%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO187+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 : n015.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 12:26:00 PM UTC 2026
% Result : Theorem 0.22s 0.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n015.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 13:15:05 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.22/0.61 % Refutation found
% 0.22/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.61 % SZS output start CNFRefutation for theBenchmark
% 0.22/0.61 fof(f2,axiom,(
% 0.22/0.61 (! [X] : ~ distinct_lines(X,X) )),
% 0.22/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/0.61 fof(f5,axiom,(
% 0.22/0.61 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 0.22/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/0.61 fof(f13,axiom,(
% 0.22/0.61 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.22/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/0.61 fof(f15,axiom,(
% 0.22/0.61 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 0.22/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/0.61 fof(f16,axiom,(
% 0.22/0.61 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 0.22/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/0.61 fof(f17,axiom,(
% 0.22/0.61 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 0.22/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/0.61 fof(f32,axiom,(
% 0.22/0.61 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 0.22/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/0.61 fof(f34,axiom,(
% 0.22/0.61 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 0.22/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/0.61 fof(f36,conjecture,(
% 0.22/0.61 (! [X,Y,U,V] :( ( distinct_points(X,Y)& distinct_points(U,V)& incident_point_and_line(X,line_connecting(U,V))& incident_point_and_line(Y,line_connecting(U,V)) )=> ( incident_point_and_line(U,line_connecting(X,Y))& incident_point_and_line(V,line_connecting(X,Y)) ) ) )),
% 0.22/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.22/0.61 fof(f37,negated_conjecture,(
% 0.22/0.61 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& distinct_points(U,V)& incident_point_and_line(X,line_connecting(U,V))& incident_point_and_line(Y,line_connecting(U,V)) )=> ( incident_point_and_line(U,line_connecting(X,Y))& incident_point_and_line(V,line_connecting(X,Y)) ) ) ))),
% 0.22/0.61 inference(negated_conjecture,[status(cth)],[f36])).
% 0.22/0.61 fof(f39,plain,(
% 0.22/0.61 ![X0]: (~distinct_lines(X0,X0))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f2])).
% 0.22/0.61 fof(f44,plain,(
% 0.22/0.61 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 0.22/0.61 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.22/0.61 fof(f45,plain,(
% 0.22/0.61 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 0.22/0.61 inference(miniscoping,[status(thm)],[f44])).
% 0.22/0.61 fof(f46,plain,(
% 0.22/0.61 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f45])).
% 0.22/0.61 fof(f63,plain,(
% 0.22/0.61 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.22/0.61 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.22/0.61 fof(f64,plain,(
% 0.22/0.61 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.22/0.61 inference(miniscoping,[status(thm)],[f63])).
% 0.22/0.61 fof(f65,plain,(
% 0.22/0.61 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f64])).
% 0.22/0.61 fof(f69,plain,(
% 0.22/0.61 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 0.22/0.61 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.22/0.61 fof(f70,plain,(
% 0.22/0.61 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f69])).
% 0.22/0.61 fof(f71,plain,(
% 0.22/0.61 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f16])).
% 0.22/0.61 fof(f72,plain,(
% 0.22/0.61 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f17])).
% 0.22/0.61 fof(f111,plain,(
% 0.22/0.61 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.22/0.61 inference(NNF_transformation,[status(thm)],[f32])).
% 0.22/0.61 fof(f112,plain,(
% 0.22/0.61 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.22/0.61 inference(miniscoping,[status(thm)],[f111])).
% 0.22/0.61 fof(f113,plain,(
% 0.22/0.61 ![X0,X1]: (~equal_lines(X0,X1)|~distinct_lines(X0,X1))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f112])).
% 0.22/0.61 fof(f114,plain,(
% 0.22/0.61 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f112])).
% 0.22/0.61 fof(f119,plain,(
% 0.22/0.61 ![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)))),
% 0.22/0.61 inference(NNF_transformation,[status(thm)],[f34])).
% 0.22/0.61 fof(f120,plain,(
% 0.22/0.61 (![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)))),
% 0.22/0.61 inference(miniscoping,[status(thm)],[f119])).
% 0.22/0.61 fof(f122,plain,(
% 0.22/0.61 ![X0,X1]: (incident_point_and_line(X0,X1)|apart_point_and_line(X0,X1))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f120])).
% 0.22/0.61 fof(f127,plain,(
% 0.22/0.61 (?[X,Y,U,V]: ((((distinct_points(X,Y)&distinct_points(U,V))&incident_point_and_line(X,line_connecting(U,V)))&incident_point_and_line(Y,line_connecting(U,V)))&(~incident_point_and_line(U,line_connecting(X,Y))|~incident_point_and_line(V,line_connecting(X,Y)))))),
% 0.22/0.61 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.22/0.61 fof(f128,plain,(
% 0.22/0.61 ((((distinct_points(sK0_skl,sK1_skl)&distinct_points(sK2_skl,sK3_skl))&incident_point_and_line(sK0_skl,line_connecting(sK2_skl,sK3_skl)))&incident_point_and_line(sK1_skl,line_connecting(sK2_skl,sK3_skl)))&(~incident_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|~incident_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))))),
% 0.22/0.61 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])).
% 0.22/0.61 fof(f133,plain,(
% 0.22/0.61 ~incident_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|~incident_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.22/0.61 inference(cnf_transformation,[status(thm)],[f128])).
% 0.22/0.61 fof(f144,definition,(
% 0.22/0.61 sQ0_spl <=> (incident_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.22/0.61 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.22/0.61 fof(f146,plain,(
% 0.22/0.61 ~incident_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))|sQ0_spl),
% 0.22/0.61 inference(component_clause,[status(thm)],[f144])).
% 0.22/0.61 fof(f147,definition,(
% 0.22/0.61 sQ1_spl <=> (incident_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.22/0.61 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.22/0.61 fof(f149,plain,(
% 0.22/0.61 ~incident_point_and_line(sK3_skl,line_connecting(sK0_skl,sK1_skl))|sQ1_spl),
% 0.22/0.61 inference(component_clause,[status(thm)],[f147])).
% 0.22/0.61 fof(f150,plain,(
% 0.22/0.61 ~sQ0_spl|~sQ1_spl),
% 0.22/0.61 inference(split_clause,[status(thm)],[f133,f144,f147])).
% 0.22/0.61 fof(f188,plain,(
% 0.22/0.61 ![X0,X1,X2]: (distinct_lines(X0,X1)|apart_point_and_line(X2,X1)|incident_point_and_line(X2,X0))),
% 0.22/0.61 inference(resolution,[status(thm)],[f65,f122])).
% 0.22/0.61 fof(f233,plain,(
% 0.22/0.61 ![X0,X1,X2]: (distinct_lines(X0,parallel_through_point(X1,X2))|incident_point_and_line(X2,X0))),
% 0.22/0.61 inference(resolution,[status(thm)],[f188,f72])).
% 0.22/0.61 fof(f239,plain,(
% 0.22/0.61 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,X0)|sQ0_spl)),
% 0.22/0.61 inference(resolution,[status(thm)],[f188,f146])).
% 0.22/0.61 fof(f304,plain,(
% 0.22/0.61 ![X0,X1]: (equal_lines(X0,X1)|convergent_lines(X0,X1))),
% 0.22/0.61 inference(resolution,[status(thm)],[f114,f70])).
% 0.22/0.61 fof(f306,plain,(
% 0.22/0.61 ![X0,X1,X2]: (equal_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.22/0.61 inference(resolution,[status(thm)],[f114,f46])).
% 0.22/0.61 fof(f470,plain,(
% 0.22/0.61 ![X0,X1]: (equal_lines(parallel_through_point(X0,X1),X0))),
% 0.22/0.61 inference(resolution,[status(thm)],[f304,f71])).
% 0.22/0.61 fof(f482,plain,(
% 0.22/0.61 ![X0,X1]: (~distinct_lines(parallel_through_point(X0,X1),X0))),
% 0.22/0.61 inference(resolution,[status(thm)],[f470,f113])).
% 0.22/0.61 fof(f851,plain,(
% 0.22/0.61 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X1,X0))),
% 0.22/0.61 inference(resolution,[status(thm)],[f306,f39])).
% 0.22/0.61 fof(f939,plain,(
% 0.22/0.61 ![X0,X1]: (equal_lines(X0,parallel_through_point(X0,X1)))),
% 0.22/0.61 inference(resolution,[status(thm)],[f851,f482])).
% 0.22/0.61 fof(f945,plain,(
% 0.22/0.61 ![X0,X1]: (~distinct_lines(X0,parallel_through_point(X0,X1)))),
% 0.22/0.61 inference(resolution,[status(thm)],[f939,f113])).
% 0.22/0.61 fof(f946,plain,(
% 0.22/0.61 ![X0]: (apart_point_and_line(sK2_skl,parallel_through_point(line_connecting(sK0_skl,sK1_skl),X0))|sQ0_spl)),
% 0.22/0.62 inference(resolution,[status(thm)],[f945,f239])).
% 0.22/0.62 fof(f947,plain,(
% 0.22/0.62 ![X0,X1]: (incident_point_and_line(X0,X1))),
% 0.22/0.62 inference(resolution,[status(thm)],[f945,f233])).
% 0.22/0.62 fof(f1011,plain,(
% 0.22/0.62 $false|sQ0_spl),
% 0.22/0.62 inference(resolution,[status(thm)],[f946,f72])).
% 0.22/0.62 fof(f1015,plain,(
% 0.22/0.62 sQ0_spl),
% 0.22/0.62 inference(contradiction_clause,[status(thm)],[f1011])).
% 0.22/0.62 fof(f1034,plain,(
% 0.22/0.62 $false|sQ1_spl),
% 0.22/0.62 inference(backward_subsumption_resolution,[status(thm)],[f149,f947])).
% 0.22/0.62 fof(f1035,plain,(
% 0.22/0.62 sQ1_spl),
% 0.22/0.62 inference(contradiction_clause,[status(thm)],[f1034])).
% 0.22/0.62 fof(f1036,plain,(
% 0.22/0.62 $false),
% 0.22/0.62 inference(sat_refutation,[status(thm)],[f150,f1015,f1035])).
% 0.22/0.62 % SZS output end CNFRefutation for theBenchmark.p
% 0.22/0.62 % Elapsed time: 0.171370 seconds
% 0.22/0.62 % CPU time: 1.206397 seconds
% 0.22/0.62 % Total memory used: 31.238 MB
% 0.22/0.62 % Net memory used: 28.745 MB
%------------------------------------------------------------------------------