%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO191+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 12:26:01 PM UTC 2026
% Result : Theorem 3.93s 0.97s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO191+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 13:18:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 3.93/0.97 % Refutation found
% 3.93/0.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.93/0.97 % SZS output start CNFRefutation for theBenchmark
% 3.93/0.97 fof(f3,axiom,(
% 3.93/0.97 (! [X] : ~ convergent_lines(X,X) )),
% 3.93/0.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.93/0.97 fof(f6,axiom,(
% 3.93/0.97 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 3.93/0.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.93/0.97 fof(f13,axiom,(
% 3.93/0.97 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 3.93/0.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.93/0.97 fof(f15,axiom,(
% 3.93/0.97 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 3.93/0.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.93/0.97 fof(f16,axiom,(
% 3.93/0.97 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 3.93/0.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.93/0.97 fof(f17,axiom,(
% 3.93/0.97 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 3.93/0.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.93/0.97 fof(f32,axiom,(
% 3.93/0.97 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 3.93/0.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.93/0.97 fof(f34,axiom,(
% 3.93/0.97 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 3.93/0.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.93/0.97 fof(f36,conjecture,(
% 3.93/0.97 (! [X,Y,U,V] :( ( convergent_lines(X,Y)& convergent_lines(U,V)& ( apart_point_and_line(intersection_point(X,Y),U)| apart_point_and_line(intersection_point(X,Y),V) ) )=> ( apart_point_and_line(intersection_point(U,V),X)| apart_point_and_line(intersection_point(U,V),Y) ) ) )),
% 3.93/0.97 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.93/0.97 fof(f37,negated_conjecture,(
% 3.93/0.97 ~((! [X,Y,U,V] :( ( convergent_lines(X,Y)& convergent_lines(U,V)& ( apart_point_and_line(intersection_point(X,Y),U)| apart_point_and_line(intersection_point(X,Y),V) ) )=> ( apart_point_and_line(intersection_point(U,V),X)| apart_point_and_line(intersection_point(U,V),Y) ) ) ))),
% 3.93/0.97 inference(negated_conjecture,[status(cth)],[f36])).
% 3.93/0.97 fof(f40,plain,(
% 3.93/0.97 ![X0]: (~convergent_lines(X0,X0))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f3])).
% 3.93/0.97 fof(f47,plain,(
% 3.93/0.97 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 3.93/0.97 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 3.93/0.97 fof(f48,plain,(
% 3.93/0.97 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 3.93/0.97 inference(miniscoping,[status(thm)],[f47])).
% 3.93/0.97 fof(f49,plain,(
% 3.93/0.97 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f48])).
% 3.93/0.97 fof(f63,plain,(
% 3.93/0.97 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 3.93/0.97 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 3.93/0.97 fof(f64,plain,(
% 3.93/0.97 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 3.93/0.97 inference(miniscoping,[status(thm)],[f63])).
% 3.93/0.97 fof(f65,plain,(
% 3.93/0.97 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f64])).
% 3.93/0.97 fof(f69,plain,(
% 3.93/0.97 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 3.93/0.97 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 3.93/0.97 fof(f70,plain,(
% 3.93/0.97 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f69])).
% 3.93/0.97 fof(f71,plain,(
% 3.93/0.97 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f16])).
% 3.93/0.97 fof(f72,plain,(
% 3.93/0.97 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f17])).
% 3.93/0.97 fof(f111,plain,(
% 3.93/0.97 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 3.93/0.97 inference(NNF_transformation,[status(thm)],[f32])).
% 3.93/0.97 fof(f112,plain,(
% 3.93/0.97 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 3.93/0.97 inference(miniscoping,[status(thm)],[f111])).
% 3.93/0.97 fof(f113,plain,(
% 3.93/0.97 ![X0,X1]: (~equal_lines(X0,X1)|~distinct_lines(X0,X1))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f112])).
% 3.93/0.97 fof(f114,plain,(
% 3.93/0.97 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f112])).
% 3.93/0.97 fof(f119,plain,(
% 3.93/0.97 ![X,Y]: ((~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y))&(incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 3.93/0.97 inference(NNF_transformation,[status(thm)],[f34])).
% 3.93/0.97 fof(f120,plain,(
% 3.93/0.97 (![X,Y]: (~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y)))&(![X,Y]: (incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 3.93/0.97 inference(miniscoping,[status(thm)],[f119])).
% 3.93/0.97 fof(f121,plain,(
% 3.93/0.97 ![X0,X1]: (~incident_point_and_line(X0,X1)|~apart_point_and_line(X0,X1))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f120])).
% 3.93/0.97 fof(f122,plain,(
% 3.93/0.97 ![X0,X1]: (incident_point_and_line(X0,X1)|apart_point_and_line(X0,X1))),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f120])).
% 3.93/0.97 fof(f127,plain,(
% 3.93/0.97 (?[X,Y,U,V]: (((convergent_lines(X,Y)&convergent_lines(U,V))&(apart_point_and_line(intersection_point(X,Y),U)|apart_point_and_line(intersection_point(X,Y),V)))&(~apart_point_and_line(intersection_point(U,V),X)&~apart_point_and_line(intersection_point(U,V),Y))))),
% 3.93/0.97 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 3.93/0.97 fof(f128,plain,(
% 3.93/0.97 (((convergent_lines(sK0_skl,sK1_skl)&convergent_lines(sK2_skl,sK3_skl))&(apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl)))&(~apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK0_skl)&~apart_point_and_line(intersection_point(sK2_skl,sK3_skl),sK1_skl)))),
% 3.93/0.97 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(U,sK2_skl),skolemize(V,sK3_skl)],[f127])).
% 3.93/0.97 fof(f131,plain,(
% 3.93/0.97 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl)),
% 3.93/0.97 inference(cnf_transformation,[status(thm)],[f128])).
% 3.93/0.97 fof(f144,definition,(
% 3.93/0.97 sQ0_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl))),
% 3.93/0.97 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 3.93/0.97 fof(f145,plain,(
% 3.93/0.97 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)|~sQ0_spl),
% 3.93/0.97 inference(component_clause,[status(thm)],[f144])).
% 3.93/0.97 fof(f147,definition,(
% 3.93/0.97 sQ1_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl))),
% 3.93/0.97 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 3.93/0.97 fof(f148,plain,(
% 3.93/0.97 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK3_skl)|~sQ1_spl),
% 3.93/0.97 inference(component_clause,[status(thm)],[f147])).
% 3.93/0.97 fof(f150,plain,(
% 3.93/0.97 sQ0_spl|sQ1_spl),
% 3.93/0.97 inference(split_clause,[status(thm)],[f131,f144,f147])).
% 3.93/0.97 fof(f294,plain,(
% 3.93/0.97 ![X0,X1]: (equal_lines(X0,X1)|convergent_lines(X0,X1))),
% 3.93/0.97 inference(resolution,[status(thm)],[f114,f70])).
% 3.93/0.97 fof(f380,plain,(
% 3.93/0.97 ![X0,X1,X2]: (equal_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 3.93/0.97 inference(resolution,[status(thm)],[f294,f49])).
% 3.93/0.97 fof(f385,plain,(
% 3.93/0.97 ![X0]: (distinct_lines(sK2_skl,X0)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|~sQ0_spl)),
% 3.93/0.97 inference(resolution,[status(thm)],[f65,f145])).
% 3.93/0.97 fof(f386,plain,(
% 3.93/0.97 ![X0,X1,X2]: (distinct_lines(X0,X1)|apart_point_and_line(X2,X1)|incident_point_and_line(X2,X0))),
% 3.93/0.97 inference(resolution,[status(thm)],[f65,f122])).
% 3.93/0.97 fof(f499,plain,(
% 3.93/0.97 ![X0,X1]: (equal_lines(X0,X1)|convergent_lines(X1,X0))),
% 3.93/0.97 inference(resolution,[status(thm)],[f380,f40])).
% 3.93/0.97 fof(f505,plain,(
% 3.93/0.97 ![X0,X1]: (equal_lines(X0,parallel_through_point(X0,X1)))),
% 3.93/0.97 inference(resolution,[status(thm)],[f499,f71])).
% 3.93/0.97 fof(f540,plain,(
% 3.93/0.97 ![X0]: (distinct_lines(sK2_skl,parallel_through_point(X0,intersection_point(sK0_skl,sK1_skl)))|~sQ0_spl)),
% 3.93/0.97 inference(resolution,[status(thm)],[f385,f72])).
% 3.93/0.97 fof(f1127,plain,(
% 3.93/0.97 ![X0,X1,X2]: (distinct_lines(X0,parallel_through_point(X1,X2))|incident_point_and_line(X2,X0))),
% 3.93/0.97 inference(resolution,[status(thm)],[f386,f72])).
% 3.93/0.97 fof(f1166,plain,(
% 3.93/0.97 ![X0,X1]: (~distinct_lines(X0,parallel_through_point(X0,X1)))),
% 3.93/0.97 inference(resolution,[status(thm)],[f113,f505])).
% 3.93/0.98 fof(f1216,plain,(
% 3.93/0.98 $false|~sQ0_spl),
% 3.93/0.98 inference(resolution,[status(thm)],[f1166,f540])).
% 3.93/0.98 fof(f1217,plain,(
% 3.93/0.98 ![X0,X1]: (incident_point_and_line(X0,X1))),
% 3.93/0.98 inference(resolution,[status(thm)],[f1166,f1127])).
% 3.93/0.98 fof(f1235,plain,(
% 3.93/0.98 ~sQ0_spl),
% 3.93/0.98 inference(contradiction_clause,[status(thm)],[f1216])).
% 3.93/0.98 fof(f1236,plain,(
% 3.93/0.98 ![X0,X1]: (~apart_point_and_line(X0,X1))),
% 3.93/0.98 inference(backward_subsumption_resolution,[status(thm)],[f121,f1217])).
% 3.93/0.98 fof(f1241,plain,(
% 3.93/0.98 $false|~sQ1_spl),
% 3.93/0.98 inference(backward_subsumption_resolution,[status(thm)],[f148,f1236])).
% 3.93/0.98 fof(f1295,plain,(
% 3.93/0.98 ~sQ1_spl),
% 3.93/0.98 inference(contradiction_clause,[status(thm)],[f1241])).
% 3.93/0.98 fof(f1296,plain,(
% 3.93/0.98 $false),
% 3.93/0.98 inference(sat_refutation,[status(thm)],[f150,f1235,f1295])).
% 3.93/0.98 % SZS output end CNFRefutation for theBenchmark.p
% 3.93/0.98 % Elapsed time: 0.608622 seconds
% 3.93/0.98 % CPU time: 4.580586 seconds
% 3.93/0.98 % Total memory used: 59.639 MB
% 3.93/0.98 % Net memory used: 50.923 MB
%------------------------------------------------------------------------------