%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO198+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 : n003.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 1.36s 0.77s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO198+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 13:21:15 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 1.36/0.77 % Refutation found
% 1.36/0.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.36/0.77 % SZS output start CNFRefutation for theBenchmark
% 1.36/0.77 fof(f3,axiom,(
% 1.36/0.77 (! [X] : ~ convergent_lines(X,X) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f6,axiom,(
% 1.36/0.77 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f13,axiom,(
% 1.36/0.77 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f15,axiom,(
% 1.36/0.77 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f16,axiom,(
% 1.36/0.77 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f17,axiom,(
% 1.36/0.77 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f32,axiom,(
% 1.36/0.77 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f33,axiom,(
% 1.36/0.77 (! [X,Y] :( parallel_lines(X,Y)<=> ~ convergent_lines(X,Y) ) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f34,axiom,(
% 1.36/0.77 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f36,conjecture,(
% 1.36/0.77 (! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(Z,Y)& convergent_lines(X,Z)& incident_point_and_line(intersection_point(X,Y),Z) )=> incident_point_and_line(intersection_point(X,Z),Y) ) )),
% 1.36/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.36/0.77 fof(f37,negated_conjecture,(
% 1.36/0.77 ~((! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(Z,Y)& convergent_lines(X,Z)& incident_point_and_line(intersection_point(X,Y),Z) )=> incident_point_and_line(intersection_point(X,Z),Y) ) ))),
% 1.36/0.77 inference(negated_conjecture,[status(cth)],[f36])).
% 1.36/0.77 fof(f40,plain,(
% 1.36/0.77 ![X0]: (~convergent_lines(X0,X0))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f3])).
% 1.36/0.77 fof(f47,plain,(
% 1.36/0.77 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 1.36/0.77 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 1.36/0.77 fof(f48,plain,(
% 1.36/0.77 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 1.36/0.77 inference(miniscoping,[status(thm)],[f47])).
% 1.36/0.77 fof(f49,plain,(
% 1.36/0.77 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f48])).
% 1.36/0.77 fof(f63,plain,(
% 1.36/0.77 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 1.36/0.77 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 1.36/0.77 fof(f64,plain,(
% 1.36/0.77 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 1.36/0.77 inference(miniscoping,[status(thm)],[f63])).
% 1.36/0.77 fof(f65,plain,(
% 1.36/0.77 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f64])).
% 1.36/0.77 fof(f69,plain,(
% 1.36/0.77 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 1.36/0.77 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 1.36/0.77 fof(f70,plain,(
% 1.36/0.77 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f69])).
% 1.36/0.77 fof(f71,plain,(
% 1.36/0.77 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f16])).
% 1.36/0.77 fof(f72,plain,(
% 1.36/0.77 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f17])).
% 1.36/0.77 fof(f111,plain,(
% 1.36/0.77 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 1.36/0.77 inference(NNF_transformation,[status(thm)],[f32])).
% 1.36/0.77 fof(f112,plain,(
% 1.36/0.77 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 1.36/0.77 inference(miniscoping,[status(thm)],[f111])).
% 1.36/0.77 fof(f113,plain,(
% 1.36/0.77 ![X0,X1]: (~equal_lines(X0,X1)|~distinct_lines(X0,X1))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f112])).
% 1.36/0.77 fof(f114,plain,(
% 1.36/0.77 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f112])).
% 1.36/0.77 fof(f115,plain,(
% 1.36/0.77 ![X,Y]: ((~parallel_lines(X,Y)|~convergent_lines(X,Y))&(parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 1.36/0.77 inference(NNF_transformation,[status(thm)],[f33])).
% 1.36/0.77 fof(f116,plain,(
% 1.36/0.77 (![X,Y]: (~parallel_lines(X,Y)|~convergent_lines(X,Y)))&(![X,Y]: (parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 1.36/0.77 inference(miniscoping,[status(thm)],[f115])).
% 1.36/0.77 fof(f117,plain,(
% 1.36/0.77 ![X0,X1]: (~parallel_lines(X0,X1)|~convergent_lines(X0,X1))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f116])).
% 1.36/0.77 fof(f118,plain,(
% 1.36/0.77 ![X0,X1]: (parallel_lines(X0,X1)|convergent_lines(X0,X1))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f116])).
% 1.36/0.77 fof(f119,plain,(
% 1.36/0.77 ![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)))),
% 1.36/0.77 inference(NNF_transformation,[status(thm)],[f34])).
% 1.36/0.77 fof(f120,plain,(
% 1.36/0.77 (![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)))),
% 1.36/0.77 inference(miniscoping,[status(thm)],[f119])).
% 1.36/0.77 fof(f122,plain,(
% 1.36/0.77 ![X0,X1]: (incident_point_and_line(X0,X1)|apart_point_and_line(X0,X1))),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f120])).
% 1.36/0.77 fof(f127,plain,(
% 1.36/0.77 (?[X,Y,Z]: ((((convergent_lines(X,Y)&convergent_lines(Z,Y))&convergent_lines(X,Z))&incident_point_and_line(intersection_point(X,Y),Z))&~incident_point_and_line(intersection_point(X,Z),Y)))),
% 1.36/0.77 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 1.36/0.77 fof(f128,plain,(
% 1.36/0.77 ((((convergent_lines(sK0_skl,sK1_skl)&convergent_lines(sK2_skl,sK1_skl))&convergent_lines(sK0_skl,sK2_skl))&incident_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl))&~incident_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl))),
% 1.36/0.77 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)],[f127])).
% 1.36/0.77 fof(f133,plain,(
% 1.36/0.77 ~incident_point_and_line(intersection_point(sK0_skl,sK2_skl),sK1_skl)),
% 1.36/0.77 inference(cnf_transformation,[status(thm)],[f128])).
% 1.36/0.77 fof(f295,plain,(
% 1.36/0.77 ![X0,X1]: (equal_lines(X0,X1)|convergent_lines(X0,X1))),
% 1.36/0.77 inference(resolution,[status(thm)],[f114,f70])).
% 1.36/0.77 fof(f298,plain,(
% 1.36/0.77 ![X0,X1,X2]: (parallel_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 1.36/0.77 inference(resolution,[status(thm)],[f118,f49])).
% 1.36/0.77 fof(f303,plain,(
% 1.36/0.77 ![X0,X1,X2]: (distinct_lines(X0,X1)|apart_point_and_line(X2,X1)|incident_point_and_line(X2,X0))),
% 1.36/0.77 inference(resolution,[status(thm)],[f65,f122])).
% 1.36/0.77 fof(f390,plain,(
% 1.36/0.77 ![X0,X1]: (parallel_lines(X0,X1)|convergent_lines(X1,X0))),
% 1.36/0.77 inference(resolution,[status(thm)],[f298,f40])).
% 1.36/0.77 fof(f400,plain,(
% 1.36/0.77 ![X0,X1]: (parallel_lines(X0,parallel_through_point(X0,X1)))),
% 1.36/0.77 inference(resolution,[status(thm)],[f390,f71])).
% 1.36/0.77 fof(f404,plain,(
% 1.36/0.77 ![X0,X1]: (~convergent_lines(X0,parallel_through_point(X0,X1)))),
% 1.36/0.77 inference(resolution,[status(thm)],[f400,f117])).
% 1.36/0.77 fof(f465,plain,(
% 1.36/0.77 ![X0,X1,X2]: (parallel_lines(X0,X1)|convergent_lines(X0,parallel_through_point(X1,X2)))),
% 1.36/0.77 inference(resolution,[status(thm)],[f404,f298])).
% 1.36/0.77 fof(f498,plain,(
% 1.36/0.77 ![X0,X1,X2]: (distinct_lines(X0,parallel_through_point(X1,X2))|incident_point_and_line(X2,X0))),
% 1.36/0.77 inference(resolution,[status(thm)],[f303,f72])).
% 1.36/0.77 fof(f771,plain,(
% 1.36/0.77 ![X0,X1,X2]: (parallel_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0))),
% 1.36/0.77 inference(resolution,[status(thm)],[f465,f71])).
% 1.36/0.77 fof(f777,plain,(
% 1.36/0.77 ![X0,X1,X2]: (~convergent_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0))),
% 1.36/0.77 inference(resolution,[status(thm)],[f771,f117])).
% 1.36/0.77 fof(f797,plain,(
% 1.36/0.77 ![X0,X1,X2]: (parallel_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)))),
% 1.36/0.77 inference(resolution,[status(thm)],[f777,f390])).
% 1.36/0.77 fof(f810,plain,(
% 1.36/0.77 ![X0,X1,X2]: (~convergent_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)))),
% 1.36/0.77 inference(resolution,[status(thm)],[f797,f117])).
% 1.36/0.77 fof(f872,plain,(
% 1.36/0.77 ![X0,X1,X2]: (equal_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)))),
% 2.59/0.77 inference(resolution,[status(thm)],[f810,f295])).
% 2.59/0.77 fof(f962,plain,(
% 2.59/0.77 ![X0,X1,X2]: (incident_point_and_line(X0,X1)|~equal_lines(X1,parallel_through_point(X2,X0)))),
% 2.59/0.77 inference(resolution,[status(thm)],[f498,f113])).
% 2.59/0.77 fof(f1154,plain,(
% 2.59/0.77 ![X0,X1]: (incident_point_and_line(X0,X1))),
% 2.59/0.77 inference(resolution,[status(thm)],[f962,f872])).
% 2.59/0.77 fof(f1159,plain,(
% 2.59/0.77 $false),
% 2.59/0.77 inference(backward_subsumption_resolution,[status(thm)],[f133,f1154])).
% 2.59/0.77 % SZS output end CNFRefutation for theBenchmark.p
% 2.59/0.78 % Elapsed time: 0.388654 seconds
% 2.59/0.78 % CPU time: 2.874694 seconds
% 2.59/0.78 % Total memory used: 47.416 MB
% 2.59/0.78 % Net memory used: 41.162 MB
%------------------------------------------------------------------------------