%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:26:06 PM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO209+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.34 % Computer : n015.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Sun Sep 20 13:29:35 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.35 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.38 fof(f2,axiom,(
% 0.11/0.38 (! [X] : ~ distinct_lines(X,X) )),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f5,axiom,(
% 0.11/0.38 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f6,axiom,(
% 0.11/0.38 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f15,axiom,(
% 0.11/0.38 (! [X,Y,Z] :( distinct_lines(Y,Z)=> ( apart_point_and_line(X,Y)| apart_point_and_line(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f16,conjecture,(
% 0.11/0.38 (! [A,L,M,N] :( ( apart_point_and_line(A,L)& ~ apart_point_and_line(A,M)& ~ apart_point_and_line(A,N)& ~ convergent_lines(M,L)& ~ convergent_lines(N,L) )=> ~ distinct_lines(M,N) ) )),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.38 fof(f17,negated_conjecture,(
% 0.11/0.38 ~((! [A,L,M,N] :( ( apart_point_and_line(A,L)& ~ apart_point_and_line(A,M)& ~ apart_point_and_line(A,N)& ~ convergent_lines(M,L)& ~ convergent_lines(N,L) )=> ~ distinct_lines(M,N) ) ))),
% 0.11/0.38 inference(negated_conjecture,[status(cth)],[f16])).
% 0.11/0.38 fof(f19,plain,(
% 0.11/0.38 ![X0]: (~distinct_lines(X0,X0))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f2])).
% 0.11/0.38 fof(f24,plain,(
% 0.11/0.38 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.11/0.38 fof(f25,plain,(
% 0.11/0.38 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 0.11/0.38 inference(miniscoping,[status(thm)],[f24])).
% 0.11/0.38 fof(f26,plain,(
% 0.11/0.38 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f25])).
% 0.11/0.38 fof(f27,plain,(
% 0.11/0.38 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.11/0.38 fof(f28,plain,(
% 0.11/0.38 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.11/0.38 inference(miniscoping,[status(thm)],[f27])).
% 0.11/0.38 fof(f29,plain,(
% 0.11/0.38 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f28])).
% 0.11/0.38 fof(f50,plain,(
% 0.11/0.38 ![X,Y,Z]: (~distinct_lines(Y,Z)|((apart_point_and_line(X,Y)|apart_point_and_line(X,Z))|convergent_lines(Y,Z)))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.11/0.38 fof(f51,plain,(
% 0.11/0.38 ![Y,Z]: (~distinct_lines(Y,Z)|((![X]: (apart_point_and_line(X,Y)|apart_point_and_line(X,Z)))|convergent_lines(Y,Z)))),
% 0.11/0.38 inference(miniscoping,[status(thm)],[f50])).
% 0.11/0.38 fof(f52,plain,(
% 0.11/0.38 ![X0,X1,X2]: (~distinct_lines(X0,X1)|apart_point_and_line(X2,X0)|apart_point_and_line(X2,X1)|convergent_lines(X0,X1))),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f51])).
% 0.11/0.38 fof(f53,plain,(
% 0.11/0.38 (?[A,L,M,N]: (((((apart_point_and_line(A,L)&~apart_point_and_line(A,M))&~apart_point_and_line(A,N))&~convergent_lines(M,L))&~convergent_lines(N,L))&distinct_lines(M,N)))),
% 0.11/0.38 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.11/0.38 fof(f54,plain,(
% 0.11/0.38 ?[M,N]: ((?[L]: (((?[A]: ((apart_point_and_line(A,L)&~apart_point_and_line(A,M))&~apart_point_and_line(A,N)))&~convergent_lines(M,L))&~convergent_lines(N,L)))&distinct_lines(M,N))),
% 0.11/0.38 inference(miniscoping,[status(thm)],[f53])).
% 0.11/0.38 fof(f55,plain,(
% 0.11/0.38 (((((apart_point_and_line(sK3_skl,sK2_skl)&~apart_point_and_line(sK3_skl,sK0_skl))&~apart_point_and_line(sK3_skl,sK1_skl))&~convergent_lines(sK0_skl,sK2_skl))&~convergent_lines(sK1_skl,sK2_skl))&distinct_lines(sK0_skl,sK1_skl))),
% 0.11/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(M,sK0_skl),skolemize(N,sK1_skl),skolemize(L,sK2_skl),skolemize(A,sK3_skl)],[f54])).
% 0.11/0.38 fof(f57,plain,(
% 0.11/0.38 ~apart_point_and_line(sK3_skl,sK0_skl)),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f55])).
% 0.11/0.38 fof(f58,plain,(
% 0.11/0.38 ~apart_point_and_line(sK3_skl,sK1_skl)),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f55])).
% 0.11/0.38 fof(f59,plain,(
% 0.11/0.38 ~convergent_lines(sK0_skl,sK2_skl)),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f55])).
% 0.11/0.38 fof(f60,plain,(
% 0.11/0.38 ~convergent_lines(sK1_skl,sK2_skl)),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f55])).
% 0.11/0.38 fof(f61,plain,(
% 0.11/0.38 distinct_lines(sK0_skl,sK1_skl)),
% 0.11/0.38 inference(cnf_transformation,[status(thm)],[f55])).
% 0.11/0.38 fof(f62,plain,(
% 0.11/0.38 ![X0]: (distinct_lines(sK0_skl,X0)|distinct_lines(sK1_skl,X0))),
% 0.11/0.38 inference(resolution,[status(thm)],[f26,f61])).
% 0.11/0.38 fof(f63,plain,(
% 0.11/0.38 ![X0,X1]: (distinct_lines(sK0_skl,X0)|distinct_lines(sK1_skl,X1)|distinct_lines(X0,X1))),
% 0.11/0.38 inference(resolution,[status(thm)],[f62,f26])).
% 0.11/0.38 fof(f79,plain,(
% 0.11/0.38 distinct_lines(sK1_skl,sK0_skl)),
% 0.11/0.38 inference(resolution,[status(thm)],[f63,f19])).
% 0.11/0.38 fof(f114,plain,(
% 0.11/0.38 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)|convergent_lines(sK1_skl,sK0_skl))),
% 0.11/0.38 inference(resolution,[status(thm)],[f52,f79])).
% 0.11/0.38 fof(f142,definition,(
% 0.11/0.38 ![X0]: (sQ9_spl <=> (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)))),
% 0.11/0.38 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.11/0.38 fof(f143,plain,(
% 0.11/0.38 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)|~sQ9_spl)),
% 0.11/0.38 inference(component_clause,[status(thm)],[f142])).
% 0.11/0.38 fof(f145,definition,(
% 0.11/0.38 sQ10_spl <=> (convergent_lines(sK1_skl,sK0_skl))),
% 0.11/0.38 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.11/0.38 fof(f146,plain,(
% 0.11/0.38 convergent_lines(sK1_skl,sK0_skl)|~sQ10_spl),
% 0.11/0.38 inference(component_clause,[status(thm)],[f145])).
% 0.11/0.38 fof(f148,plain,(
% 0.11/0.38 sQ9_spl|sQ10_spl),
% 0.11/0.38 inference(split_clause,[status(thm)],[f114,f142,f145])).
% 0.11/0.38 fof(f208,plain,(
% 0.11/0.38 apart_point_and_line(sK3_skl,sK0_skl)|~sQ9_spl),
% 0.11/0.38 inference(resolution,[status(thm)],[f143,f58])).
% 0.11/0.38 fof(f211,plain,(
% 0.11/0.38 $false|~sQ9_spl),
% 0.11/0.38 inference(forward_subsumption_resolution,[status(thm)],[f208,f57])).
% 0.11/0.38 fof(f212,plain,(
% 0.11/0.38 ~sQ9_spl),
% 0.11/0.38 inference(contradiction_clause,[status(thm)],[f211])).
% 0.11/0.38 fof(f214,plain,(
% 0.11/0.38 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0)|~sQ10_spl)),
% 0.11/0.38 inference(resolution,[status(thm)],[f146,f29])).
% 0.11/0.38 fof(f223,plain,(
% 0.11/0.38 convergent_lines(sK0_skl,sK2_skl)|~sQ10_spl),
% 0.11/0.38 inference(resolution,[status(thm)],[f214,f60])).
% 0.11/0.38 fof(f228,plain,(
% 0.11/0.38 $false|~sQ10_spl),
% 0.11/0.38 inference(forward_subsumption_resolution,[status(thm)],[f223,f59])).
% 0.11/0.38 fof(f229,plain,(
% 0.11/0.38 ~sQ10_spl),
% 0.11/0.38 inference(contradiction_clause,[status(thm)],[f228])).
% 0.11/0.38 fof(f230,plain,(
% 0.11/0.38 $false),
% 0.11/0.38 inference(sat_refutation,[status(thm)],[f148,f212,f229])).
% 0.11/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.41 % Elapsed time: 0.048904 seconds
% 0.11/0.41 % CPU time: 0.135435 seconds
% 0.11/0.41 % Total memory used: 17.801 MB
% 0.11/0.41 % Net memory used: 17.412 MB
%------------------------------------------------------------------------------