%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO213+2 : 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 : n009.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 0.11s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO213+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 13:33:57 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.11/0.36 % 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(f2,axiom,(
% 0.11/0.39 (! [X] : ~ distinct_lines(X,X) )),
% 0.11/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f3,axiom,(
% 0.11/0.39 (! [X] : ~ convergent_lines(X,X) )),
% 0.11/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f5,axiom,(
% 0.11/0.39 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 0.11/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f6,axiom,(
% 0.11/0.39 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.11/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f12,axiom,(
% 0.11/0.39 (! [X,Y] :( convergent_lines(X,Y)=> distinct_lines(X,Y) ) )),
% 0.11/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f16,axiom,(
% 0.11/0.39 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 0.11/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.39 fof(f17,axiom,(
% 0.11/0.39 (! [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) ) ) ) )),
% 0.11/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.40 fof(f21,conjecture,(
% 0.11/0.40 (! [L,M,N] :( unorthogonal_lines(L,M)=> ( distinct_lines(L,N)| unorthogonal_lines(M,N) ) ) )),
% 0.11/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.40 fof(f22,negated_conjecture,(
% 0.11/0.40 ~((! [L,M,N] :( unorthogonal_lines(L,M)=> ( distinct_lines(L,N)| unorthogonal_lines(M,N) ) ) ))),
% 0.11/0.40 inference(negated_conjecture,[status(cth)],[f21])).
% 0.11/0.40 fof(f24,plain,(
% 0.11/0.40 ![X0]: (~distinct_lines(X0,X0))),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.11/0.40 fof(f25,plain,(
% 0.11/0.40 ![X0]: (~convergent_lines(X0,X0))),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.11/0.40 fof(f29,plain,(
% 0.11/0.40 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 0.11/0.40 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.11/0.40 fof(f30,plain,(
% 0.11/0.40 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 0.11/0.40 inference(miniscoping,[status(thm)],[f29])).
% 0.11/0.40 fof(f31,plain,(
% 0.11/0.40 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f30])).
% 0.11/0.40 fof(f32,plain,(
% 0.11/0.40 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.11/0.40 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.11/0.40 fof(f33,plain,(
% 0.11/0.40 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.11/0.40 inference(miniscoping,[status(thm)],[f32])).
% 0.11/0.40 fof(f34,plain,(
% 0.11/0.40 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f33])).
% 0.11/0.40 fof(f51,plain,(
% 0.11/0.40 ![X,Y]: (~convergent_lines(X,Y)|distinct_lines(X,Y))),
% 0.11/0.40 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.11/0.40 fof(f52,plain,(
% 0.11/0.40 ![X0,X1]: (~convergent_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f51])).
% 0.11/0.40 fof(f58,plain,(
% 0.11/0.40 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f16])).
% 0.11/0.40 fof(f59,plain,(
% 0.11/0.40 ![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))))),
% 0.11/0.40 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.11/0.40 fof(f60,definition,(
% 0.11/0.40 ![L,N]: (sP0_prd(N,L)<=>(convergent_lines(L,N)&unorthogonal_lines(L,N)))),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.11/0.40 fof(f61,plain,(
% 0.11/0.40 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 0.11/0.40 inference(formula_renaming,[status(thm)],[f59,f60])).
% 0.11/0.40 fof(f62,plain,(
% 0.11/0.40 ![L,M]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(![N]: (sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N)))))),
% 0.11/0.40 inference(miniscoping,[status(thm)],[f61])).
% 0.11/0.40 fof(f64,plain,(
% 0.11/0.40 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~unorthogonal_lines(X0,X1)|sP0_prd(X2,X0)|unorthogonal_lines(X1,X2))),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f62])).
% 0.11/0.40 fof(f70,plain,(
% 0.11/0.40 (?[L,M,N]: (unorthogonal_lines(L,M)&(~distinct_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.11/0.40 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 0.11/0.40 fof(f71,plain,(
% 0.11/0.40 ?[L,M]: (unorthogonal_lines(L,M)&(?[N]: (~distinct_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.11/0.40 inference(miniscoping,[status(thm)],[f70])).
% 0.11/0.40 fof(f72,plain,(
% 0.11/0.40 (unorthogonal_lines(sK0_skl,sK1_skl)&(~distinct_lines(sK0_skl,sK2_skl)&~unorthogonal_lines(sK1_skl,sK2_skl)))),
% 0.11/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl),skolemize(N,sK2_skl)],[f71])).
% 0.11/0.40 fof(f73,plain,(
% 0.11/0.40 unorthogonal_lines(sK0_skl,sK1_skl)),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f72])).
% 0.11/0.40 fof(f74,plain,(
% 0.11/0.40 ~distinct_lines(sK0_skl,sK2_skl)),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f72])).
% 0.11/0.40 fof(f75,plain,(
% 0.11/0.40 ~unorthogonal_lines(sK1_skl,sK2_skl)),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f72])).
% 0.11/0.40 fof(f76,plain,(
% 0.11/0.40 ![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))))),
% 0.11/0.40 inference(NNF_transformation,[status(thm)],[f60])).
% 0.11/0.40 fof(f77,plain,(
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(miniscoping,[status(thm)],[f76])).
% 0.11/0.40 fof(f78,plain,(
% 0.11/0.40 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.11/0.40 inference(cnf_transformation,[status(thm)],[f77])).
% 0.11/0.40 fof(f81,plain,(
% 0.11/0.40 convergent_lines(sK1_skl,sK2_skl)),
% 0.11/0.40 inference(resolution,[status(thm)],[f58,f75])).
% 0.11/0.40 fof(f90,plain,(
% 0.11/0.40 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK2_skl,X0))),
% 0.11/0.40 inference(resolution,[status(thm)],[f34,f81])).
% 0.11/0.40 fof(f93,plain,(
% 0.11/0.40 ![X0]: (convergent_lines(sK1_skl,X0)|distinct_lines(sK2_skl,X0))),
% 0.11/0.40 inference(resolution,[status(thm)],[f90,f52])).
% 0.11/0.40 fof(f94,plain,(
% 0.11/0.40 ![X0,X1]: (distinct_lines(sK2_skl,X0)|convergent_lines(sK1_skl,X1)|convergent_lines(X0,X1))),
% 0.11/0.40 inference(resolution,[status(thm)],[f93,f34])).
% 0.11/0.40 fof(f207,definition,(
% 0.11/0.40 sQ11_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.11/0.40 fof(f209,plain,(
% 0.11/0.40 ~convergent_lines(sK0_skl,sK1_skl)|sQ11_spl),
% 0.11/0.40 inference(component_clause,[status(thm)],[f207])).
% 0.11/0.40 fof(f257,definition,(
% 0.11/0.40 sQ15_spl <=> (convergent_lines(sK1_skl,sK1_skl))),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.11/0.40 fof(f258,plain,(
% 0.11/0.40 convergent_lines(sK1_skl,sK1_skl)|~sQ15_spl),
% 0.11/0.40 inference(component_clause,[status(thm)],[f257])).
% 0.11/0.40 fof(f367,plain,(
% 0.11/0.40 ![X0]: (~convergent_lines(sK0_skl,sK1_skl)|sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0))),
% 0.11/0.40 inference(resolution,[status(thm)],[f64,f73])).
% 0.11/0.40 fof(f369,definition,(
% 0.11/0.40 ![X0]: (sQ25_spl <=> (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)))),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.11/0.40 fof(f370,plain,(
% 0.11/0.40 ![X0]: (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)|~sQ25_spl)),
% 0.11/0.40 inference(component_clause,[status(thm)],[f369])).
% 0.11/0.40 fof(f372,plain,(
% 0.11/0.40 ~sQ11_spl|sQ25_spl),
% 0.11/0.40 inference(split_clause,[status(thm)],[f367,f207,f369])).
% 0.11/0.40 fof(f391,plain,(
% 0.11/0.40 distinct_lines(sK2_skl,sK0_skl)|convergent_lines(sK1_skl,sK1_skl)|sQ11_spl),
% 0.11/0.40 inference(resolution,[status(thm)],[f209,f94])).
% 0.11/0.40 fof(f395,definition,(
% 0.11/0.40 sQ28_spl <=> (distinct_lines(sK2_skl,sK0_skl))),
% 0.11/0.40 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.11/0.40 fof(f396,plain,(
% 0.11/0.40 distinct_lines(sK2_skl,sK0_skl)|~sQ28_spl),
% 0.11/0.40 inference(component_clause,[status(thm)],[f395])).
% 0.11/0.40 fof(f398,plain,(
% 0.11/0.40 sQ28_spl|sQ15_spl|sQ11_spl),
% 0.11/0.40 inference(split_clause,[status(thm)],[f391,f395,f257,f207])).
% 0.11/0.40 fof(f400,plain,(
% 0.11/0.40 $false|~sQ15_spl),
% 0.11/0.40 inference(forward_subsumption_resolution,[status(thm)],[f258,f25])).
% 0.11/0.40 fof(f401,plain,(
% 0.11/0.40 ~sQ15_spl),
% 0.11/0.40 inference(contradiction_clause,[status(thm)],[f400])).
% 0.11/0.40 fof(f411,plain,(
% 0.11/0.40 ![X0]: (distinct_lines(sK2_skl,X0)|distinct_lines(sK0_skl,X0)|~sQ28_spl)),
% 0.11/0.40 inference(resolution,[status(thm)],[f396,f31])).
% 0.11/0.40 fof(f436,plain,(
% 0.11/0.40 sP0_prd(sK2_skl,sK0_skl)|~sQ25_spl),
% 0.11/0.40 inference(resolution,[status(thm)],[f370,f75])).
% 0.11/0.40 fof(f456,plain,(
% 0.11/0.40 convergent_lines(sK0_skl,sK2_skl)|~sQ25_spl),
% 0.11/0.40 inference(resolution,[status(thm)],[f436,f78])).
% 0.11/0.40 fof(f476,plain,(
% 0.11/0.40 distinct_lines(sK0_skl,sK2_skl)|~sQ25_spl),
% 0.11/0.40 inference(resolution,[status(thm)],[f456,f52])).
% 0.11/0.40 fof(f477,plain,(
% 0.11/0.40 $false|~sQ25_spl),
% 0.11/0.40 inference(forward_subsumption_resolution,[status(thm)],[f476,f74])).
% 0.11/0.40 fof(f478,plain,(
% 0.11/0.40 ~sQ25_spl),
% 0.11/0.40 inference(contradiction_clause,[status(thm)],[f477])).
% 0.11/0.40 fof(f554,plain,(
% 0.11/0.40 distinct_lines(sK0_skl,sK2_skl)|~sQ28_spl),
% 0.11/0.40 inference(resolution,[status(thm)],[f411,f24])).
% 0.11/0.40 fof(f555,plain,(
% 0.11/0.40 $false|~sQ28_spl),
% 0.11/0.40 inference(forward_subsumption_resolution,[status(thm)],[f554,f74])).
% 0.11/0.40 fof(f556,plain,(
% 0.11/0.40 ~sQ28_spl),
% 0.11/0.40 inference(contradiction_clause,[status(thm)],[f555])).
% 0.11/0.40 fof(f557,plain,(
% 0.11/0.40 $false),
% 0.11/0.40 inference(sat_refutation,[status(thm)],[f372,f398,f401,f478,f556])).
% 0.11/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.42 % Elapsed time: 0.058176 seconds
% 0.11/0.42 % CPU time: 0.205609 seconds
% 0.11/0.42 % Total memory used: 19.156 MB
% 0.11/0.42 % Net memory used: 18.649 MB
%------------------------------------------------------------------------------