%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO210+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.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 13:24:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.39 fof(f21,axiom,(
% 0.11/0.39 (! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) )),
% 0.11/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f22,axiom,(
% 0.11/0.39 (! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)) )),
% 0.11/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f23,axiom,(
% 0.11/0.39 (! [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) ) ) )),
% 0.11/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f32,axiom,(
% 0.11/0.39 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 0.11/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f34,axiom,(
% 0.11/0.39 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 0.11/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f35,axiom,(
% 0.11/0.39 (! [X,Y] :( orthogonal_lines(X,Y)<=> ~ unorthogonal_lines(X,Y) ) )),
% 0.11/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f36,conjecture,(
% 0.11/0.39 (! [A,L,M] :( ( incident_point_and_line(A,L)& orthogonal_lines(L,M) )=> equal_lines(L,orthogonal_through_point(M,A)) ) )),
% 0.11/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f37,negated_conjecture,(
% 0.11/0.39 ~((! [A,L,M] :( ( incident_point_and_line(A,L)& orthogonal_lines(L,M) )=> equal_lines(L,orthogonal_through_point(M,A)) ) ))),
% 0.11/0.39 inference(negated_conjecture,[status(cth)],[f36])).
% 0.11/0.39 fof(f83,plain,(
% 0.11/0.39 ![X0,X1]: (~unorthogonal_lines(orthogonal_through_point(X0,X1),X0))),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f21])).
% 0.11/0.39 fof(f84,plain,(
% 0.11/0.39 ![X0,X1]: (~apart_point_and_line(X0,orthogonal_through_point(X1,X0)))),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f22])).
% 0.11/0.39 fof(f85,plain,(
% 0.11/0.39 ![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)))),
% 0.11/0.39 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.11/0.39 fof(f86,plain,(
% 0.11/0.39 ![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))))),
% 0.11/0.39 inference(miniscoping,[status(thm)],[f85])).
% 0.11/0.39 fof(f87,plain,(
% 0.11/0.39 ![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))),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f86])).
% 0.11/0.39 fof(f111,plain,(
% 0.11/0.39 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.11/0.39 inference(NNF_transformation,[status(thm)],[f32])).
% 0.11/0.39 fof(f112,plain,(
% 0.11/0.39 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.11/0.39 inference(miniscoping,[status(thm)],[f111])).
% 0.11/0.39 fof(f114,plain,(
% 0.11/0.39 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f112])).
% 0.11/0.39 fof(f119,plain,(
% 0.11/0.39 ![X,Y]: ((~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y))&(incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 0.11/0.39 inference(NNF_transformation,[status(thm)],[f34])).
% 0.11/0.39 fof(f120,plain,(
% 0.11/0.39 (![X,Y]: (~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y)))&(![X,Y]: (incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 0.11/0.39 inference(miniscoping,[status(thm)],[f119])).
% 0.11/0.39 fof(f121,plain,(
% 0.11/0.39 ![X0,X1]: (~incident_point_and_line(X0,X1)|~apart_point_and_line(X0,X1))),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f120])).
% 0.11/0.39 fof(f123,plain,(
% 0.11/0.39 ![X,Y]: ((~orthogonal_lines(X,Y)|~unorthogonal_lines(X,Y))&(orthogonal_lines(X,Y)|unorthogonal_lines(X,Y)))),
% 0.11/0.39 inference(NNF_transformation,[status(thm)],[f35])).
% 0.11/0.39 fof(f124,plain,(
% 0.11/0.39 (![X,Y]: (~orthogonal_lines(X,Y)|~unorthogonal_lines(X,Y)))&(![X,Y]: (orthogonal_lines(X,Y)|unorthogonal_lines(X,Y)))),
% 0.11/0.39 inference(miniscoping,[status(thm)],[f123])).
% 0.11/0.39 fof(f125,plain,(
% 0.11/0.39 ![X0,X1]: (~orthogonal_lines(X0,X1)|~unorthogonal_lines(X0,X1))),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f124])).
% 0.11/0.39 fof(f127,plain,(
% 0.11/0.39 (?[A,L,M]: ((incident_point_and_line(A,L)&orthogonal_lines(L,M))&~equal_lines(L,orthogonal_through_point(M,A))))),
% 0.11/0.39 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.11/0.39 fof(f128,plain,(
% 0.11/0.39 ((incident_point_and_line(sK0_skl,sK1_skl)&orthogonal_lines(sK1_skl,sK2_skl))&~equal_lines(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl)))),
% 0.11/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(L,sK1_skl),skolemize(M,sK2_skl)],[f127])).
% 0.11/0.39 fof(f129,plain,(
% 0.11/0.39 incident_point_and_line(sK0_skl,sK1_skl)),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f128])).
% 0.11/0.39 fof(f130,plain,(
% 0.11/0.39 orthogonal_lines(sK1_skl,sK2_skl)),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f128])).
% 0.11/0.39 fof(f131,plain,(
% 0.11/0.39 ~equal_lines(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl))),
% 0.11/0.39 inference(cnf_transformation,[status(thm)],[f128])).
% 0.11/0.39 fof(f142,plain,(
% 0.11/0.39 ~apart_point_and_line(sK0_skl,sK1_skl)),
% 0.11/0.39 inference(resolution,[status(thm)],[f121,f129])).
% 0.11/0.39 fof(f143,plain,(
% 0.11/0.39 ~unorthogonal_lines(sK1_skl,sK2_skl)),
% 0.11/0.39 inference(resolution,[status(thm)],[f125,f130])).
% 0.11/0.39 fof(f144,plain,(
% 0.11/0.39 distinct_lines(sK1_skl,orthogonal_through_point(sK2_skl,sK0_skl))),
% 0.11/0.39 inference(resolution,[status(thm)],[f114,f131])).
% 0.11/0.39 fof(f154,plain,(
% 0.11/0.39 ![X0,X1]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))|unorthogonal_lines(sK1_skl,X1)|unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),X1))),
% 0.11/0.39 inference(resolution,[status(thm)],[f144,f87])).
% 0.11/0.39 fof(f157,definition,(
% 0.11/0.39 ![X0]: (sQ0_spl <=> (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))))),
% 0.11/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.11/0.39 fof(f158,plain,(
% 0.11/0.39 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,orthogonal_through_point(sK2_skl,sK0_skl))|~sQ0_spl)),
% 0.11/0.39 inference(component_clause,[status(thm)],[f157])).
% 0.11/0.39 fof(f160,definition,(
% 0.11/0.39 ![X1]: (sQ1_spl <=> (unorthogonal_lines(sK1_skl,X1)|unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),X1)))),
% 0.11/0.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.11/0.39 fof(f161,plain,(
% 0.11/0.39 ![X0]: (unorthogonal_lines(sK1_skl,X0)|unorthogonal_lines(orthogonal_through_point(sK2_skl,sK0_skl),X0)|~sQ1_spl)),
% 0.11/0.39 inference(component_clause,[status(thm)],[f160])).
% 0.11/0.39 fof(f163,plain,(
% 0.11/0.39 sQ0_spl|sQ1_spl),
% 0.11/0.39 inference(split_clause,[status(thm)],[f154,f157,f160])).
% 0.11/0.39 fof(f170,plain,(
% 0.11/0.39 apart_point_and_line(sK0_skl,sK1_skl)|~sQ0_spl),
% 0.11/0.39 inference(resolution,[status(thm)],[f158,f84])).
% 0.11/0.39 fof(f173,plain,(
% 0.11/0.39 $false|~sQ0_spl),
% 0.11/0.39 inference(forward_subsumption_resolution,[status(thm)],[f170,f142])).
% 0.11/0.39 fof(f174,plain,(
% 0.11/0.39 ~sQ0_spl),
% 0.11/0.39 inference(contradiction_clause,[status(thm)],[f173])).
% 0.11/0.39 fof(f175,plain,(
% 0.11/0.39 unorthogonal_lines(sK1_skl,sK2_skl)|~sQ1_spl),
% 0.11/0.39 inference(resolution,[status(thm)],[f161,f83])).
% 0.11/0.39 fof(f180,plain,(
% 0.11/0.39 $false|~sQ1_spl),
% 0.11/0.39 inference(forward_subsumption_resolution,[status(thm)],[f175,f143])).
% 0.11/0.39 fof(f181,plain,(
% 0.11/0.39 ~sQ1_spl),
% 0.11/0.39 inference(contradiction_clause,[status(thm)],[f180])).
% 0.11/0.39 fof(f182,plain,(
% 0.11/0.39 $false),
% 0.11/0.39 inference(sat_refutation,[status(thm)],[f163,f174,f181])).
% 0.11/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.41 % Elapsed time: 0.031427 seconds
% 0.15/0.41 % CPU time: 0.066745 seconds
% 0.15/0.41 % Total memory used: 4.530 MB
% 0.15/0.41 % Net memory used: 4.429 MB
%------------------------------------------------------------------------------