%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO202+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 : 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 12:26:04 PM UTC 2026
% Result : Theorem 0.07s 10.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO202+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/10.31 % Computer : n012.cluster.edu
% 0.03/10.31 % Model : x86_64 x86_64
% 0.03/10.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.31 % Memory : 8046.5625MB
% 0.03/10.31 % OS : Linux 6.8.0-71-generic
% 0.03/10.31 % CPULimit : 300
% 0.03/10.31 % WCLimit : 300
% 0.03/10.31 % DateTime : Sun Sep 20 13:22:21 UTC 2026
% 0.03/10.31 % CPUTime :
% 0.03/10.32 % Drodi V4.1.1
% 0.07/10.43 % Refutation found
% 0.07/10.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/10.43 % SZS output start CNFRefutation for theBenchmark
% 0.07/10.43 fof(f3,axiom,(
% 0.07/10.43 (! [X] : ~ convergent_lines(X,X) )),
% 0.07/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/10.43 fof(f7,axiom,(
% 0.07/10.43 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.07/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/10.43 fof(f9,axiom,(
% 0.07/10.43 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.07/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/10.43 fof(f10,axiom,(
% 0.07/10.43 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.07/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/10.43 fof(f11,axiom,(
% 0.07/10.43 (! [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) ) ) )),
% 0.07/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/10.43 fof(f14,axiom,(
% 0.07/10.43 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.07/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/10.43 fof(f15,conjecture,(
% 0.07/10.43 (! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ) )),
% 0.07/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.07/10.43 fof(f16,negated_conjecture,(
% 0.07/10.43 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )=> ~ distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ) ))),
% 0.07/10.43 inference(negated_conjecture,[status(cth)],[f15])).
% 0.07/10.43 fof(f19,plain,(
% 0.07/10.43 ![X0]: (~convergent_lines(X0,X0))),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f3])).
% 0.07/10.43 fof(f29,plain,(
% 0.07/10.43 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.07/10.43 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.07/10.43 fof(f30,plain,(
% 0.07/10.43 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f29])).
% 0.07/10.43 fof(f33,plain,(
% 0.07/10.43 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.07/10.43 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.07/10.43 fof(f34,plain,(
% 0.07/10.43 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f33])).
% 0.07/10.43 fof(f35,plain,(
% 0.07/10.43 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.07/10.43 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.07/10.43 fof(f36,plain,(
% 0.07/10.43 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f35])).
% 0.07/10.43 fof(f37,plain,(
% 0.07/10.43 ![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)))),
% 0.07/10.43 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.07/10.43 fof(f38,plain,(
% 0.07/10.43 ![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))),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f37])).
% 0.07/10.43 fof(f45,plain,(
% 0.07/10.43 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.07/10.43 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.07/10.43 fof(f46,plain,(
% 0.07/10.43 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.07/10.43 inference(miniscoping,[status(thm)],[f45])).
% 0.07/10.43 fof(f47,plain,(
% 0.07/10.43 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f46])).
% 0.07/10.43 fof(f48,plain,(
% 0.07/10.43 (?[X,Y,Z]: (((distinct_points(X,Y)&distinct_points(X,Z))&convergent_lines(line_connecting(X,Y),line_connecting(X,Z)))&distinct_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X)))),
% 0.07/10.43 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.07/10.43 fof(f49,plain,(
% 0.07/10.43 (((distinct_points(sK0_skl,sK1_skl)&distinct_points(sK0_skl,sK2_skl))&convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)))&distinct_points(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),sK0_skl))),
% 0.07/10.43 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])).
% 0.07/10.43 fof(f50,plain,(
% 0.07/10.43 distinct_points(sK0_skl,sK1_skl)),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f49])).
% 0.07/10.43 fof(f51,plain,(
% 0.07/10.43 distinct_points(sK0_skl,sK2_skl)),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f49])).
% 0.07/10.43 fof(f52,plain,(
% 0.07/10.43 convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f49])).
% 0.07/10.43 fof(f53,plain,(
% 0.07/10.43 distinct_points(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),sK0_skl)),
% 0.07/10.43 inference(cnf_transformation,[status(thm)],[f49])).
% 0.07/10.43 fof(f407,plain,(
% 0.07/10.43 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK2_skl),X0)|convergent_lines(line_connecting(sK0_skl,sK1_skl),X0))),
% 0.07/10.43 inference(resolution,[status(thm)],[f47,f52])).
% 0.07/10.43 fof(f624,plain,(
% 0.07/10.43 ![X0,X1]: (~distinct_lines(X0,X1)|apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),X0)|apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),X1)|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK0_skl,X1))),
% 0.07/10.43 inference(resolution,[status(thm)],[f38,f53])).
% 0.07/10.43 fof(f820,plain,(
% 0.07/10.43 distinct_lines(line_connecting(sK0_skl,sK2_skl),line_connecting(sK0_skl,sK1_skl))),
% 0.07/10.43 inference(resolution,[status(thm)],[f407,f19])).
% 0.07/10.43 fof(f879,definition,(
% 0.07/10.43 sQ40_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.07/10.43 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.07/10.43 fof(f880,plain,(
% 0.07/10.43 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|~sQ40_spl),
% 0.07/10.43 inference(component_clause,[status(thm)],[f879])).
% 0.07/10.43 fof(f890,definition,(
% 0.07/10.43 sQ43_spl <=> (apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK2_skl)))),
% 0.07/10.43 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.07/10.43 fof(f891,plain,(
% 0.07/10.43 apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK2_skl))|~sQ43_spl),
% 0.07/10.43 inference(component_clause,[status(thm)],[f890])).
% 0.07/10.43 fof(f1056,plain,(
% 0.07/10.43 ~distinct_points(sK0_skl,sK2_skl)|~sQ40_spl),
% 0.07/10.43 inference(resolution,[status(thm)],[f880,f30])).
% 0.07/10.43 fof(f1059,plain,(
% 0.07/10.43 $false|~sQ40_spl),
% 0.07/10.43 inference(forward_subsumption_resolution,[status(thm)],[f1056,f51])).
% 0.07/10.43 fof(f1060,plain,(
% 0.07/10.43 ~sQ40_spl),
% 0.07/10.43 inference(contradiction_clause,[status(thm)],[f1059])).
% 0.07/10.43 fof(f1071,plain,(
% 0.07/10.43 apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.07/10.43 inference(resolution,[status(thm)],[f820,f624])).
% 0.07/10.43 fof(f1073,definition,(
% 0.07/10.43 sQ67_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.07/10.43 introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition])).
% 0.07/10.43 fof(f1074,plain,(
% 0.07/10.43 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ67_spl),
% 0.07/10.43 inference(component_clause,[status(thm)],[f1073])).
% 0.07/10.43 fof(f1088,definition,(
% 0.07/10.43 sQ71_spl <=> (apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK1_skl)))),
% 0.07/10.43 introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition])).
% 0.07/10.43 fof(f1089,plain,(
% 0.07/10.43 apart_point_and_line(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),line_connecting(sK0_skl,sK1_skl))|~sQ71_spl),
% 0.07/10.43 inference(component_clause,[status(thm)],[f1088])).
% 0.07/10.43 fof(f1091,plain,(
% 0.07/10.43 sQ43_spl|sQ71_spl|sQ40_spl|sQ67_spl),
% 0.07/10.43 inference(split_clause,[status(thm)],[f1071,f890,f1088,f879,f1073])).
% 0.07/10.43 fof(f1094,plain,(
% 0.07/10.43 ~distinct_points(sK0_skl,sK1_skl)|~sQ67_spl),
% 0.07/10.43 inference(resolution,[status(thm)],[f1074,f30])).
% 0.07/10.43 fof(f1097,plain,(
% 0.07/10.43 $false|~sQ67_spl),
% 0.07/10.43 inference(forward_subsumption_resolution,[status(thm)],[f1094,f50])).
% 0.07/10.43 fof(f1098,plain,(
% 0.07/10.43 ~sQ67_spl),
% 0.07/10.43 inference(contradiction_clause,[status(thm)],[f1097])).
% 0.07/10.43 fof(f1103,plain,(
% 0.07/10.43 ~convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))|~sQ43_spl),
% 0.07/10.43 inference(resolution,[status(thm)],[f891,f36])).
% 0.07/10.43 fof(f1106,plain,(
% 0.07/10.43 $false|~sQ43_spl),
% 0.07/10.43 inference(forward_subsumption_resolution,[status(thm)],[f1103,f52])).
% 0.07/10.43 fof(f1107,plain,(
% 0.07/10.43 ~sQ43_spl),
% 0.07/10.43 inference(contradiction_clause,[status(thm)],[f1106])).
% 0.07/10.43 fof(f2203,plain,(
% 0.07/10.43 ~convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))|~sQ71_spl),
% 0.07/10.43 inference(resolution,[status(thm)],[f1089,f34])).
% 0.07/10.43 fof(f2206,plain,(
% 0.07/10.43 $false|~sQ71_spl),
% 0.07/10.43 inference(forward_subsumption_resolution,[status(thm)],[f2203,f52])).
% 0.07/10.43 fof(f2207,plain,(
% 0.07/10.43 ~sQ71_spl),
% 0.07/10.43 inference(contradiction_clause,[status(thm)],[f2206])).
% 0.07/10.43 fof(f2208,plain,(
% 0.07/10.43 $false),
% 0.07/10.43 inference(sat_refutation,[status(thm)],[f1060,f1091,f1098,f1107,f2207])).
% 0.07/10.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.07/10.44 % Elapsed time: 0.123700 seconds
% 0.07/10.44 % CPU time: 0.745261 seconds
% 0.07/10.44 % Total memory used: 30.322 MB
% 0.07/10.44 % Net memory used: 27.434 MB
%------------------------------------------------------------------------------