%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO206+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 : n001.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 12:26:05 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO206+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n001.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 13:29:27 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.38 fof(f6,axiom,(
% 0.13/0.38 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f15,axiom,(
% 0.13/0.38 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f16,axiom,(
% 0.13/0.38 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f17,axiom,(
% 0.13/0.38 (! [X,Y,Z] :( distinct_lines(Y,Z)=> ( apart_point_and_line(X,Y)| apart_point_and_line(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f18,conjecture,(
% 0.13/0.38 (! [X,Y,Z] :( ( ~ apart_point_and_line(X,Y)& ~ convergent_lines(Y,Z) )=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ) )),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f19,negated_conjecture,(
% 0.13/0.38 ~((! [X,Y,Z] :( ( ~ apart_point_and_line(X,Y)& ~ convergent_lines(Y,Z) )=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ) ))),
% 0.13/0.38 inference(negated_conjecture,[status(cth)],[f18])).
% 0.13/0.38 fof(f29,plain,(
% 0.13/0.38 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.13/0.38 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.38 fof(f30,plain,(
% 0.13/0.38 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.13/0.38 inference(miniscoping,[status(thm)],[f29])).
% 0.13/0.38 fof(f31,plain,(
% 0.13/0.38 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f30])).
% 0.13/0.38 fof(f51,plain,(
% 0.13/0.38 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f15])).
% 0.13/0.38 fof(f52,plain,(
% 0.13/0.38 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f16])).
% 0.13/0.38 fof(f53,plain,(
% 0.13/0.38 ![X,Y,Z]: (~distinct_lines(Y,Z)|((apart_point_and_line(X,Y)|apart_point_and_line(X,Z))|convergent_lines(Y,Z)))),
% 0.13/0.38 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.13/0.38 fof(f54,plain,(
% 0.13/0.38 ![Y,Z]: (~distinct_lines(Y,Z)|((![X]: (apart_point_and_line(X,Y)|apart_point_and_line(X,Z)))|convergent_lines(Y,Z)))),
% 0.13/0.38 inference(miniscoping,[status(thm)],[f53])).
% 0.13/0.38 fof(f55,plain,(
% 0.13/0.38 ![X0,X1,X2]: (~distinct_lines(X0,X1)|apart_point_and_line(X2,X0)|apart_point_and_line(X2,X1)|convergent_lines(X0,X1))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f54])).
% 0.13/0.38 fof(f56,plain,(
% 0.13/0.38 (?[X,Y,Z]: ((~apart_point_and_line(X,Y)&~convergent_lines(Y,Z))&distinct_lines(Y,parallel_through_point(Z,X))))),
% 0.13/0.38 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.13/0.38 fof(f57,plain,(
% 0.13/0.38 ((~apart_point_and_line(sK0_skl,sK1_skl)&~convergent_lines(sK1_skl,sK2_skl))&distinct_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)))),
% 0.13/0.38 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)],[f56])).
% 0.13/0.38 fof(f58,plain,(
% 0.13/0.38 ~apart_point_and_line(sK0_skl,sK1_skl)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f57])).
% 0.13/0.38 fof(f59,plain,(
% 0.13/0.38 ~convergent_lines(sK1_skl,sK2_skl)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f57])).
% 0.13/0.38 fof(f60,plain,(
% 0.13/0.38 distinct_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f57])).
% 0.13/0.38 fof(f65,plain,(
% 0.13/0.38 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,parallel_through_point(sK2_skl,sK0_skl))|convergent_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)))),
% 0.13/0.38 inference(resolution,[status(thm)],[f55,f60])).
% 0.13/0.38 fof(f66,definition,(
% 0.13/0.38 ![X0]: (sQ0_spl <=> (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,parallel_through_point(sK2_skl,sK0_skl))))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f67,plain,(
% 0.13/0.38 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,parallel_through_point(sK2_skl,sK0_skl))|~sQ0_spl)),
% 0.13/0.38 inference(component_clause,[status(thm)],[f66])).
% 0.13/0.38 fof(f69,definition,(
% 0.13/0.38 sQ1_spl <=> (convergent_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl)))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f70,plain,(
% 0.13/0.38 convergent_lines(sK1_skl,parallel_through_point(sK2_skl,sK0_skl))|~sQ1_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f69])).
% 0.13/0.38 fof(f72,plain,(
% 0.13/0.38 sQ0_spl|sQ1_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f65,f66,f69])).
% 0.13/0.38 fof(f73,plain,(
% 0.13/0.38 apart_point_and_line(sK0_skl,sK1_skl)|~sQ0_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f67,f52])).
% 0.13/0.38 fof(f75,plain,(
% 0.13/0.38 $false|~sQ0_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f73,f58])).
% 0.13/0.38 fof(f76,plain,(
% 0.13/0.38 ~sQ0_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f75])).
% 0.13/0.38 fof(f78,plain,(
% 0.13/0.38 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(parallel_through_point(sK2_skl,sK0_skl),X0)|~sQ1_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f70,f31])).
% 0.13/0.38 fof(f82,plain,(
% 0.13/0.38 convergent_lines(sK1_skl,sK2_skl)|~sQ1_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f78,f51])).
% 0.13/0.38 fof(f86,plain,(
% 0.13/0.38 $false|~sQ1_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f82,f59])).
% 0.13/0.38 fof(f87,plain,(
% 0.13/0.38 ~sQ1_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f86])).
% 0.13/0.38 fof(f88,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(sat_refutation,[status(thm)],[f72,f76,f87])).
% 0.13/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.40 % Elapsed time: 0.043783 seconds
% 0.13/0.40 % CPU time: 0.134628 seconds
% 0.13/0.40 % Total memory used: 17.727 MB
% 0.13/0.40 % Net memory used: 17.274 MB
%------------------------------------------------------------------------------