%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO221+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 : n005.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 12:26:09 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO221+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
% 0.09/0.36 % Computer : n005.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 13:45:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f20,axiom,(
% 0.09/0.40 (! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f21,axiom,(
% 0.09/0.40 (! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f22,axiom,(
% 0.09/0.40 (! [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) ) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f23,conjecture,(
% 0.09/0.40 (! [A,B,L] :( ~ apart_point_and_line(B,orthogonal_through_point(L,A))=> ~ distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f24,negated_conjecture,(
% 0.09/0.40 ~((! [A,B,L] :( ~ apart_point_and_line(B,orthogonal_through_point(L,A))=> ~ distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ) ))),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f23])).
% 0.09/0.40 fof(f68,plain,(
% 0.09/0.40 ![X0,X1]: (~unorthogonal_lines(orthogonal_through_point(X0,X1),X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f20])).
% 0.09/0.40 fof(f69,plain,(
% 0.09/0.40 ![X0,X1]: (~apart_point_and_line(X0,orthogonal_through_point(X1,X0)))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f21])).
% 0.09/0.40 fof(f70,plain,(
% 0.09/0.40 ![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)))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 0.09/0.40 fof(f71,plain,(
% 0.09/0.40 ![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))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f70])).
% 0.09/0.40 fof(f72,plain,(
% 0.09/0.40 ![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))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f71])).
% 0.09/0.40 fof(f73,plain,(
% 0.09/0.40 (?[A,B,L]: (~apart_point_and_line(B,orthogonal_through_point(L,A))&distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B))))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.09/0.40 fof(f74,plain,(
% 0.09/0.40 (~apart_point_and_line(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl))&distinct_lines(orthogonal_through_point(sK2_skl,sK0_skl),orthogonal_through_point(sK2_skl,sK1_skl)))),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(L,sK2_skl)],[f73])).
% 0.09/0.40 fof(f75,plain,(
% 0.09/0.40 ~apart_point_and_line(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f74])).
% 0.09/0.40 fof(f76,plain,(
% 0.09/0.40 distinct_lines(orthogonal_through_point(sK2_skl,sK0_skl),orthogonal_through_point(sK2_skl,sK1_skl))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f74])).
% 0.09/0.40 fof(f84,definition,(
% 0.09/0.40 ![X0]: (sQ0_spl <=> (apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK1_skl))))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f85,plain,(
% 0.09/0.40 ![X0]: (apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK1_skl))|~sQ0_spl)),
% 0.09/0.40 inference(component_clause,[status(thm)],[f84])).
% 0.09/0.40 fof(f96,plain,(
% 0.09/0.40 apart_point_and_line(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl))|~sQ0_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f85,f69])).
% 0.09/0.40 fof(f98,plain,(
% 0.09/0.40 $false|~sQ0_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f96,f75])).
% 0.09/0.40 fof(f99,plain,(
% 0.09/0.40 ~sQ0_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f98])).
% 0.09/0.40 fof(f262,plain,(
% 0.09/0.40 ![X0,X1]: (apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK1_skl))|unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),X1)|unorthogonal_lines(orthogonal_through_point(sK2_skl,sK1_skl),X1))),
% 0.09/0.40 inference(resolution,[status(thm)],[f72,f76])).
% 0.09/0.40 fof(f272,definition,(
% 0.09/0.40 ![X1]: (sQ23_spl <=> (unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),X1)|unorthogonal_lines(orthogonal_through_point(sK2_skl,sK1_skl),X1)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f273,plain,(
% 0.09/0.40 ![X0]: (unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),X0)|unorthogonal_lines(orthogonal_through_point(sK2_skl,sK1_skl),X0)|~sQ23_spl)),
% 0.09/0.40 inference(component_clause,[status(thm)],[f272])).
% 0.09/0.40 fof(f275,plain,(
% 0.09/0.40 sQ0_spl|sQ23_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f262,f84,f272])).
% 0.09/0.40 fof(f286,plain,(
% 0.09/0.40 unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),sK2_skl)|~sQ23_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f273,f68])).
% 0.09/0.40 fof(f289,plain,(
% 0.09/0.40 $false|~sQ23_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f286,f68])).
% 0.09/0.40 fof(f290,plain,(
% 0.09/0.40 ~sQ23_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f289])).
% 0.09/0.40 fof(f291,plain,(
% 0.09/0.40 $false),
% 0.09/0.40 inference(sat_refutation,[status(thm)],[f99,f275,f290])).
% 0.09/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.43 % Elapsed time: 0.047982 seconds
% 0.09/0.43 % CPU time: 0.170050 seconds
% 0.09/0.43 % Total memory used: 17.973 MB
% 0.09/0.43 % Net memory used: 17.618 MB
%------------------------------------------------------------------------------