%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO198+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 : n010.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 12:26:03 PM UTC 2026
% Result : Theorem 1.22s 0.78s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO198+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
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 13:17:54 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 1.22/0.78 % Refutation found
% 1.22/0.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.22/0.78 % SZS output start CNFRefutation for theBenchmark
% 1.22/0.78 fof(f3,axiom,(
% 1.22/0.78 (! [X] : ~ convergent_lines(X,X) )),
% 1.22/0.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.22/0.78 fof(f9,axiom,(
% 1.22/0.78 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 1.22/0.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.22/0.78 fof(f10,axiom,(
% 1.22/0.78 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 1.22/0.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.22/0.78 fof(f11,axiom,(
% 1.22/0.78 (! [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) ) ) )),
% 1.22/0.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.22/0.78 fof(f12,axiom,(
% 1.22/0.78 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 1.22/0.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.22/0.78 fof(f14,axiom,(
% 1.22/0.78 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 1.22/0.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.22/0.78 fof(f15,conjecture,(
% 1.22/0.78 (! [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(X,Z),Y) ) )),
% 1.22/0.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.22/0.78 fof(f16,negated_conjecture,(
% 1.22/0.78 ~((! [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(X,Z),Y) ) ))),
% 1.22/0.78 inference(negated_conjecture,[status(cth)],[f15])).
% 1.22/0.78 fof(f19,plain,(
% 1.22/0.78 ![X0]: (~convergent_lines(X0,X0))),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f3])).
% 1.22/0.78 fof(f33,plain,(
% 1.22/0.78 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 1.22/0.78 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 1.22/0.78 fof(f34,plain,(
% 1.22/0.78 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f33])).
% 1.22/0.78 fof(f35,plain,(
% 1.22/0.78 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 1.22/0.78 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 1.22/0.78 fof(f36,plain,(
% 1.22/0.78 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f35])).
% 1.22/0.78 fof(f37,plain,(
% 1.22/0.78 ![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)))),
% 1.22/0.78 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 1.22/0.78 fof(f38,plain,(
% 1.22/0.78 ![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))),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f37])).
% 1.22/0.78 fof(f39,plain,(
% 1.22/0.78 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 1.22/0.78 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 1.22/0.78 fof(f40,plain,(
% 1.22/0.78 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 1.22/0.78 inference(miniscoping,[status(thm)],[f39])).
% 1.22/0.78 fof(f41,plain,(
% 1.22/0.78 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f40])).
% 1.22/0.78 fof(f45,plain,(
% 1.22/0.78 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 1.22/0.78 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 1.22/0.78 fof(f46,plain,(
% 1.22/0.78 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 1.22/0.78 inference(miniscoping,[status(thm)],[f45])).
% 1.22/0.78 fof(f47,plain,(
% 1.22/0.78 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f46])).
% 1.22/0.78 fof(f48,plain,(
% 1.22/0.78 (?[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(X,Z),Y)))),
% 1.22/0.78 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 1.22/0.78 fof(f49,plain,(
% 1.22/0.78 ((((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(sK0_skl,sK2_skl),sK1_skl))),
% 1.22/0.78 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])).
% 1.22/0.78 fof(f50,plain,(
% 1.22/0.78 convergent_lines(sK0_skl,sK1_skl)),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f49])).
% 1.22/0.78 fof(f52,plain,(
% 1.22/0.78 convergent_lines(sK0_skl,sK2_skl)),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f49])).
% 1.22/0.78 fof(f53,plain,(
% 1.22/0.78 ~apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f49])).
% 1.22/0.78 fof(f54,plain,(
% 1.22/0.78 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)),
% 1.22/0.78 inference(cnf_transformation,[status(thm)],[f49])).
% 1.22/0.78 fof(f492,plain,(
% 1.22/0.78 ![X0]: (distinct_points(intersection_point(sK0_skl,sK2_skl),X0)|apart_point_and_line(X0,sK1_skl))),
% 1.22/0.78 inference(resolution,[status(thm)],[f41,f54])).
% 1.22/0.78 fof(f495,plain,(
% 1.22/0.78 ![X0]: (distinct_lines(sK2_skl,X0)|convergent_lines(sK0_skl,X0))),
% 1.22/0.78 inference(resolution,[status(thm)],[f47,f52])).
% 1.22/0.78 fof(f685,plain,(
% 1.22/0.78 distinct_lines(sK2_skl,sK0_skl)),
% 1.22/0.78 inference(resolution,[status(thm)],[f495,f19])).
% 1.22/0.78 fof(f695,plain,(
% 1.22/0.78 ![X0,X1,X2]: (apart_point_and_line(X0,sK1_skl)|~distinct_lines(X1,X2)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X1)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X2)|apart_point_and_line(X0,X1)|apart_point_and_line(X0,X2))),
% 1.22/0.78 inference(resolution,[status(thm)],[f492,f38])).
% 1.22/0.78 fof(f1091,plain,(
% 1.22/0.78 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK0_skl))),
% 1.22/0.78 inference(resolution,[status(thm)],[f695,f685])).
% 1.22/0.78 fof(f1110,definition,(
% 1.22/0.78 ![X0]: (sQ36_spl <=> (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK0_skl)))),
% 1.22/0.78 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 1.22/0.78 fof(f1111,plain,(
% 1.22/0.78 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK0_skl)|~sQ36_spl)),
% 1.22/0.78 inference(component_clause,[status(thm)],[f1110])).
% 1.22/0.78 fof(f1113,definition,(
% 1.22/0.78 sQ37_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl))),
% 1.22/0.78 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 1.22/0.78 fof(f1114,plain,(
% 1.22/0.78 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK2_skl)|~sQ37_spl),
% 1.22/0.78 inference(component_clause,[status(thm)],[f1113])).
% 1.22/0.78 fof(f1116,definition,(
% 1.22/0.78 sQ38_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl))),
% 1.22/0.78 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 1.22/0.78 fof(f1117,plain,(
% 1.22/0.78 apart_point_and_line(intersection_point(sK0_skl,sK2_skl),sK0_skl)|~sQ38_spl),
% 1.22/0.78 inference(component_clause,[status(thm)],[f1116])).
% 1.22/0.78 fof(f1119,plain,(
% 1.22/0.78 sQ36_spl|sQ37_spl|sQ38_spl),
% 1.22/0.78 inference(split_clause,[status(thm)],[f1091,f1110,f1113,f1116])).
% 1.22/0.78 fof(f1169,plain,(
% 1.22/0.78 ~convergent_lines(sK0_skl,sK2_skl)|~sQ37_spl),
% 1.22/0.78 inference(resolution,[status(thm)],[f1114,f36])).
% 1.22/0.78 fof(f1172,plain,(
% 1.22/0.78 $false|~sQ37_spl),
% 1.22/0.78 inference(forward_subsumption_resolution,[status(thm)],[f1169,f52])).
% 1.22/0.78 fof(f1173,plain,(
% 1.22/0.78 ~sQ37_spl),
% 1.22/0.78 inference(contradiction_clause,[status(thm)],[f1172])).
% 1.22/0.78 fof(f1174,plain,(
% 1.22/0.78 ~convergent_lines(sK0_skl,sK2_skl)|~sQ38_spl),
% 1.22/0.78 inference(resolution,[status(thm)],[f1117,f34])).
% 1.22/0.78 fof(f1177,plain,(
% 1.22/0.78 $false|~sQ38_spl),
% 1.22/0.78 inference(forward_subsumption_resolution,[status(thm)],[f1174,f52])).
% 1.22/0.78 fof(f1178,plain,(
% 1.22/0.78 ~sQ38_spl),
% 1.22/0.78 inference(contradiction_clause,[status(thm)],[f1177])).
% 1.22/0.78 fof(f1229,plain,(
% 1.22/0.78 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ36_spl),
% 2.56/0.79 inference(resolution,[status(thm)],[f1111,f53])).
% 2.56/0.79 fof(f1234,definition,(
% 2.56/0.79 sQ47_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 2.56/0.79 introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 2.56/0.79 fof(f1235,plain,(
% 2.56/0.79 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ47_spl),
% 2.56/0.79 inference(component_clause,[status(thm)],[f1234])).
% 2.56/0.79 fof(f1237,definition,(
% 2.56/0.79 sQ48_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 2.56/0.79 introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition])).
% 2.56/0.79 fof(f1238,plain,(
% 2.56/0.79 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ48_spl),
% 2.56/0.79 inference(component_clause,[status(thm)],[f1237])).
% 2.56/0.79 fof(f1240,plain,(
% 2.56/0.79 sQ47_spl|sQ48_spl|~sQ36_spl),
% 2.56/0.79 inference(split_clause,[status(thm)],[f1229,f1234,f1237,f1110])).
% 2.56/0.79 fof(f1241,plain,(
% 2.56/0.79 ~convergent_lines(sK0_skl,sK1_skl)|~sQ47_spl),
% 2.56/0.79 inference(resolution,[status(thm)],[f1235,f36])).
% 2.56/0.79 fof(f1244,plain,(
% 2.56/0.79 $false|~sQ47_spl),
% 2.56/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1241,f50])).
% 2.56/0.79 fof(f1245,plain,(
% 2.56/0.79 ~sQ47_spl),
% 2.56/0.79 inference(contradiction_clause,[status(thm)],[f1244])).
% 2.56/0.79 fof(f1246,plain,(
% 2.56/0.79 ~convergent_lines(sK0_skl,sK1_skl)|~sQ48_spl),
% 2.56/0.79 inference(resolution,[status(thm)],[f1238,f34])).
% 2.56/0.79 fof(f1249,plain,(
% 2.56/0.79 $false|~sQ48_spl),
% 2.56/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1246,f50])).
% 2.56/0.79 fof(f1250,plain,(
% 2.56/0.79 ~sQ48_spl),
% 2.56/0.79 inference(contradiction_clause,[status(thm)],[f1249])).
% 2.56/0.79 fof(f1251,plain,(
% 2.56/0.79 $false),
% 2.56/0.79 inference(sat_refutation,[status(thm)],[f1119,f1173,f1178,f1240,f1245,f1250])).
% 2.56/0.79 % SZS output end CNFRefutation for theBenchmark.p
% 2.56/0.81 % Elapsed time: 0.432416 seconds
% 2.56/0.81 % CPU time: 3.202390 seconds
% 2.56/0.81 % Total memory used: 44.942 MB
% 2.56/0.81 % Net memory used: 37.328 MB
%------------------------------------------------------------------------------