plain,(
% 5.42/16.10 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ268_spl),
% 5.42/16.10 inference(component_clause,[status(thm)],[f5331])).
% 5.42/16.10 fof(f5668,plain,(
% 5.42/16.10 distinct_lines(sK2_skl,sK2_skl)|distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))),
% 5.42/16.10 inference(resolution,[status(thm)],[f861,f52])).
% 5.42/16.10 fof(f6020,plain,(
% 5.42/16.10 sQ53_spl|sQ43_spl),
% 5.42/16.10 inference(split_clause,[status(thm)],[f5668,f1310,f871])).
% 5.42/16.10 fof(f7576,plain,(
% 5.42/16.10 ~convergent_lines(sK0_skl,sK1_skl)|~sQ268_spl),
% 5.42/16.10 inference(resolution,[status(thm)],[f5332,f34])).
% 5.42/16.10 fof(f7579,plain,(
% 5.42/16.10 $false|~sQ268_spl),
% 5.42/16.10 inference(forward_subsumption_resolution,[status(thm)],[f7576,f50])).
% 5.42/16.10 fof(f7580,plain,(
% 5.42/16.10 ~sQ268_spl),
% 5.42/16.10 inference(contradiction_clause,[status(thm)],[f7579])).
% 5.42/16.10 fof(f8018,plain,(
% 5.42/16.10 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(intersection_point(sK0_skl,sK2_skl),sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|~sQ43_spl),
% 5.42/16.10 inference(resolution,[status(thm)],[f872,f781])).
% 5.42/16.10 fof(f8026,definition,(
% 5.42/16.10 sQ497_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl))),
% 5.42/16.10 introduced(definition,[new_symbols(definition,[sQ497_spl])],[split_symbol_definition])).
% 5.42/16.10 fof(f8027,plain,(
% 5.42/16.10 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)|~sQ497_spl),
% 5.42/16.10 inference(component_clause,[status(thm)],[f8026])).
% 5.42/16.10 fof(f8029,definition,(
% 5.42/16.10 sQ498_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl))),
% 5.42/16.10 introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition])).
% 5.42/16.10 fof(f8030,plain,(
% 5.42/16.10 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|~sQ498_spl),
% 5.42/16.10 inference(component_clause,[status(thm)],[f8029])).
% 5.42/16.10 fof(f8032,plain,(
% 5.42/16.10 sQ65_spl|sQ268_spl|sQ497_spl|sQ498_spl|~sQ43_spl),
% 5.42/16.10 inference(split_clause,[status(thm)],[f8018,f1716,f5331,f8026,f8029,f871])).
% 5.42/16.10 fof(f8057,plain,(
% 5.42/16.10 $false|~sQ497_spl),
% 5.42/16.10 inference(forward_subsumption_resolution,[status(thm)],[f8027,f54])).
% 5.42/16.10 fof(f8058,plain,(
% 5.42/16.10 ~sQ497_spl),
% 5.42/16.10 inference(contradiction_clause,[status(thm)],[f8057])).
% 5.42/16.10 fof(f8059,plain,(
% 5.42/16.10 ~convergent_lines(sK0_skl,sK2_skl)|~sQ498_spl),
% 5.42/16.10 inference(resolution,[status(thm)],[f8030,f34])).
% 5.42/16.10 fof(f8062,plain,(
% 5.42/16.10 $false|~sQ498_spl),
% 5.42/16.10 inference(forward_subsumption_resolution,[status(thm)],[f8059,f52])).
% 5.42/16.10 fof(f8063,plain,(
% 5.42/16.10 ~sQ498_spl),
% 5.42/16.10 inference(contradiction_clause,[status(thm)],[f8062])).
% 5.42/16.10 fof(f8064,plain,(
% 5.42/16.10 $false),
% 5.42/16.10 inference(sat_refutation,[status(thm)],[f2253,f4176,f6020,f7580,f8032,f8058,f8063])).
% 5.42/16.10 % SZS output end CNFRefutation for theBenchmark.p
% 5.42/16.12 % Elapsed time: 0.774237 seconds
% 5.42/16.12 % CPU time: 6.018188 seconds
% 5.42/16.12 % Total memory used: 79.119 MB
% 5.42/16.12 % Net memory used: 63.236 MB
%------------------------------------------------------------------------------