%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO209+1 : 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 : 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 12:26:06 PM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO209+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 13:29:36 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.39 fof(f2,axiom,(
% 0.15/0.39 (! [X] : ~ distinct_lines(X,X) )),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f5,axiom,(
% 0.15/0.39 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f6,axiom,(
% 0.15/0.39 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f17,axiom,(
% 0.15/0.39 (! [X,Y,Z] :( distinct_lines(Y,Z)=> ( apart_point_and_line(X,Y)| apart_point_and_line(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f18,conjecture,(
% 0.15/0.39 (! [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) ) )),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.39 fof(f19,negated_conjecture,(
% 0.15/0.39 ~((! [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) ) ))),
% 0.15/0.39 inference(negated_conjecture,[status(cth)],[f18])).
% 0.15/0.39 fof(f21,plain,(
% 0.15/0.39 ![X0]: (~distinct_lines(X0,X0))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.15/0.39 fof(f26,plain,(
% 0.15/0.39 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 0.15/0.39 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.15/0.39 fof(f27,plain,(
% 0.15/0.39 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 0.15/0.39 inference(miniscoping,[status(thm)],[f26])).
% 0.15/0.39 fof(f28,plain,(
% 0.15/0.39 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.15/0.39 fof(f29,plain,(
% 0.15/0.39 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.15/0.39 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.15/0.39 fof(f30,plain,(
% 0.15/0.39 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.15/0.39 inference(miniscoping,[status(thm)],[f29])).
% 0.15/0.39 fof(f31,plain,(
% 0.15/0.39 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f30])).
% 0.15/0.39 fof(f53,plain,(
% 0.15/0.39 ![X,Y,Z]: (~distinct_lines(Y,Z)|((apart_point_and_line(X,Y)|apart_point_and_line(X,Z))|convergent_lines(Y,Z)))),
% 0.15/0.39 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.15/0.39 fof(f54,plain,(
% 0.15/0.39 ![Y,Z]: (~distinct_lines(Y,Z)|((![X]: (apart_point_and_line(X,Y)|apart_point_and_line(X,Z)))|convergent_lines(Y,Z)))),
% 0.15/0.39 inference(miniscoping,[status(thm)],[f53])).
% 0.15/0.39 fof(f55,plain,(
% 0.15/0.39 ![X0,X1,X2]: (~distinct_lines(X0,X1)|apart_point_and_line(X2,X0)|apart_point_and_line(X2,X1)|convergent_lines(X0,X1))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f54])).
% 0.15/0.39 fof(f56,plain,(
% 0.15/0.39 (?[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)))),
% 0.15/0.39 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.15/0.39 fof(f57,plain,(
% 0.15/0.39 ?[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))),
% 0.15/0.39 inference(miniscoping,[status(thm)],[f56])).
% 0.15/0.39 fof(f58,plain,(
% 0.15/0.39 (((((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))),
% 0.15/0.39 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)],[f57])).
% 0.15/0.39 fof(f60,plain,(
% 0.15/0.39 ~apart_point_and_line(sK3_skl,sK0_skl)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f58])).
% 0.15/0.39 fof(f61,plain,(
% 0.15/0.39 ~apart_point_and_line(sK3_skl,sK1_skl)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f58])).
% 0.15/0.39 fof(f62,plain,(
% 0.15/0.39 ~convergent_lines(sK0_skl,sK2_skl)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f58])).
% 0.15/0.39 fof(f63,plain,(
% 0.15/0.39 ~convergent_lines(sK1_skl,sK2_skl)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f58])).
% 0.15/0.39 fof(f64,plain,(
% 0.15/0.39 distinct_lines(sK0_skl,sK1_skl)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f58])).
% 0.15/0.39 fof(f65,plain,(
% 0.15/0.39 ![X0]: (distinct_lines(sK0_skl,X0)|distinct_lines(sK1_skl,X0))),
% 0.15/0.39 inference(resolution,[status(thm)],[f28,f64])).
% 0.15/0.39 fof(f66,plain,(
% 0.15/0.39 ![X0,X1]: (distinct_lines(sK0_skl,X0)|distinct_lines(sK1_skl,X1)|distinct_lines(X0,X1))),
% 0.15/0.39 inference(resolution,[status(thm)],[f65,f28])).
% 0.15/0.39 fof(f86,plain,(
% 0.15/0.39 distinct_lines(sK1_skl,sK0_skl)),
% 0.15/0.39 inference(resolution,[status(thm)],[f66,f21])).
% 0.15/0.39 fof(f143,plain,(
% 0.15/0.39 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)|convergent_lines(sK1_skl,sK0_skl))),
% 0.15/0.39 inference(resolution,[status(thm)],[f55,f86])).
% 0.15/0.39 fof(f180,definition,(
% 0.15/0.39 ![X0]: (sQ12_spl <=> (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)))),
% 0.15/0.39 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.15/0.39 fof(f181,plain,(
% 0.15/0.39 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,sK0_skl)|~sQ12_spl)),
% 0.15/0.39 inference(component_clause,[status(thm)],[f180])).
% 0.15/0.39 fof(f183,definition,(
% 0.15/0.39 sQ13_spl <=> (convergent_lines(sK1_skl,sK0_skl))),
% 0.15/0.39 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.15/0.39 fof(f184,plain,(
% 0.15/0.39 convergent_lines(sK1_skl,sK0_skl)|~sQ13_spl),
% 0.15/0.39 inference(component_clause,[status(thm)],[f183])).
% 0.15/0.39 fof(f186,plain,(
% 0.15/0.39 sQ12_spl|sQ13_spl),
% 0.15/0.39 inference(split_clause,[status(thm)],[f143,f180,f183])).
% 0.15/0.39 fof(f237,plain,(
% 0.15/0.39 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0)|~sQ13_spl)),
% 0.15/0.39 inference(resolution,[status(thm)],[f184,f31])).
% 0.15/0.39 fof(f244,plain,(
% 0.15/0.39 apart_point_and_line(sK3_skl,sK0_skl)|~sQ12_spl),
% 0.15/0.39 inference(resolution,[status(thm)],[f181,f61])).
% 0.15/0.39 fof(f246,plain,(
% 0.15/0.39 $false|~sQ12_spl),
% 0.15/0.39 inference(forward_subsumption_resolution,[status(thm)],[f244,f60])).
% 0.15/0.39 fof(f247,plain,(
% 0.15/0.39 ~sQ12_spl),
% 0.15/0.39 inference(contradiction_clause,[status(thm)],[f246])).
% 0.15/0.39 fof(f256,plain,(
% 0.15/0.39 convergent_lines(sK0_skl,sK2_skl)|~sQ13_spl),
% 0.15/0.39 inference(resolution,[status(thm)],[f237,f63])).
% 0.15/0.39 fof(f260,plain,(
% 0.15/0.39 $false|~sQ13_spl),
% 0.15/0.39 inference(forward_subsumption_resolution,[status(thm)],[f256,f62])).
% 0.15/0.39 fof(f261,plain,(
% 0.15/0.39 ~sQ13_spl),
% 0.15/0.39 inference(contradiction_clause,[status(thm)],[f260])).
% 0.15/0.39 fof(f262,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(sat_refutation,[status(thm)],[f186,f247,f261])).
% 0.15/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.42 % Elapsed time: 0.035926 seconds
% 0.15/0.42 % CPU time: 0.062452 seconds
% 0.15/0.42 % Total memory used: 3.560 MB
% 0.15/0.42 % Net memory used: 3.478 MB
%------------------------------------------------------------------------------