%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO215+2 : 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 : n016.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 12:26:08 PM UTC 2026
% Result : Theorem 1.26s 0.67s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO215+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 13:33:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 1.26/0.67 % Refutation found
% 1.26/0.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.26/0.67 % SZS output start CNFRefutation for theBenchmark
% 1.26/0.67 fof(f1,axiom,(
% 1.26/0.67 (! [X] : ~ distinct_points(X,X) )),
% 1.26/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.26/0.67 fof(f2,axiom,(
% 1.26/0.67 (! [X] : ~ distinct_lines(X,X) )),
% 1.26/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.26/0.67 fof(f6,axiom,(
% 1.26/0.67 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 1.26/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.26/0.67 fof(f8,axiom,(
% 1.26/0.67 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( ( apart_point_and_line(Z,X)| apart_point_and_line(Z,Y) )=> distinct_points(Z,intersection_point(X,Y)) ) ) )),
% 1.26/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.26/0.67 fof(f11,axiom,(
% 1.26/0.67 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 1.26/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.26/0.67 fof(f12,axiom,(
% 1.26/0.67 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 1.26/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.26/0.67 fof(f20,axiom,(
% 1.26/0.67 (! [A,L,M,N] :( distinct_lines(L,M)=> ( apart_point_and_line(A,L)| apart_point_and_line(A,M)| unorthogonal_lines(L,N)| unorthogonal_lines(M,N) ) ) )),
% 1.26/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.26/0.67 fof(f21,conjecture,(
% 1.26/0.67 (! [L,M,N] :( convergent_lines(L,M)=> ( unorthogonal_lines(L,N)| unorthogonal_lines(M,N) ) ) )),
% 1.26/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.26/0.67 fof(f22,negated_conjecture,(
% 1.26/0.67 ~((! [L,M,N] :( convergent_lines(L,M)=> ( unorthogonal_lines(L,N)| unorthogonal_lines(M,N) ) ) ))),
% 1.26/0.67 inference(negated_conjecture,[status(cth)],[f21])).
% 1.26/0.67 fof(f23,plain,(
% 1.26/0.67 ![X0]: (~distinct_points(X0,X0))),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f1])).
% 1.26/0.67 fof(f24,plain,(
% 1.26/0.67 ![X0]: (~distinct_lines(X0,X0))),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f2])).
% 1.26/0.67 fof(f32,plain,(
% 1.26/0.67 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 1.26/0.67 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 1.26/0.67 fof(f33,plain,(
% 1.26/0.67 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 1.26/0.67 inference(miniscoping,[status(thm)],[f32])).
% 1.26/0.67 fof(f34,plain,(
% 1.26/0.67 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f33])).
% 1.26/0.67 fof(f39,plain,(
% 1.26/0.67 ![X,Y,Z]: (~convergent_lines(X,Y)|((~apart_point_and_line(Z,X)&~apart_point_and_line(Z,Y))|distinct_points(Z,intersection_point(X,Y))))),
% 1.26/0.67 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 1.26/0.67 fof(f40,plain,(
% 1.26/0.67 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: ((~apart_point_and_line(Z,X)&~apart_point_and_line(Z,Y))|distinct_points(Z,intersection_point(X,Y)))))),
% 1.26/0.67 inference(miniscoping,[status(thm)],[f39])).
% 1.26/0.67 fof(f41,plain,(
% 1.26/0.67 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X0)|distinct_points(X2,intersection_point(X0,X1)))),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f40])).
% 1.26/0.67 fof(f42,plain,(
% 1.26/0.67 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~apart_point_and_line(X2,X1)|distinct_points(X2,intersection_point(X0,X1)))),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f40])).
% 1.26/0.67 fof(f48,plain,(
% 1.26/0.67 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 1.26/0.67 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 1.26/0.67 fof(f49,plain,(
% 1.26/0.67 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 1.26/0.67 inference(miniscoping,[status(thm)],[f48])).
% 1.26/0.67 fof(f50,plain,(
% 1.26/0.67 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f49])).
% 1.26/0.67 fof(f51,plain,(
% 1.26/0.67 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 1.26/0.67 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 1.26/0.67 fof(f52,plain,(
% 1.26/0.67 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f51])).
% 1.26/0.67 fof(f67,plain,(
% 1.26/0.67 ![A,L,M,N]: (~distinct_lines(L,M)|(((apart_point_and_line(A,L)|apart_point_and_line(A,M))|unorthogonal_lines(L,N))|unorthogonal_lines(M,N)))),
% 1.26/0.67 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 1.26/0.67 fof(f68,plain,(
% 1.26/0.67 ![L,M]: (~distinct_lines(L,M)|(![N]: (((![A]: (apart_point_and_line(A,L)|apart_point_and_line(A,M)))|unorthogonal_lines(L,N))|unorthogonal_lines(M,N))))),
% 1.26/0.67 inference(miniscoping,[status(thm)],[f67])).
% 1.26/0.67 fof(f69,plain,(
% 1.26/0.67 ![X0,X1,X2,X3]: (~distinct_lines(X0,X1)|apart_point_and_line(X2,X0)|apart_point_and_line(X2,X1)|unorthogonal_lines(X0,X3)|unorthogonal_lines(X1,X3))),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f68])).
% 1.26/0.67 fof(f70,plain,(
% 1.26/0.67 (?[L,M,N]: (convergent_lines(L,M)&(~unorthogonal_lines(L,N)&~unorthogonal_lines(M,N))))),
% 1.26/0.67 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 1.26/0.67 fof(f71,plain,(
% 1.26/0.67 ?[L,M]: (convergent_lines(L,M)&(?[N]: (~unorthogonal_lines(L,N)&~unorthogonal_lines(M,N))))),
% 1.26/0.67 inference(miniscoping,[status(thm)],[f70])).
% 1.26/0.67 fof(f72,plain,(
% 1.26/0.67 (convergent_lines(sK0_skl,sK1_skl)&(~unorthogonal_lines(sK0_skl,sK2_skl)&~unorthogonal_lines(sK1_skl,sK2_skl)))),
% 1.26/0.67 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl),skolemize(N,sK2_skl)],[f71])).
% 1.26/0.67 fof(f73,plain,(
% 1.26/0.67 convergent_lines(sK0_skl,sK1_skl)),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f72])).
% 1.26/0.67 fof(f74,plain,(
% 1.26/0.67 ~unorthogonal_lines(sK0_skl,sK2_skl)),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f72])).
% 1.26/0.67 fof(f75,plain,(
% 1.26/0.67 ~unorthogonal_lines(sK1_skl,sK2_skl)),
% 1.26/0.67 inference(cnf_transformation,[status(thm)],[f72])).
% 1.26/0.67 fof(f81,plain,(
% 1.26/0.67 distinct_lines(sK0_skl,sK1_skl)),
% 1.26/0.67 inference(resolution,[status(thm)],[f52,f73])).
% 1.26/0.67 fof(f87,plain,(
% 1.26/0.67 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 1.26/0.67 inference(resolution,[status(thm)],[f34,f73])).
% 1.26/0.67 fof(f91,plain,(
% 1.26/0.67 ![X0]: (convergent_lines(sK0_skl,X0)|distinct_lines(sK1_skl,X0))),
% 1.26/0.67 inference(resolution,[status(thm)],[f87,f52])).
% 1.26/0.67 fof(f94,plain,(
% 1.26/0.67 ![X0,X1]: (distinct_lines(sK1_skl,X0)|~apart_point_and_line(X1,X0)|distinct_points(X1,intersection_point(sK0_skl,X0)))),
% 1.26/0.67 inference(resolution,[status(thm)],[f91,f42])).
% 1.26/0.67 fof(f95,plain,(
% 1.26/0.67 ![X0,X1]: (distinct_lines(sK1_skl,X0)|~apart_point_and_line(X1,sK0_skl)|distinct_points(X1,intersection_point(sK0_skl,X0)))),
% 1.26/0.67 inference(resolution,[status(thm)],[f91,f41])).
% 1.26/0.67 fof(f709,definition,(
% 1.26/0.67 ![X0]: (sQ32_spl <=> (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)))),
% 1.26/0.67 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 1.26/0.67 fof(f710,plain,(
% 1.26/0.67 ![X0]: (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)|~sQ32_spl)),
% 1.26/0.67 inference(component_clause,[status(thm)],[f709])).
% 1.26/0.67 fof(f737,plain,(
% 1.26/0.67 ![X0,X1]: (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK1_skl)|unorthogonal_lines(sK0_skl,X1)|unorthogonal_lines(sK1_skl,X1))),
% 1.26/0.67 inference(resolution,[status(thm)],[f69,f81])).
% 1.26/0.67 fof(f759,definition,(
% 1.26/0.67 ![X1]: (sQ37_spl <=> (unorthogonal_lines(sK0_skl,X1)|unorthogonal_lines(sK1_skl,X1)))),
% 1.26/0.67 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 1.26/0.67 fof(f760,plain,(
% 1.26/0.67 ![X0]: (unorthogonal_lines(sK0_skl,X0)|unorthogonal_lines(sK1_skl,X0)|~sQ37_spl)),
% 1.26/0.67 inference(component_clause,[status(thm)],[f759])).
% 1.26/0.67 fof(f762,plain,(
% 1.26/0.67 sQ32_spl|sQ37_spl),
% 1.26/0.67 inference(split_clause,[status(thm)],[f737,f709,f759])).
% 1.26/0.67 fof(f772,plain,(
% 1.26/0.67 ![X0,X1]: (apart_point_and_line(X0,sK0_skl)|distinct_lines(sK1_skl,X1)|apart_point_and_line(X0,X1)|~sQ32_spl)),
% 1.26/0.67 inference(resolution,[status(thm)],[f710,f50])).
% 1.26/0.67 fof(f795,plain,(
% 1.26/0.67 unorthogonal_lines(sK0_skl,sK2_skl)|~sQ37_spl),
% 1.26/0.67 inference(resolution,[status(thm)],[f760,f75])).
% 1.26/0.67 fof(f798,plain,(
% 1.26/0.67 $false|~sQ37_spl),
% 1.26/0.67 inference(forward_subsumption_resolution,[status(thm)],[f795,f74])).
% 1.26/0.67 fof(f799,plain,(
% 1.26/0.67 ~sQ37_spl),
% 1.26/0.67 inference(contradiction_clause,[status(thm)],[f798])).
% 1.26/0.67 fof(f927,plain,(
% 1.26/0.67 ![X0,X1]: (apart_point_and_line(X0,sK0_skl)|distinct_lines(sK1_skl,X1)|distinct_lines(sK1_skl,X1)|distinct_points(X0,intersection_point(sK0_skl,X1))|~sQ32_spl)),
% 1.26/0.67 inference(resolution,[status(thm)],[f772,f94])).
% 1.26/0.67 fof(f1016,plain,(
% 1.26/0.67 ![X0,X1]: (apart_point_and_line(X0,sK0_skl)|distinct_lines(sK1_skl,X1)|distinct_points(X0,intersection_point(sK0_skl,X1))|~sQ32_spl)),
% 1.26/0.67 inference(duplicate_literals_removal,[status(thm)],[f927])).
% 1.26/0.68 fof(f1017,plain,(
% 1.26/0.68 ![X0,X1]: (distinct_lines(sK1_skl,X0)|distinct_points(X1,intersection_point(sK0_skl,X0))|~sQ32_spl)),
% 1.26/0.68 inference(forward_subsumption_resolution,[status(thm)],[f1016,f95])).
% 1.26/0.68 fof(f1106,plain,(
% 1.26/0.68 ![X0]: (distinct_lines(sK1_skl,X0)|~sQ32_spl)),
% 1.26/0.68 inference(resolution,[status(thm)],[f1017,f23])).
% 1.26/0.68 fof(f1727,plain,(
% 1.26/0.68 $false|~sQ32_spl),
% 1.26/0.68 inference(resolution,[status(thm)],[f1106,f24])).
% 1.26/0.68 fof(f1728,plain,(
% 1.26/0.68 ~sQ32_spl),
% 1.26/0.68 inference(contradiction_clause,[status(thm)],[f1727])).
% 1.26/0.68 fof(f1729,plain,(
% 1.26/0.68 $false),
% 1.26/0.68 inference(sat_refutation,[status(thm)],[f762,f799,f1728])).
% 1.26/0.68 % SZS output end CNFRefutation for theBenchmark.p
% 1.26/0.69 % Elapsed time: 0.315140 seconds
% 1.26/0.69 % CPU time: 2.253466 seconds
% 1.26/0.69 % Total memory used: 38.377 MB
% 1.26/0.69 % Net memory used: 33.039 MB
%------------------------------------------------------------------------------