%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO177+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 : 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 12:25:57 PM UTC 2026
% Result : Theorem 0.08s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO177+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 20 13:01:53 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.40 fof(f2,axiom,(
% 0.08/0.40 (! [X] : ~ distinct_lines(X,X) )),
% 0.08/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.40 fof(f5,axiom,(
% 0.08/0.40 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 0.08/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.40 fof(f13,axiom,(
% 0.08/0.40 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.08/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.40 fof(f15,axiom,(
% 0.08/0.40 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 0.08/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.40 fof(f16,axiom,(
% 0.08/0.40 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 0.08/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.40 fof(f17,axiom,(
% 0.08/0.40 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 0.08/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.40 fof(f32,axiom,(
% 0.08/0.40 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 0.08/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.40 fof(f36,conjecture,(
% 0.08/0.40 (! [X,Y,U,V] :( ( distinct_points(X,Y)& distinct_points(U,V) )=> ( ( apart_point_and_line(X,line_connecting(U,V))| apart_point_and_line(Y,line_connecting(U,V)) )=> ( apart_point_and_line(U,line_connecting(X,Y))| apart_point_and_line(V,line_connecting(X,Y)) ) ) ) )),
% 0.08/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.40 fof(f37,negated_conjecture,(
% 0.08/0.40 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& distinct_points(U,V) )=> ( ( apart_point_and_line(X,line_connecting(U,V))| apart_point_and_line(Y,line_connecting(U,V)) )=> ( apart_point_and_line(U,line_connecting(X,Y))| apart_point_and_line(V,line_connecting(X,Y)) ) ) ) ))),
% 0.08/0.40 inference(negated_conjecture,[status(cth)],[f36])).
% 0.08/0.40 fof(f39,plain,(
% 0.08/0.40 ![X0]: (~distinct_lines(X0,X0))),
% 0.08/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.08/0.40 fof(f44,plain,(
% 0.08/0.40 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 0.08/0.40 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.08/0.40 fof(f45,plain,(
% 0.08/0.40 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 0.08/0.40 inference(miniscoping,[status(thm)],[f44])).
% 0.08/0.40 fof(f46,plain,(
% 0.08/0.40 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.08/0.40 inference(cnf_transformation,[status(thm)],[f45])).
% 0.08/0.40 fof(f63,plain,(
% 0.08/0.40 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.08/0.40 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.08/0.40 fof(f64,plain,(
% 0.08/0.40 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.08/0.40 inference(miniscoping,[status(thm)],[f63])).
% 0.08/0.40 fof(f65,plain,(
% 0.08/0.40 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.08/0.40 inference(cnf_transformation,[status(thm)],[f64])).
% 0.08/0.40 fof(f69,plain,(
% 0.08/0.40 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 0.08/0.40 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.08/0.40 fof(f70,plain,(
% 0.08/0.40 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 0.08/0.40 inference(cnf_transformation,[status(thm)],[f69])).
% 0.08/0.40 fof(f71,plain,(
% 0.08/0.40 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 0.08/0.40 inference(cnf_transformation,[status(thm)],[f16])).
% 0.08/0.40 fof(f72,plain,(
% 0.08/0.40 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 0.08/0.40 inference(cnf_transformation,[status(thm)],[f17])).
% 0.08/0.40 fof(f111,plain,(
% 0.08/0.40 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.08/0.40 inference(NNF_transformation,[status(thm)],[f32])).
% 0.08/0.40 fof(f112,plain,(
% 0.08/0.40 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.08/0.40 inference(miniscoping,[status(thm)],[f111])).
% 0.08/0.40 fof(f113,plain,(
% 0.08/0.40 ![X0,X1]: (~equal_lines(X0,X1)|~distinct_lines(X0,X1))),
% 0.08/0.40 inference(cnf_transformation,[status(thm)],[f112])).
% 0.08/0.40 fof(f114,plain,(
% 0.08/0.40 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.08/0.40 inference(cnf_transformation,[status(thm)],[f112])).
% 0.08/0.40 fof(f127,plain,(
% 0.08/0.40 (?[X,Y,U,V]: ((distinct_points(X,Y)&distinct_points(U,V))&((apart_point_and_line(X,line_connecting(U,V))|apart_point_and_line(Y,line_connecting(U,V)))&(~apart_point_and_line(U,line_connecting(X,Y))&~apart_point_and_line(V,line_connecting(X,Y))))))),
% 0.08/0.40 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.08/0.40 fof(f128,plain,(
% 0.08/0.40 ((distinct_points(sK0_skl,sK1_skl)&distinct_points(sK2_skl,sK3_skl))&((apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)))&(~apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))&~apart_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)))))),
% 0.08/0.40 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])).
% 0.08/0.40 fof(f131,plain,(
% 0.08/0.40 apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))|apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))),
% 0.08/0.40 inference(cnf_transformation,[status(thm)],[f128])).
% 0.08/0.40 fof(f144,definition,(
% 0.08/0.40 sQ0_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)))),
% 0.08/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/0.40 fof(f145,plain,(
% 0.08/0.40 apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl))|~sQ0_spl),
% 0.08/0.40 inference(component_clause,[status(thm)],[f144])).
% 0.08/0.40 fof(f147,definition,(
% 0.08/0.40 sQ1_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)))),
% 0.08/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.08/0.40 fof(f148,plain,(
% 0.08/0.40 apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl))|~sQ1_spl),
% 0.08/0.40 inference(component_clause,[status(thm)],[f147])).
% 0.08/0.40 fof(f150,plain,(
% 0.08/0.40 sQ0_spl|sQ1_spl),
% 0.08/0.40 inference(split_clause,[status(thm)],[f131,f144,f147])).
% 0.08/0.40 fof(f247,plain,(
% 0.08/0.40 ![X0]: (distinct_lines(line_connecting(sK2_skl,sK3_skl),X0)|apart_point_and_line(sK1_skl,X0)|~sQ1_spl)),
% 0.08/0.40 inference(resolution,[status(thm)],[f148,f65])).
% 0.08/0.40 fof(f434,plain,(
% 0.08/0.40 ![X0]: (distinct_lines(line_connecting(sK2_skl,sK3_skl),X0)|apart_point_and_line(sK0_skl,X0)|~sQ0_spl)),
% 0.08/0.40 inference(resolution,[status(thm)],[f145,f65])).
% 0.08/0.40 fof(f489,plain,(
% 0.08/0.40 ![X0,X1]: (equal_lines(X0,X1)|convergent_lines(X0,X1))),
% 0.08/0.40 inference(resolution,[status(thm)],[f114,f70])).
% 0.08/0.40 fof(f491,plain,(
% 0.08/0.40 ![X0,X1,X2]: (equal_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.08/0.40 inference(resolution,[status(thm)],[f114,f46])).
% 0.08/0.40 fof(f597,plain,(
% 0.08/0.40 ![X0,X1]: (equal_lines(parallel_through_point(X0,X1),X0))),
% 0.08/0.40 inference(resolution,[status(thm)],[f489,f71])).
% 0.08/0.40 fof(f641,plain,(
% 0.08/0.40 ![X0,X1]: (~distinct_lines(parallel_through_point(X0,X1),X0))),
% 0.08/0.40 inference(resolution,[status(thm)],[f597,f113])).
% 0.08/0.40 fof(f933,plain,(
% 0.08/0.40 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X1,X0))),
% 0.08/0.40 inference(resolution,[status(thm)],[f491,f39])).
% 0.08/0.40 fof(f1294,plain,(
% 0.08/0.40 ![X0,X1]: (equal_lines(X0,parallel_through_point(X0,X1)))),
% 0.08/0.40 inference(resolution,[status(thm)],[f933,f641])).
% 0.08/0.40 fof(f1300,plain,(
% 0.08/0.40 ![X0,X1]: (~distinct_lines(X0,parallel_through_point(X0,X1)))),
% 0.08/0.40 inference(resolution,[status(thm)],[f1294,f113])).
% 0.08/0.40 fof(f1441,plain,(
% 0.08/0.40 ![X0]: (apart_point_and_line(sK0_skl,parallel_through_point(line_connecting(sK2_skl,sK3_skl),X0))|~sQ0_spl)),
% 0.08/0.40 inference(resolution,[status(thm)],[f1300,f434])).
% 0.08/0.40 fof(f1669,plain,(
% 0.08/0.40 $false|~sQ0_spl),
% 0.08/0.40 inference(resolution,[status(thm)],[f1441,f72])).
% 0.08/0.40 fof(f1672,plain,(
% 0.08/0.40 ~sQ0_spl),
% 0.08/0.40 inference(contradiction_clause,[status(thm)],[f1669])).
% 0.08/0.40 fof(f1781,plain,(
% 0.08/0.40 ![X0]: (apart_point_and_line(sK1_skl,parallel_through_point(line_connecting(sK2_skl,sK3_skl),X0))|~sQ1_spl)),
% 0.08/0.40 inference(resolution,[status(thm)],[f247,f1300])).
% 0.08/0.40 fof(f1871,plain,(
% 0.08/0.40 $false|~sQ1_spl),
% 0.08/0.40 inference(resolution,[status(thm)],[f1781,f72])).
% 0.08/0.40 fof(f1874,plain,(
% 0.08/0.40 ~sQ1_spl),
% 0.08/0.40 inference(contradiction_clause,[status(thm)],[f1871])).
% 0.08/0.40 fof(f1875,plain,(
% 0.08/0.40 $false),
% 0.08/0.40 inference(sat_refutation,[status(thm)],[f150,f1672,f1874])).
% 0.08/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.40 % Elapsed time: 0.095098 seconds
% 0.08/0.40 % CPU time: 0.542287 seconds
% 0.08/0.40 % Total memory used: 28.981 MB
% 0.08/0.40 % Net memory used: 27.290 MB
%------------------------------------------------------------------------------