%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO181+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 : n009.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 12:25:58 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO181+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 13:06:12 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.44 fof(f2,axiom,(
% 0.14/0.44 (! [X] : ~ distinct_lines(X,X) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f5,axiom,(
% 0.14/0.44 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f13,axiom,(
% 0.14/0.44 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f15,axiom,(
% 0.14/0.44 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f16,axiom,(
% 0.14/0.44 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f17,axiom,(
% 0.14/0.44 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f36,conjecture,(
% 0.14/0.44 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(Y,line_connecting(X,Z)) ) ) )),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f37,negated_conjecture,(
% 0.14/0.44 ~((! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> apart_point_and_line(Y,line_connecting(X,Z)) ) ) ))),
% 0.14/0.44 inference(negated_conjecture,[status(cth)],[f36])).
% 0.14/0.44 fof(f39,plain,(
% 0.14/0.44 ![X0]: (~distinct_lines(X0,X0))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.44 fof(f44,plain,(
% 0.14/0.44 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 0.14/0.44 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.14/0.44 fof(f45,plain,(
% 0.14/0.44 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 0.14/0.44 inference(miniscoping,[status(thm)],[f44])).
% 0.14/0.44 fof(f46,plain,(
% 0.14/0.44 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f45])).
% 0.14/0.44 fof(f63,plain,(
% 0.14/0.44 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.14/0.44 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.14/0.44 fof(f64,plain,(
% 0.14/0.44 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.14/0.44 inference(miniscoping,[status(thm)],[f63])).
% 0.14/0.44 fof(f65,plain,(
% 0.14/0.44 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f64])).
% 0.14/0.44 fof(f69,plain,(
% 0.14/0.44 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 0.14/0.44 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.14/0.44 fof(f70,plain,(
% 0.14/0.44 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f69])).
% 0.14/0.44 fof(f71,plain,(
% 0.14/0.44 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f16])).
% 0.14/0.44 fof(f72,plain,(
% 0.14/0.44 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f17])).
% 0.14/0.44 fof(f127,plain,(
% 0.14/0.44 (?[X,Y,Z]: (distinct_points(X,Y)&(apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(Y,line_connecting(X,Z)))))),
% 0.14/0.44 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.14/0.44 fof(f128,plain,(
% 0.14/0.44 ?[X,Y]: (distinct_points(X,Y)&(?[Z]: (apart_point_and_line(Z,line_connecting(X,Y))&~apart_point_and_line(Y,line_connecting(X,Z)))))),
% 0.14/0.44 inference(miniscoping,[status(thm)],[f127])).
% 0.14/0.44 fof(f129,plain,(
% 0.14/0.44 (distinct_points(sK0_skl,sK1_skl)&(apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))&~apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))))),
% 0.14/0.44 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)],[f128])).
% 0.14/0.44 fof(f131,plain,(
% 0.14/0.44 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f129])).
% 0.14/0.44 fof(f245,plain,(
% 0.14/0.44 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK1_skl),X0)|apart_point_and_line(sK2_skl,X0))),
% 0.14/0.44 inference(resolution,[status(thm)],[f65,f131])).
% 0.14/0.45 fof(f255,plain,(
% 0.14/0.45 ![X0,X1]: (apart_point_and_line(sK2_skl,X0)|distinct_lines(line_connecting(sK0_skl,sK1_skl),X1)|distinct_lines(X0,X1))),
% 0.14/0.45 inference(resolution,[status(thm)],[f245,f46])).
% 0.14/0.45 fof(f294,plain,(
% 0.14/0.45 ![X0]: (apart_point_and_line(sK2_skl,X0)|distinct_lines(X0,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/0.45 inference(resolution,[status(thm)],[f255,f39])).
% 0.14/0.45 fof(f907,plain,(
% 0.14/0.45 ![X0]: (apart_point_and_line(sK2_skl,X0)|convergent_lines(X0,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/0.45 inference(resolution,[status(thm)],[f294,f70])).
% 0.14/0.45 fof(f1306,plain,(
% 0.14/0.45 ![X0]: (apart_point_and_line(sK2_skl,parallel_through_point(line_connecting(sK0_skl,sK1_skl),X0)))),
% 0.14/0.45 inference(resolution,[status(thm)],[f907,f71])).
% 0.14/0.45 fof(f1320,plain,(
% 0.14/0.45 $false),
% 0.14/0.45 inference(resolution,[status(thm)],[f1306,f72])).
% 0.14/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.45 % Elapsed time: 0.090870 seconds
% 0.14/0.45 % CPU time: 0.507831 seconds
% 0.14/0.45 % Total memory used: 24.628 MB
% 0.14/0.45 % Net memory used: 23.639 MB
%------------------------------------------------------------------------------