%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO201+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 : n014.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 12:26:04 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:35:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f3,axiom,(
% 0.09/0.40 (! [X] : ~ convergent_lines(X,X) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f6,axiom,(
% 0.09/0.40 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f9,axiom,(
% 0.09/0.40 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f10,axiom,(
% 0.09/0.40 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f11,axiom,(
% 0.09/0.40 (! [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) ) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f14,axiom,(
% 0.09/0.40 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f15,conjecture,(
% 0.09/0.40 (! [X,Y] :( convergent_lines(X,Y)=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f16,negated_conjecture,(
% 0.09/0.40 ~((! [X,Y] :( convergent_lines(X,Y)=> ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ) ))),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f15])).
% 0.09/0.40 fof(f19,plain,(
% 0.09/0.40 ![X0]: (~convergent_lines(X0,X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/0.40 fof(f26,plain,(
% 0.09/0.40 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.09/0.40 fof(f27,plain,(
% 0.09/0.40 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f26])).
% 0.09/0.40 fof(f28,plain,(
% 0.09/0.40 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f27])).
% 0.09/0.40 fof(f33,plain,(
% 0.09/0.40 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.09/0.40 fof(f34,plain,(
% 0.09/0.40 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f33])).
% 0.09/0.40 fof(f35,plain,(
% 0.09/0.40 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.09/0.40 fof(f36,plain,(
% 0.09/0.40 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f35])).
% 0.09/0.40 fof(f37,plain,(
% 0.09/0.40 ![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)))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.09/0.40 fof(f38,plain,(
% 0.09/0.40 ![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))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f37])).
% 0.09/0.40 fof(f45,plain,(
% 0.09/0.40 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.09/0.40 fof(f46,plain,(
% 0.09/0.40 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f45])).
% 0.09/0.40 fof(f47,plain,(
% 0.09/0.40 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f46])).
% 0.09/0.40 fof(f48,plain,(
% 0.09/0.40 (?[X,Y]: (convergent_lines(X,Y)&distinct_points(intersection_point(X,Y),intersection_point(Y,X))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.09/0.40 fof(f49,plain,(
% 0.09/0.40 (convergent_lines(sK0_skl,sK1_skl)&distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl)))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f48])).
% 0.09/0.40 fof(f50,plain,(
% 0.09/0.40 convergent_lines(sK0_skl,sK1_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.09/0.40 fof(f51,plain,(
% 0.09/0.40 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.09/0.40 fof(f53,plain,(
% 0.09/0.40 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.09/0.40 inference(resolution,[status(thm)],[f28,f50])).
% 0.09/0.40 fof(f55,plain,(
% 0.09/0.40 convergent_lines(sK1_skl,sK0_skl)),
% 0.09/0.40 inference(resolution,[status(thm)],[f53,f19])).
% 0.09/0.40 fof(f60,plain,(
% 0.09/0.40 ![X0]: (distinct_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.09/0.40 inference(resolution,[status(thm)],[f47,f50])).
% 0.09/0.40 fof(f103,plain,(
% 0.09/0.40 ![X0,X1]: (~distinct_lines(X0,X1)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X1))),
% 0.09/0.40 inference(resolution,[status(thm)],[f38,f51])).
% 0.09/0.40 fof(f105,plain,(
% 0.09/0.40 ![X0]: (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0)|convergent_lines(sK0_skl,X0))),
% 0.09/0.40 inference(resolution,[status(thm)],[f103,f60])).
% 0.09/0.40 fof(f107,definition,(
% 0.09/0.40 sQ6_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f108,plain,(
% 0.09/0.40 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ6_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f107])).
% 0.09/0.40 fof(f110,definition,(
% 0.09/0.40 ![X0]: (sQ7_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0)|convergent_lines(sK0_skl,X0)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f111,plain,(
% 0.09/0.40 ![X0]: (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0)|convergent_lines(sK0_skl,X0)|~sQ7_spl)),
% 0.09/0.40 inference(component_clause,[status(thm)],[f110])).
% 0.09/0.40 fof(f113,definition,(
% 0.09/0.40 sQ8_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f114,plain,(
% 0.09/0.40 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|~sQ8_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f113])).
% 0.09/0.40 fof(f116,plain,(
% 0.09/0.40 sQ6_spl|sQ7_spl|sQ8_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f105,f107,f110,f113])).
% 0.09/0.40 fof(f117,definition,(
% 0.09/0.40 sQ9_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f118,plain,(
% 0.09/0.40 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ9_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f117])).
% 0.09/0.40 fof(f119,plain,(
% 0.09/0.40 ~apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|sQ9_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f117])).
% 0.09/0.40 fof(f123,definition,(
% 0.09/0.40 sQ11_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f124,plain,(
% 0.09/0.40 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|~sQ11_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f123])).
% 0.09/0.40 fof(f176,plain,(
% 0.09/0.40 ~convergent_lines(sK1_skl,sK0_skl)|~sQ11_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f124,f36])).
% 0.09/0.40 fof(f179,plain,(
% 0.09/0.40 $false|~sQ11_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f176,f55])).
% 0.09/0.40 fof(f180,plain,(
% 0.09/0.40 ~sQ11_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f179])).
% 0.09/0.40 fof(f183,plain,(
% 0.09/0.40 ~convergent_lines(sK0_skl,sK1_skl)|~sQ9_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f118,f34])).
% 0.09/0.40 fof(f186,plain,(
% 0.09/0.41 $false|~sQ9_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f183,f50])).
% 0.09/0.41 fof(f187,plain,(
% 0.09/0.41 ~sQ9_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f186])).
% 0.09/0.41 fof(f188,plain,(
% 0.09/0.41 ~convergent_lines(sK1_skl,sK0_skl)|~sQ8_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f114,f34])).
% 0.09/0.41 fof(f191,plain,(
% 0.09/0.41 $false|~sQ8_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f188,f55])).
% 0.09/0.41 fof(f192,plain,(
% 0.09/0.41 ~sQ8_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f191])).
% 0.09/0.41 fof(f193,plain,(
% 0.09/0.41 ~convergent_lines(sK0_skl,sK1_skl)|~sQ6_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f108,f36])).
% 0.09/0.41 fof(f196,plain,(
% 0.09/0.41 $false|~sQ6_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f193,f50])).
% 0.09/0.41 fof(f197,plain,(
% 0.09/0.41 ~sQ6_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f196])).
% 0.09/0.41 fof(f359,plain,(
% 0.09/0.41 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|convergent_lines(sK0_skl,sK0_skl)|~sQ7_spl|sQ9_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f111,f119])).
% 0.09/0.41 fof(f367,definition,(
% 0.09/0.41 sQ34_spl <=> (convergent_lines(sK0_skl,sK0_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f368,plain,(
% 0.09/0.41 convergent_lines(sK0_skl,sK0_skl)|~sQ34_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f367])).
% 0.09/0.41 fof(f370,plain,(
% 0.09/0.41 sQ11_spl|sQ34_spl|~sQ7_spl|sQ9_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f359,f123,f367,f110,f117])).
% 0.09/0.41 fof(f373,plain,(
% 0.09/0.41 $false|~sQ34_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f368,f19])).
% 0.09/0.41 fof(f374,plain,(
% 0.09/0.41 ~sQ34_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f373])).
% 0.09/0.41 fof(f375,plain,(
% 0.09/0.41 $false),
% 0.09/0.41 inference(sat_refutation,[status(thm)],[f116,f180,f187,f192,f197,f370,f374])).
% 0.09/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.42 % Elapsed time: 0.052769 seconds
% 0.09/0.42 % CPU time: 0.180763 seconds
% 0.09/0.42 % Total memory used: 18.368 MB
% 0.09/0.42 % Net memory used: 17.765 MB
%------------------------------------------------------------------------------