%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO202+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 5.46s 1.32s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n007.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.58 % DateTime : Sun Sep 20 13:21:21 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.59 % Drodi V4.1.1
% 5.46/1.32 % Refutation found
% 5.46/1.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.46/1.32 % SZS output start CNFRefutation for theBenchmark
% 5.46/1.32 fof(f1,axiom,(
% 5.46/1.32 (! [X] : ~ distinct_points(X,X) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f3,axiom,(
% 5.46/1.32 (! [X] : ~ convergent_lines(X,X) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f4,axiom,(
% 5.46/1.32 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f6,axiom,(
% 5.46/1.32 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f7,axiom,(
% 5.46/1.32 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f8,axiom,(
% 5.46/1.32 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f11,axiom,(
% 5.46/1.32 (! [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) ) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f13,axiom,(
% 5.46/1.32 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f14,axiom,(
% 5.46/1.32 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f15,axiom,(
% 5.46/1.32 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f16,axiom,(
% 5.46/1.32 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f17,axiom,(
% 5.46/1.32 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f32,axiom,(
% 5.46/1.32 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f33,axiom,(
% 5.46/1.32 (! [X,Y] :( parallel_lines(X,Y)<=> ~ convergent_lines(X,Y) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f34,axiom,(
% 5.46/1.32 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f36,conjecture,(
% 5.46/1.32 (! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ) )),
% 5.46/1.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.46/1.32 fof(f37,negated_conjecture,(
% 5.46/1.32 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& convergent_lines(line_connecting(X,Y),line_connecting(X,Z)) )=> equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X) ) ))),
% 5.46/1.32 inference(negated_conjecture,[status(cth)],[f36])).
% 5.46/1.32 fof(f38,plain,(
% 5.46/1.32 ![X0]: (~distinct_points(X0,X0))),
% 5.46/1.32 inference(cnf_transformation,[status(thm)],[f1])).
% 5.46/1.32 fof(f40,plain,(
% 5.46/1.32 ![X0]: (~convergent_lines(X0,X0))),
% 5.46/1.32 inference(cnf_transformation,[status(thm)],[f3])).
% 5.46/1.32 fof(f41,plain,(
% 5.46/1.32 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 5.46/1.32 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 5.46/1.32 fof(f42,plain,(
% 5.46/1.32 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 5.46/1.32 inference(miniscoping,[status(thm)],[f41])).
% 5.46/1.32 fof(f43,plain,(
% 5.46/1.32 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 5.46/1.32 inference(cnf_transformation,[status(thm)],[f42])).
% 5.46/1.32 fof(f47,plain,(
% 5.46/1.32 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 5.46/1.32 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 5.46/1.32 fof(f48,plain,(
% 5.46/1.32 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 5.46/1.32 inference(miniscoping,[status(thm)],[f47])).
% 5.46/1.33 fof(f49,plain,(
% 5.46/1.33 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f48])).
% 5.46/1.33 fof(f50,plain,(
% 5.46/1.33 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 5.46/1.33 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 5.46/1.33 fof(f51,plain,(
% 5.46/1.33 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f50])).
% 5.46/1.33 fof(f52,plain,(
% 5.46/1.33 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 5.46/1.33 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 5.46/1.33 fof(f53,plain,(
% 5.46/1.33 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f52])).
% 5.46/1.33 fof(f58,plain,(
% 5.46/1.33 ![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)))),
% 5.46/1.33 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 5.46/1.33 fof(f59,plain,(
% 5.46/1.33 ![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))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f58])).
% 5.46/1.33 fof(f63,plain,(
% 5.46/1.33 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 5.46/1.33 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 5.46/1.33 fof(f64,plain,(
% 5.46/1.33 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 5.46/1.33 inference(miniscoping,[status(thm)],[f63])).
% 5.46/1.33 fof(f65,plain,(
% 5.46/1.33 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f64])).
% 5.46/1.33 fof(f66,plain,(
% 5.46/1.33 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 5.46/1.33 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 5.46/1.33 fof(f67,plain,(
% 5.46/1.33 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 5.46/1.33 inference(miniscoping,[status(thm)],[f66])).
% 5.46/1.33 fof(f68,plain,(
% 5.46/1.33 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f67])).
% 5.46/1.33 fof(f69,plain,(
% 5.46/1.33 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 5.46/1.33 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 5.46/1.33 fof(f70,plain,(
% 5.46/1.33 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f69])).
% 5.46/1.33 fof(f71,plain,(
% 5.46/1.33 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f16])).
% 5.46/1.33 fof(f72,plain,(
% 5.46/1.33 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f17])).
% 5.46/1.33 fof(f111,plain,(
% 5.46/1.33 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 5.46/1.33 inference(NNF_transformation,[status(thm)],[f32])).
% 5.46/1.33 fof(f112,plain,(
% 5.46/1.33 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 5.46/1.33 inference(miniscoping,[status(thm)],[f111])).
% 5.46/1.33 fof(f113,plain,(
% 5.46/1.33 ![X0,X1]: (~equal_lines(X0,X1)|~distinct_lines(X0,X1))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f112])).
% 5.46/1.33 fof(f114,plain,(
% 5.46/1.33 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f112])).
% 5.46/1.33 fof(f115,plain,(
% 5.46/1.33 ![X,Y]: ((~parallel_lines(X,Y)|~convergent_lines(X,Y))&(parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 5.46/1.33 inference(NNF_transformation,[status(thm)],[f33])).
% 5.46/1.33 fof(f116,plain,(
% 5.46/1.33 (![X,Y]: (~parallel_lines(X,Y)|~convergent_lines(X,Y)))&(![X,Y]: (parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 5.46/1.33 inference(miniscoping,[status(thm)],[f115])).
% 5.46/1.33 fof(f117,plain,(
% 5.46/1.33 ![X0,X1]: (~parallel_lines(X0,X1)|~convergent_lines(X0,X1))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f116])).
% 5.46/1.33 fof(f118,plain,(
% 5.46/1.33 ![X0,X1]: (parallel_lines(X0,X1)|convergent_lines(X0,X1))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f116])).
% 5.46/1.33 fof(f119,plain,(
% 5.46/1.33 ![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)))),
% 5.46/1.33 inference(NNF_transformation,[status(thm)],[f34])).
% 5.46/1.33 fof(f120,plain,(
% 5.46/1.33 (![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)))),
% 5.46/1.33 inference(miniscoping,[status(thm)],[f119])).
% 5.46/1.33 fof(f121,plain,(
% 5.46/1.33 ![X0,X1]: (~incident_point_and_line(X0,X1)|~apart_point_and_line(X0,X1))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f120])).
% 5.46/1.33 fof(f122,plain,(
% 5.46/1.33 ![X0,X1]: (incident_point_and_line(X0,X1)|apart_point_and_line(X0,X1))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f120])).
% 5.46/1.33 fof(f127,plain,(
% 5.46/1.33 (?[X,Y,Z]: (((distinct_points(X,Y)&distinct_points(X,Z))&convergent_lines(line_connecting(X,Y),line_connecting(X,Z)))&~equal_points(intersection_point(line_connecting(X,Y),line_connecting(X,Z)),X)))),
% 5.46/1.33 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 5.46/1.33 fof(f128,plain,(
% 5.46/1.33 (((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)))&~equal_points(intersection_point(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)),sK0_skl))),
% 5.46/1.33 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])).
% 5.46/1.33 fof(f130,plain,(
% 5.46/1.33 distinct_points(sK0_skl,sK2_skl)),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f128])).
% 5.46/1.33 fof(f131,plain,(
% 5.46/1.33 convergent_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))),
% 5.46/1.33 inference(cnf_transformation,[status(thm)],[f128])).
% 5.46/1.33 fof(f145,plain,(
% 5.46/1.33 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK2_skl,X0))),
% 5.46/1.33 inference(resolution,[status(thm)],[f43,f130])).
% 5.46/1.33 fof(f153,plain,(
% 5.46/1.33 distinct_points(sK2_skl,sK0_skl)),
% 5.46/1.33 inference(resolution,[status(thm)],[f145,f38])).
% 5.46/1.33 fof(f206,plain,(
% 5.46/1.33 ![X0,X1]: (equal_lines(X0,X1)|convergent_lines(X0,X1))),
% 5.46/1.33 inference(resolution,[status(thm)],[f114,f70])).
% 5.46/1.33 fof(f209,plain,(
% 5.46/1.33 ![X0,X1,X2]: (parallel_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 5.46/1.33 inference(resolution,[status(thm)],[f118,f49])).
% 5.46/1.33 fof(f222,plain,(
% 5.46/1.33 ![X0,X1,X2]: (distinct_lines(X0,X1)|apart_point_and_line(X2,X1)|incident_point_and_line(X2,X0))),
% 5.46/1.33 inference(resolution,[status(thm)],[f65,f122])).
% 5.46/1.33 fof(f223,plain,(
% 5.46/1.33 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK2_skl),X0)|convergent_lines(line_connecting(sK0_skl,sK1_skl),X0))),
% 5.46/1.33 inference(resolution,[status(thm)],[f68,f131])).
% 5.46/1.33 fof(f263,plain,(
% 5.46/1.33 ![X0,X1,X2]: (convergent_lines(line_connecting(sK0_skl,sK1_skl),X0)|~distinct_points(X1,X2)|apart_point_and_line(X1,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(X1,X0)|apart_point_and_line(X2,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(X2,X0))),
% 5.46/1.33 inference(resolution,[status(thm)],[f223,f59])).
% 5.46/1.33 fof(f291,plain,(
% 5.46/1.33 ![X0,X1]: (parallel_lines(X0,X1)|convergent_lines(X1,X0))),
% 5.46/1.33 inference(resolution,[status(thm)],[f209,f40])).
% 5.46/1.33 fof(f368,plain,(
% 5.46/1.33 ![X0,X1]: (parallel_lines(X0,parallel_through_point(X0,X1)))),
% 5.46/1.33 inference(resolution,[status(thm)],[f291,f71])).
% 5.46/1.33 fof(f372,plain,(
% 5.46/1.33 ![X0,X1]: (~convergent_lines(X0,parallel_through_point(X0,X1)))),
% 5.46/1.33 inference(resolution,[status(thm)],[f368,f117])).
% 5.46/1.33 fof(f382,plain,(
% 5.46/1.33 ![X0,X1,X2]: (parallel_lines(X0,X1)|convergent_lines(X0,parallel_through_point(X1,X2)))),
% 5.46/1.33 inference(resolution,[status(thm)],[f372,f209])).
% 5.46/1.33 fof(f519,plain,(
% 5.46/1.33 ![X0,X1,X2]: (parallel_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0))),
% 5.46/1.33 inference(resolution,[status(thm)],[f382,f71])).
% 5.46/1.33 fof(f525,plain,(
% 5.46/1.33 ![X0,X1,X2]: (~convergent_lines(parallel_through_point(parallel_through_point(X0,X1),X2),X0))),
% 5.46/1.33 inference(resolution,[status(thm)],[f519,f117])).
% 5.46/1.33 fof(f528,plain,(
% 5.46/1.33 ![X0,X1,X2]: (parallel_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)))),
% 5.46/1.33 inference(resolution,[status(thm)],[f525,f291])).
% 5.46/1.33 fof(f541,plain,(
% 5.46/1.33 ![X0,X1,X2]: (~convergent_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)))),
% 5.46/1.33 inference(resolution,[status(thm)],[f528,f117])).
% 5.46/1.33 fof(f582,plain,(
% 5.46/1.33 ![X0,X1,X2]: (equal_lines(X0,parallel_through_point(parallel_through_point(X0,X1),X2)))),
% 5.46/1.33 inference(resolution,[status(thm)],[f541,f206])).
% 5.46/1.33 fof(f937,plain,(
% 5.46/1.33 ![X0,X1,X2]: (distinct_lines(X0,parallel_through_point(X1,X2))|incident_point_and_line(X2,X0))),
% 5.46/1.33 inference(resolution,[status(thm)],[f222,f72])).
% 5.46/1.33 fof(f1023,plain,(
% 5.46/1.33 ![X0]: (convergent_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK0_skl,X0))),
% 5.46/1.33 inference(resolution,[status(thm)],[f263,f153])).
% 5.46/1.33 fof(f1111,definition,(
% 5.46/1.33 sQ29_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)))),
% 5.46/1.33 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 5.46/1.33 fof(f1112,plain,(
% 5.46/1.33 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|~sQ29_spl),
% 5.46/1.33 inference(component_clause,[status(thm)],[f1111])).
% 5.46/1.33 fof(f1140,definition,(
% 5.46/1.33 ![X0]: (sQ36_spl <=> (convergent_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK0_skl,X0)))),
% 5.46/1.33 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 5.46/1.33 fof(f1141,plain,(
% 5.46/1.33 ![X0]: (convergent_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK0_skl,X0)|~sQ36_spl)),
% 5.46/1.33 inference(component_clause,[status(thm)],[f1140])).
% 5.46/1.33 fof(f1143,definition,(
% 5.46/1.33 sQ37_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl)))),
% 5.46/1.33 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 5.46/1.33 fof(f1144,plain,(
% 5.46/1.33 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl))|~sQ37_spl),
% 5.46/1.33 inference(component_clause,[status(thm)],[f1143])).
% 5.46/1.33 fof(f1146,plain,(
% 5.46/1.33 sQ36_spl|sQ37_spl|sQ29_spl),
% 5.46/1.33 inference(split_clause,[status(thm)],[f1023,f1140,f1143,f1111])).
% 5.46/1.33 fof(f1284,plain,(
% 5.46/1.33 ~distinct_points(sK0_skl,sK2_skl)|~sQ29_spl),
% 5.46/1.33 inference(resolution,[status(thm)],[f1112,f51])).
% 5.46/1.33 fof(f1288,plain,(
% 5.46/1.33 $false|~sQ29_spl),
% 5.46/1.33 inference(forward_subsumption_resolution,[status(thm)],[f1284,f130])).
% 5.46/1.33 fof(f1289,plain,(
% 5.46/1.33 ~sQ29_spl),
% 5.46/1.33 inference(contradiction_clause,[status(thm)],[f1288])).
% 5.46/1.33 fof(f1290,plain,(
% 5.46/1.33 ~distinct_points(sK0_skl,sK2_skl)|~sQ37_spl),
% 5.46/1.33 inference(resolution,[status(thm)],[f1144,f53])).
% 5.46/1.33 fof(f1294,plain,(
% 5.46/1.33 $false|~sQ37_spl),
% 5.46/1.33 inference(forward_subsumption_resolution,[status(thm)],[f1290,f130])).
% 5.46/1.33 fof(f1295,plain,(
% 5.46/1.33 ~sQ37_spl),
% 5.46/1.33 inference(contradiction_clause,[status(thm)],[f1294])).
% 5.46/1.33 fof(f1413,plain,(
% 5.46/1.33 ![X0,X1,X2]: (incident_point_and_line(X0,X1)|~equal_lines(X1,parallel_through_point(X2,X0)))),
% 5.46/1.33 inference(resolution,[status(thm)],[f937,f113])).
% 5.46/1.33 fof(f1759,plain,(
% 5.46/1.33 ![X0,X1]: (incident_point_and_line(X0,X1))),
% 5.46/1.33 inference(resolution,[status(thm)],[f1413,f582])).
% 5.46/1.33 fof(f1765,plain,(
% 5.46/1.33 ![X0,X1]: (~apart_point_and_line(X0,X1))),
% 5.46/1.33 inference(backward_subsumption_resolution,[status(thm)],[f121,f1759])).
% 5.46/1.33 fof(f1775,plain,(
% 5.46/1.33 ![X0]: (convergent_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK0_skl,X0)|~sQ36_spl)),
% 5.46/1.33 inference(backward_subsumption_resolution,[status(thm)],[f1141,f1765])).
% 5.46/1.33 fof(f1878,plain,(
% 5.46/1.33 ![X0]: (convergent_lines(line_connecting(sK0_skl,sK1_skl),X0)|~sQ36_spl)),
% 5.46/1.33 inference(forward_subsumption_resolution,[status(thm)],[f1775,f1765])).
% 5.46/1.33 fof(f1923,plain,(
% 5.46/1.33 $false|~sQ36_spl),
% 5.46/1.33 inference(resolution,[status(thm)],[f1878,f541])).
% 5.46/1.33 fof(f1932,plain,(
% 5.46/1.33 ~sQ36_spl),
% 5.46/1.33 inference(contradiction_clause,[status(thm)],[f1923])).
% 5.46/1.33 fof(f1933,plain,(
% 5.46/1.33 $false),
% 5.46/1.33 inference(sat_refutation,[status(thm)],[f1146,f1289,f1295,f1932])).
% 5.46/1.33 % SZS output end CNFRefutation for theBenchmark.p
% 5.46/1.34 % Elapsed time: 0.750765 seconds
% 5.46/1.34 % CPU time: 5.768439 seconds
% 5.46/1.34 % Total memory used: 63.557 MB
% 5.46/1.34 % Net memory used: 54.009 MB
%------------------------------------------------------------------------------