%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO214+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 : n014.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 12:26:07 PM UTC 2026
% Result : Theorem 0.15s 5.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO214+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n014.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 13:32:41 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.15/5.41 % Refutation found
% 0.15/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.41 % SZS output start CNFRefutation for theBenchmark
% 0.15/5.41 fof(f2,axiom,(
% 0.15/5.41 (! [X] : ~ distinct_lines(X,X) )),
% 0.15/5.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f3,axiom,(
% 0.15/5.41 (! [X] : ~ convergent_lines(X,X) )),
% 0.15/5.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f6,axiom,(
% 0.15/5.41 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.15/5.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f12,axiom,(
% 0.15/5.41 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 0.15/5.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f16,axiom,(
% 0.15/5.41 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 0.15/5.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f17,axiom,(
% 0.15/5.41 (! [L,M,N] :( ( convergent_lines(L,M)& unorthogonal_lines(L,M) )=> ( ( convergent_lines(L,N)& unorthogonal_lines(L,N) )| ( convergent_lines(M,N)& unorthogonal_lines(M,N) ) ) ) )),
% 0.15/5.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f21,conjecture,(
% 0.15/5.41 (! [L,M] :( unorthogonal_lines(L,M)=> unorthogonal_lines(M,L) ) )),
% 0.15/5.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.41 fof(f22,negated_conjecture,(
% 0.15/5.41 ~((! [L,M] :( unorthogonal_lines(L,M)=> unorthogonal_lines(M,L) ) ))),
% 0.15/5.41 inference(negated_conjecture,[status(cth)],[f21])).
% 0.15/5.41 fof(f24,plain,(
% 0.15/5.41 ![X0]: (~distinct_lines(X0,X0))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f2])).
% 0.15/5.41 fof(f25,plain,(
% 0.15/5.41 ![X0]: (~convergent_lines(X0,X0))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f3])).
% 0.15/5.41 fof(f32,plain,(
% 0.15/5.41 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.15/5.41 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.15/5.41 fof(f33,plain,(
% 0.15/5.41 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.15/5.41 inference(miniscoping,[status(thm)],[f32])).
% 0.15/5.41 fof(f34,plain,(
% 0.15/5.41 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f33])).
% 0.15/5.41 fof(f51,plain,(
% 0.15/5.41 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 0.15/5.41 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.15/5.41 fof(f52,plain,(
% 0.15/5.41 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f51])).
% 0.15/5.41 fof(f58,plain,(
% 0.15/5.41 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/5.41 fof(f59,plain,(
% 0.15/5.41 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|((convergent_lines(L,N)&unorthogonal_lines(L,N))|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 0.15/5.41 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.15/5.41 fof(f60,definition,(
% 0.15/5.41 ![L,N]: (sP0_prd(N,L)<=>(convergent_lines(L,N)&unorthogonal_lines(L,N)))),
% 0.15/5.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.15/5.41 fof(f61,plain,(
% 0.15/5.41 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 0.15/5.41 inference(formula_renaming,[status(thm)],[f59,f60])).
% 0.15/5.41 fof(f62,plain,(
% 0.15/5.41 ![L,M]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(![N]: (sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N)))))),
% 0.15/5.41 inference(miniscoping,[status(thm)],[f61])).
% 0.15/5.41 fof(f64,plain,(
% 0.15/5.41 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~unorthogonal_lines(X0,X1)|sP0_prd(X2,X0)|unorthogonal_lines(X1,X2))),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f62])).
% 0.15/5.41 fof(f70,plain,(
% 0.15/5.41 (?[L,M]: (unorthogonal_lines(L,M)&~unorthogonal_lines(M,L)))),
% 0.15/5.41 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 0.15/5.41 fof(f71,plain,(
% 0.15/5.41 (unorthogonal_lines(sK0_skl,sK1_skl)&~unorthogonal_lines(sK1_skl,sK0_skl))),
% 0.15/5.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl)],[f70])).
% 0.15/5.41 fof(f72,plain,(
% 0.15/5.41 unorthogonal_lines(sK0_skl,sK1_skl)),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f71])).
% 0.15/5.41 fof(f73,plain,(
% 0.15/5.41 ~unorthogonal_lines(sK1_skl,sK0_skl)),
% 0.15/5.41 inference(cnf_transformation,[status(thm)],[f71])).
% 0.15/5.41 fof(f74,plain,(
% 0.15/5.41 ![L,N]: ((~sP0_prd(N,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N)))&(sP0_prd(N,L)|(~convergent_lines(L,N)|~unorthogonal_lines(L,N))))),
% 0.15/5.42 inference(NNF_transformation,[status(thm)],[f60])).
% 0.15/5.42 fof(f75,plain,(
% 0.15/5.42 (![L,N]: (~sP0_prd(N,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N))))&(![L,N]: (sP0_prd(N,L)|(~convergent_lines(L,N)|~unorthogonal_lines(L,N))))),
% 0.15/5.42 inference(miniscoping,[status(thm)],[f74])).
% 0.15/5.42 fof(f76,plain,(
% 0.15/5.42 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.15/5.42 inference(cnf_transformation,[status(thm)],[f75])).
% 0.15/5.42 fof(f79,plain,(
% 0.15/5.42 convergent_lines(sK1_skl,sK0_skl)),
% 0.15/5.42 inference(resolution,[status(thm)],[f58,f73])).
% 0.15/5.42 fof(f89,plain,(
% 0.15/5.42 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.15/5.42 inference(resolution,[status(thm)],[f34,f79])).
% 0.15/5.42 fof(f90,plain,(
% 0.15/5.42 ![X0,X1]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X1)|convergent_lines(X0,X1))),
% 0.15/5.42 inference(resolution,[status(thm)],[f89,f34])).
% 0.15/5.42 fof(f106,plain,(
% 0.15/5.42 ![X0]: (convergent_lines(sK0_skl,sK1_skl)|distinct_lines(sK1_skl,X0))),
% 0.15/5.42 inference(resolution,[status(thm)],[f90,f52])).
% 0.15/5.42 fof(f125,definition,(
% 0.15/5.42 sQ3_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.15/5.42 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.15/5.42 fof(f132,definition,(
% 0.15/5.42 ![X0]: (sQ5_spl <=> (distinct_lines(sK1_skl,X0)))),
% 0.15/5.42 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.15/5.42 fof(f133,plain,(
% 0.15/5.42 ![X0]: (distinct_lines(sK1_skl,X0)|~sQ5_spl)),
% 0.15/5.42 inference(component_clause,[status(thm)],[f132])).
% 0.15/5.42 fof(f135,plain,(
% 0.15/5.42 sQ3_spl|sQ5_spl),
% 0.15/5.42 inference(split_clause,[status(thm)],[f106,f125,f132])).
% 0.15/5.42 fof(f312,plain,(
% 0.15/5.42 $false|~sQ5_spl),
% 0.15/5.42 inference(resolution,[status(thm)],[f133,f24])).
% 0.15/5.42 fof(f313,plain,(
% 0.15/5.42 ~sQ5_spl),
% 0.15/5.42 inference(contradiction_clause,[status(thm)],[f312])).
% 0.15/5.42 fof(f337,plain,(
% 0.15/5.42 ![X0]: (~convergent_lines(sK0_skl,sK1_skl)|sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0))),
% 0.15/5.42 inference(resolution,[status(thm)],[f64,f72])).
% 0.15/5.42 fof(f339,definition,(
% 0.15/5.42 ![X0]: (sQ16_spl <=> (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)))),
% 0.15/5.42 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.15/5.42 fof(f340,plain,(
% 0.15/5.42 ![X0]: (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)|~sQ16_spl)),
% 0.15/5.42 inference(component_clause,[status(thm)],[f339])).
% 0.15/5.42 fof(f342,plain,(
% 0.15/5.42 ~sQ3_spl|sQ16_spl),
% 0.15/5.42 inference(split_clause,[status(thm)],[f337,f125,f339])).
% 0.15/5.42 fof(f367,plain,(
% 0.15/5.42 sP0_prd(sK0_skl,sK0_skl)|~sQ16_spl),
% 0.15/5.42 inference(resolution,[status(thm)],[f340,f73])).
% 0.15/5.42 fof(f375,plain,(
% 0.15/5.42 convergent_lines(sK0_skl,sK0_skl)|~sQ16_spl),
% 0.15/5.42 inference(resolution,[status(thm)],[f367,f76])).
% 0.15/5.42 fof(f376,plain,(
% 0.15/5.42 $false|~sQ16_spl),
% 0.15/5.42 inference(forward_subsumption_resolution,[status(thm)],[f375,f25])).
% 0.15/5.42 fof(f377,plain,(
% 0.15/5.42 ~sQ16_spl),
% 0.15/5.42 inference(contradiction_clause,[status(thm)],[f376])).
% 0.15/5.42 fof(f378,plain,(
% 0.15/5.42 $false),
% 0.15/5.42 inference(sat_refutation,[status(thm)],[f135,f313,f342,f377])).
% 0.15/5.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/5.44 % Elapsed time: 0.045727 seconds
% 0.15/5.44 % CPU time: 0.173717 seconds
% 0.15/5.44 % Total memory used: 18.662 MB
% 0.15/5.44 % Net memory used: 18.222 MB
%------------------------------------------------------------------------------