%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO215+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 : n002.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 0.14s 10.86s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO215+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n002.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sun Sep 20 13:34:59 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.39 % Drodi V4.1.1
% 0.14/10.86 % Refutation found
% 0.14/10.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.86 % SZS output start CNFRefutation for theBenchmark
% 0.14/10.86 fof(f2,axiom,(
% 0.14/10.86 (! [X] : ~ distinct_lines(X,X) )),
% 0.14/10.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.86 fof(f3,axiom,(
% 0.14/10.86 (! [X] : ~ convergent_lines(X,X) )),
% 0.14/10.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.86 fof(f6,axiom,(
% 0.14/10.86 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.14/10.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.86 fof(f9,axiom,(
% 0.14/10.86 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.14/10.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.86 fof(f10,axiom,(
% 0.14/10.86 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.14/10.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.86 fof(f14,axiom,(
% 0.14/10.86 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.14/10.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.86 fof(f22,axiom,(
% 0.14/10.86 (! [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) ) ) )),
% 0.14/10.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.86 fof(f23,conjecture,(
% 0.14/10.86 (! [L,M,N] :( convergent_lines(L,M)=> ( unorthogonal_lines(L,N)| unorthogonal_lines(M,N) ) ) )),
% 0.14/10.86 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.86 fof(f24,negated_conjecture,(
% 0.14/10.86 ~((! [L,M,N] :( convergent_lines(L,M)=> ( unorthogonal_lines(L,N)| unorthogonal_lines(M,N) ) ) ))),
% 0.14/10.86 inference(negated_conjecture,[status(cth)],[f23])).
% 0.14/10.86 fof(f26,plain,(
% 0.14/10.86 ![X0]: (~distinct_lines(X0,X0))),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/10.86 fof(f27,plain,(
% 0.14/10.86 ![X0]: (~convergent_lines(X0,X0))),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/10.86 fof(f34,plain,(
% 0.14/10.86 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.14/10.86 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.14/10.86 fof(f35,plain,(
% 0.14/10.86 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.14/10.86 inference(miniscoping,[status(thm)],[f34])).
% 0.14/10.86 fof(f36,plain,(
% 0.14/10.86 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f35])).
% 0.14/10.86 fof(f41,plain,(
% 0.14/10.86 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.14/10.86 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.14/10.86 fof(f42,plain,(
% 0.14/10.86 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f41])).
% 0.14/10.86 fof(f43,plain,(
% 0.14/10.86 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.14/10.86 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.14/10.86 fof(f44,plain,(
% 0.14/10.86 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/10.86 fof(f53,plain,(
% 0.14/10.86 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.14/10.86 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.14/10.86 fof(f54,plain,(
% 0.14/10.86 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.14/10.86 inference(miniscoping,[status(thm)],[f53])).
% 0.14/10.86 fof(f55,plain,(
% 0.14/10.86 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f54])).
% 0.14/10.86 fof(f70,plain,(
% 0.14/10.86 ![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)))),
% 0.14/10.86 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 0.14/10.86 fof(f71,plain,(
% 0.14/10.86 ![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))))),
% 0.14/10.86 inference(miniscoping,[status(thm)],[f70])).
% 0.14/10.86 fof(f72,plain,(
% 0.14/10.86 ![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))),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f71])).
% 0.14/10.86 fof(f73,plain,(
% 0.14/10.86 (?[L,M,N]: (convergent_lines(L,M)&(~unorthogonal_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.14/10.86 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.14/10.86 fof(f74,plain,(
% 0.14/10.86 ?[L,M]: (convergent_lines(L,M)&(?[N]: (~unorthogonal_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.14/10.86 inference(miniscoping,[status(thm)],[f73])).
% 0.14/10.86 fof(f75,plain,(
% 0.14/10.86 (convergent_lines(sK0_skl,sK1_skl)&(~unorthogonal_lines(sK0_skl,sK2_skl)&~unorthogonal_lines(sK1_skl,sK2_skl)))),
% 0.14/10.86 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)],[f74])).
% 0.14/10.86 fof(f76,plain,(
% 0.14/10.86 convergent_lines(sK0_skl,sK1_skl)),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f75])).
% 0.14/10.86 fof(f77,plain,(
% 0.14/10.86 ~unorthogonal_lines(sK0_skl,sK2_skl)),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f75])).
% 0.14/10.86 fof(f78,plain,(
% 0.14/10.86 ~unorthogonal_lines(sK1_skl,sK2_skl)),
% 0.14/10.86 inference(cnf_transformation,[status(thm)],[f75])).
% 0.14/10.86 fof(f88,plain,(
% 0.14/10.86 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.14/10.86 inference(resolution,[status(thm)],[f36,f76])).
% 0.14/10.86 fof(f93,plain,(
% 0.14/10.86 ![X0,X1]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X1)|convergent_lines(X0,X1))),
% 0.14/10.86 inference(resolution,[status(thm)],[f88,f36])).
% 0.14/10.86 fof(f102,plain,(
% 0.14/10.86 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(X0,sK1_skl))),
% 0.14/10.86 inference(resolution,[status(thm)],[f93,f27])).
% 0.14/10.86 fof(f112,definition,(
% 0.14/10.86 sQ2_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.14/10.86 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/10.86 fof(f123,plain,(
% 0.14/10.86 ![X0,X1]: (convergent_lines(X0,sK1_skl)|convergent_lines(sK0_skl,X1)|convergent_lines(X0,X1))),
% 0.14/10.86 inference(resolution,[status(thm)],[f102,f36])).
% 0.14/10.86 fof(f205,definition,(
% 0.14/10.86 ![X1,X2]: (sQ11_spl <=> (convergent_lines(sK0_skl,X1)|convergent_lines(X2,X1)))),
% 0.14/10.86 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.14/10.86 fof(f206,plain,(
% 0.14/10.86 ![X0,X1]: (convergent_lines(sK0_skl,X0)|convergent_lines(X1,X0)|~sQ11_spl)),
% 0.14/10.86 inference(component_clause,[status(thm)],[f205])).
% 0.14/10.86 fof(f260,plain,(
% 0.14/10.86 ![X0]: (distinct_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.14/10.86 inference(resolution,[status(thm)],[f55,f76])).
% 0.14/10.86 fof(f285,definition,(
% 0.14/10.86 ![X0]: (sQ12_spl <=> (distinct_lines(sK0_skl,X0)|convergent_lines(sK0_skl,X0)))),
% 0.14/10.86 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.14/10.86 fof(f286,plain,(
% 0.14/10.86 ![X0]: (distinct_lines(sK0_skl,X0)|convergent_lines(sK0_skl,X0)|~sQ12_spl)),
% 0.14/10.86 inference(component_clause,[status(thm)],[f285])).
% 0.14/10.86 fof(f294,plain,(
% 0.14/10.86 ![X0,X1]: (distinct_lines(sK1_skl,X0)|distinct_lines(X0,X1)|convergent_lines(sK0_skl,X1))),
% 0.14/10.86 inference(resolution,[status(thm)],[f260,f55])).
% 0.14/10.86 fof(f314,definition,(
% 0.14/10.86 ![X0]: (sQ15_spl <=> (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)))),
% 0.14/10.86 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.14/10.86 fof(f315,plain,(
% 0.14/10.86 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)|~sQ15_spl)),
% 0.14/10.86 inference(component_clause,[status(thm)],[f314])).
% 0.14/10.86 fof(f409,plain,(
% 0.14/10.86 ![X0,X1,X2,X3]: (distinct_lines(X0,X1)|convergent_lines(sK0_skl,X1)|apart_point_and_line(X2,sK1_skl)|apart_point_and_line(X2,X0)|unorthogonal_lines(sK1_skl,X3)|unorthogonal_lines(X0,X3))),
% 0.14/10.86 inference(resolution,[status(thm)],[f294,f72])).
% 0.14/10.86 fof(f442,plain,(
% 0.14/10.86 ![X0]: (apart_point_and_line(intersection_point(X0,sK1_skl),sK0_skl)|~convergent_lines(X0,sK1_skl)|~sQ15_spl)),
% 0.14/10.86 inference(resolution,[status(thm)],[f315,f44])).
% 0.14/10.86 fof(f476,plain,(
% 0.14/10.86 $false|~sQ11_spl),
% 0.14/10.86 inference(resolution,[status(thm)],[f206,f27])).
% 0.14/10.86 fof(f482,plain,(
% 0.14/10.86 ~sQ11_spl),
% 0.14/10.86 inference(contradiction_clause,[status(thm)],[f476])).
% 0.14/10.86 fof(f689,plain,(
% 0.14/10.86 ![X0,X1]: (convergent_lines(sK0_skl,sK1_skl)|convergent_lines(sK0_skl,X0)|convergent_lines(X1,X0))),
% 0.14/10.86 inference(resolution,[status(thm)],[f123,f36])).
% 0.14/10.86 fof(f698,plain,(
% 0.14/10.86 sQ2_spl|sQ11_spl),
% 0.14/10.86 inference(split_clause,[status(thm)],[f689,f112,f205])).
% 0.14/10.86 fof(f1801,plain,(
% 0.14/10.86 ![X0,X1]: (distinct_lines(sK0_skl,X0)|convergent_lines(sK0_skl,X0)|apart_point_and_line(X1,sK1_skl)|apart_point_and_line(X1,sK0_skl)|unorthogonal_lines(sK1_skl,sK2_skl))),
% 0.14/10.87 inference(resolution,[status(thm)],[f409,f77])).
% 0.14/10.87 fof(f1834,definition,(
% 0.14/10.87 sQ66_spl <=> (unorthogonal_lines(sK1_skl,sK2_skl))),
% 0.14/10.87 introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition])).
% 0.14/10.87 fof(f1835,plain,(
% 0.14/10.87 unorthogonal_lines(sK1_skl,sK2_skl)|~sQ66_spl),
% 0.14/10.87 inference(component_clause,[status(thm)],[f1834])).
% 0.14/10.87 fof(f1838,plain,(
% 0.14/10.87 sQ12_spl|sQ15_spl|sQ66_spl),
% 0.14/10.87 inference(split_clause,[status(thm)],[f1801,f285,f314,f1834])).
% 0.14/10.87 fof(f2535,plain,(
% 0.14/10.87 ~convergent_lines(sK0_skl,sK1_skl)|~convergent_lines(sK0_skl,sK1_skl)|~sQ15_spl),
% 0.14/10.87 inference(resolution,[status(thm)],[f442,f42])).
% 0.14/10.87 fof(f2538,plain,(
% 0.14/10.87 ~sQ2_spl|~sQ15_spl),
% 0.14/10.87 inference(split_clause,[status(thm)],[f2535,f112,f314])).
% 0.14/10.87 fof(f2541,plain,(
% 0.14/10.87 distinct_lines(sK0_skl,sK0_skl)|~sQ12_spl),
% 0.14/10.87 inference(resolution,[status(thm)],[f286,f27])).
% 0.14/10.87 fof(f2542,plain,(
% 0.14/10.87 $false|~sQ12_spl),
% 0.14/10.87 inference(forward_subsumption_resolution,[status(thm)],[f2541,f26])).
% 0.14/10.87 fof(f2543,plain,(
% 0.14/10.87 ~sQ12_spl),
% 0.14/10.87 inference(contradiction_clause,[status(thm)],[f2542])).
% 0.14/10.87 fof(f2544,plain,(
% 0.14/10.87 $false|~sQ66_spl),
% 0.14/10.87 inference(forward_subsumption_resolution,[status(thm)],[f1835,f78])).
% 0.14/10.87 fof(f2545,plain,(
% 0.14/10.87 ~sQ66_spl),
% 0.14/10.87 inference(contradiction_clause,[status(thm)],[f2544])).
% 0.14/10.87 fof(f2546,plain,(
% 0.14/10.87 $false),
% 0.14/10.87 inference(sat_refutation,[status(thm)],[f482,f698,f1838,f2538,f2543,f2545])).
% 0.14/10.87 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/10.89 % Elapsed time: 0.489620 seconds
% 0.14/10.89 % CPU time: 3.690321 seconds
% 0.14/10.89 % Total memory used: 43.623 MB
% 0.14/10.89 % Net memory used: 36.389 MB
%------------------------------------------------------------------------------