%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO193+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 : n004.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 0.13s 5.74s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO193+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n004.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sun Sep 20 13:17:26 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.13/5.74 % Refutation found
% 0.13/5.74 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.74 % SZS output start CNFRefutation for theBenchmark
% 0.13/5.74 fof(f3,axiom,(
% 0.13/5.74 (! [X] : ~ convergent_lines(X,X) )),
% 0.13/5.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.74 fof(f9,axiom,(
% 0.13/5.74 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.13/5.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.74 fof(f10,axiom,(
% 0.13/5.74 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.13/5.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.74 fof(f11,axiom,(
% 0.13/5.74 (! [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) ) ) )),
% 0.13/5.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.74 fof(f12,axiom,(
% 0.13/5.74 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 0.13/5.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.74 fof(f14,axiom,(
% 0.13/5.74 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.13/5.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.74 fof(f15,conjecture,(
% 0.13/5.74 (! [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(Z,Y),X) ) ) )),
% 0.13/5.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/5.74 fof(f16,negated_conjecture,(
% 0.13/5.74 ~((! [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(Z,Y),X) ) ) ))),
% 0.13/5.74 inference(negated_conjecture,[status(cth)],[f15])).
% 0.13/5.74 fof(f19,plain,(
% 0.13/5.74 ![X0]: (~convergent_lines(X0,X0))),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/5.74 fof(f33,plain,(
% 0.13/5.74 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.13/5.74 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.13/5.74 fof(f34,plain,(
% 0.13/5.74 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f33])).
% 0.13/5.74 fof(f35,plain,(
% 0.13/5.74 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.13/5.74 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.13/5.74 fof(f36,plain,(
% 0.13/5.74 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f35])).
% 0.13/5.74 fof(f37,plain,(
% 0.13/5.74 ![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)))),
% 0.13/5.74 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.13/5.74 fof(f38,plain,(
% 0.13/5.74 ![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))),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f37])).
% 0.13/5.74 fof(f39,plain,(
% 0.13/5.74 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 0.13/5.74 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.13/5.74 fof(f40,plain,(
% 0.13/5.74 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 0.13/5.74 inference(miniscoping,[status(thm)],[f39])).
% 0.13/5.74 fof(f41,plain,(
% 0.13/5.74 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f40])).
% 0.13/5.74 fof(f45,plain,(
% 0.13/5.74 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.13/5.74 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.13/5.74 fof(f46,plain,(
% 0.13/5.74 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.13/5.74 inference(miniscoping,[status(thm)],[f45])).
% 0.13/5.74 fof(f47,plain,(
% 0.13/5.74 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f46])).
% 0.13/5.74 fof(f48,plain,(
% 0.13/5.74 (?[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(Z,Y),X))))),
% 0.13/5.74 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.13/5.74 fof(f49,plain,(
% 0.13/5.74 (((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(sK2_skl,sK1_skl),sK0_skl)))),
% 0.13/5.74 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])).
% 0.13/5.74 fof(f50,plain,(
% 0.13/5.74 convergent_lines(sK0_skl,sK1_skl)),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/5.74 fof(f51,plain,(
% 0.13/5.74 convergent_lines(sK2_skl,sK1_skl)),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/5.74 fof(f53,plain,(
% 0.13/5.74 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/5.74 fof(f54,plain,(
% 0.13/5.74 ~apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK0_skl)),
% 0.13/5.74 inference(cnf_transformation,[status(thm)],[f49])).
% 0.13/5.74 fof(f66,plain,(
% 0.13/5.74 ![X0]: (distinct_points(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(X0,sK2_skl))),
% 0.13/5.74 inference(resolution,[status(thm)],[f41,f53])).
% 0.13/5.74 fof(f73,plain,(
% 0.13/5.74 ![X0]: (distinct_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.13/5.74 inference(resolution,[status(thm)],[f47,f50])).
% 0.13/5.74 fof(f82,plain,(
% 0.13/5.74 ![X0,X1,X2]: (apart_point_and_line(X0,sK2_skl)|~distinct_lines(X1,X2)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X2)|apart_point_and_line(X0,X1)|apart_point_and_line(X0,X2))),
% 0.13/5.74 inference(resolution,[status(thm)],[f66,f38])).
% 0.13/5.74 fof(f145,definition,(
% 0.13/5.74 sQ7_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.13/5.74 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.13/5.74 fof(f147,plain,(
% 0.13/5.74 ~convergent_lines(sK0_skl,sK1_skl)|sQ7_spl),
% 0.13/5.74 inference(component_clause,[status(thm)],[f145])).
% 0.13/5.74 fof(f153,plain,(
% 0.13/5.74 $false|sQ7_spl),
% 0.13/5.74 inference(forward_subsumption_resolution,[status(thm)],[f147,f50])).
% 0.13/5.74 fof(f154,plain,(
% 0.13/5.74 sQ7_spl),
% 0.13/5.74 inference(contradiction_clause,[status(thm)],[f153])).
% 0.13/5.74 fof(f255,plain,(
% 0.13/5.74 ![X0,X1]: (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,X1)|convergent_lines(sK0_skl,X1))),
% 0.13/5.74 inference(resolution,[status(thm)],[f82,f73])).
% 0.13/5.74 fof(f271,definition,(
% 0.13/5.74 sQ19_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.13/5.74 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.13/5.74 fof(f272,plain,(
% 0.13/5.74 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ19_spl),
% 0.13/5.74 inference(component_clause,[status(thm)],[f271])).
% 0.13/5.74 fof(f278,definition,(
% 0.13/5.74 sQ21_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 0.13/5.74 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.13/5.74 fof(f279,plain,(
% 0.13/5.74 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ21_spl),
% 0.13/5.74 inference(component_clause,[status(thm)],[f278])).
% 0.13/5.74 fof(f302,definition,(
% 0.13/5.74 ![X0,X1]: (sQ27_spl <=> (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,X1)|convergent_lines(sK0_skl,X1)))),
% 0.13/5.74 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.13/5.74 fof(f303,plain,(
% 0.13/5.74 ![X0,X1]: (apart_point_and_line(X0,sK2_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,X1)|convergent_lines(sK0_skl,X1)|~sQ27_spl)),
% 0.13/5.74 inference(component_clause,[status(thm)],[f302])).
% 0.13/5.74 fof(f305,plain,(
% 0.13/5.74 sQ27_spl|sQ21_spl),
% 0.13/5.74 inference(split_clause,[status(thm)],[f255,f302,f278])).
% 0.13/5.74 fof(f327,plain,(
% 0.13/5.74 ~convergent_lines(sK0_skl,sK1_skl)|~sQ21_spl),
% 0.13/5.74 inference(resolution,[status(thm)],[f279,f36])).
% 0.13/5.74 fof(f330,plain,(
% 0.13/5.74 ~sQ7_spl|~sQ21_spl),
% 0.13/5.74 inference(split_clause,[status(thm)],[f327,f145,f278])).
% 0.13/5.74 fof(f331,plain,(
% 0.13/5.74 ~convergent_lines(sK0_skl,sK1_skl)|~sQ19_spl),
% 0.13/5.74 inference(resolution,[status(thm)],[f272,f34])).
% 0.13/5.74 fof(f334,plain,(
% 0.13/5.74 ~sQ7_spl|~sQ19_spl),
% 0.13/5.74 inference(split_clause,[status(thm)],[f331,f145,f271])).
% 0.13/5.74 fof(f1660,plain,(
% 0.13/5.74 apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl)|convergent_lines(sK0_skl,sK0_skl)|~sQ27_spl),
% 0.13/5.74 inference(resolution,[status(thm)],[f303,f54])).
% 0.13/5.74 fof(f1667,definition,(
% 0.13/5.74 sQ101_spl <=> (convergent_lines(sK0_skl,sK0_skl))),
% 0.13/5.74 introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition])).
% 0.13/5.74 fof(f1668,plain,(
% 0.13/5.74 convergent_lines(sK0_skl,sK0_skl)|~sQ101_spl),
% 0.13/5.74 inference(component_clause,[status(thm)],[f1667])).
% 0.13/5.74 fof(f1717,definition,(
% 0.13/5.74 sQ111_spl <=> (apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl))),
% 0.13/5.74 introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition])).
% 0.13/5.74 fof(f1718,plain,(
% 0.13/5.74 apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl)|~sQ111_spl),
% 0.13/5.74 inference(component_clause,[status(thm)],[f1717])).
% 0.13/5.74 fof(f1720,definition,(
% 0.13/5.74 sQ112_spl <=> (apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl))),
% 0.13/5.74 introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition])).
% 0.13/5.74 fof(f1721,plain,(
% 0.13/5.74 apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl)|~sQ112_spl),
% 0.13/5.74 inference(component_clause,[status(thm)],[f1720])).
% 0.13/5.74 fof(f1723,plain,(
% 0.13/5.74 sQ111_spl|sQ19_spl|sQ112_spl|sQ101_spl|~sQ27_spl),
% 0.13/5.74 inference(split_clause,[status(thm)],[f1660,f1717,f271,f1720,f1667,f302])).
% 0.13/5.74 fof(f1724,plain,(
% 0.13/5.74 $false|~sQ101_spl),
% 0.13/5.74 inference(forward_subsumption_resolution,[status(thm)],[f1668,f19])).
% 0.13/5.74 fof(f1725,plain,(
% 0.13/5.74 ~sQ101_spl),
% 0.13/5.74 inference(contradiction_clause,[status(thm)],[f1724])).
% 0.13/5.74 fof(f1726,plain,(
% 0.13/5.74 ~convergent_lines(sK2_skl,sK1_skl)|~sQ111_spl),
% 0.13/5.74 inference(resolution,[status(thm)],[f1718,f34])).
% 0.13/5.74 fof(f1729,plain,(
% 0.13/5.74 $false|~sQ111_spl),
% 0.13/5.74 inference(forward_subsumption_resolution,[status(thm)],[f1726,f51])).
% 0.13/5.74 fof(f1730,plain,(
% 0.13/5.74 ~sQ111_spl),
% 0.13/5.74 inference(contradiction_clause,[status(thm)],[f1729])).
% 0.13/5.74 fof(f1731,plain,(
% 0.13/5.74 ~convergent_lines(sK2_skl,sK1_skl)|~sQ112_spl),
% 0.13/5.74 inference(resolution,[status(thm)],[f1721,f36])).
% 0.13/5.74 fof(f1734,plain,(
% 0.13/5.74 $false|~sQ112_spl),
% 0.13/5.74 inference(forward_subsumption_resolution,[status(thm)],[f1731,f51])).
% 0.13/5.74 fof(f1735,plain,(
% 0.13/5.74 ~sQ112_spl),
% 0.13/5.74 inference(contradiction_clause,[status(thm)],[f1734])).
% 0.13/5.74 fof(f1736,plain,(
% 0.13/5.74 $false),
% 0.13/5.74 inference(sat_refutation,[status(thm)],[f154,f305,f330,f334,f1723,f1725,f1730,f1735])).
% 0.13/5.74 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/5.76 % Elapsed time: 0.363400 seconds
% 0.13/5.76 % CPU time: 2.721371 seconds
% 0.13/5.76 % Total memory used: 41.221 MB
% 0.13/5.76 % Net memory used: 34.563 MB
%------------------------------------------------------------------------------