%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO212+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 : n008.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 10.60s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO212+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
% 0.11/10.54 % Computer : n008.cluster.edu
% 0.11/10.54 % Model : x86_64 x86_64
% 0.11/10.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.54 % Memory : 8046.5625MB
% 0.11/10.54 % OS : Linux 6.8.0-71-generic
% 0.11/10.55 % CPULimit : 300
% 0.11/10.55 % WCLimit : 300
% 0.11/10.55 % DateTime : Sun Sep 20 13:30:36 UTC 2026
% 0.11/10.55 % CPUTime :
% 0.11/10.56 % Drodi V4.1.1
% 0.11/10.60 % Refutation found
% 0.11/10.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/10.60 % SZS output start CNFRefutation for theBenchmark
% 0.11/10.60 fof(f3,axiom,(
% 0.11/10.60 (! [X] : ~ convergent_lines(X,X) )),
% 0.11/10.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/10.60 fof(f6,axiom,(
% 0.11/10.60 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.11/10.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/10.60 fof(f16,axiom,(
% 0.11/10.60 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 0.11/10.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/10.60 fof(f17,axiom,(
% 0.11/10.60 (! [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) ) ) ) )),
% 0.11/10.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/10.60 fof(f21,conjecture,(
% 0.11/10.60 (! [L,M,N] :( unorthogonal_lines(L,M)=> ( convergent_lines(L,N)| unorthogonal_lines(M,N) ) ) )),
% 0.11/10.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.11/10.60 fof(f22,negated_conjecture,(
% 0.11/10.60 ~((! [L,M,N] :( unorthogonal_lines(L,M)=> ( convergent_lines(L,N)| unorthogonal_lines(M,N) ) ) ))),
% 0.11/10.60 inference(negated_conjecture,[status(cth)],[f21])).
% 0.11/10.60 fof(f25,plain,(
% 0.11/10.60 ![X0]: (~convergent_lines(X0,X0))),
% 0.11/10.60 inference(cnf_transformation,[status(thm)],[f3])).
% 0.11/10.60 fof(f32,plain,(
% 0.11/10.60 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.11/10.60 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.11/10.60 fof(f33,plain,(
% 0.11/10.60 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.11/10.60 inference(miniscoping,[status(thm)],[f32])).
% 0.11/10.60 fof(f34,plain,(
% 0.11/10.60 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.11/10.60 inference(cnf_transformation,[status(thm)],[f33])).
% 0.11/10.60 fof(f58,plain,(
% 0.11/10.60 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.11/10.60 inference(cnf_transformation,[status(thm)],[f16])).
% 0.11/10.60 fof(f59,plain,(
% 0.11/10.60 ![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))))),
% 0.15/10.60 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.15/10.60 fof(f60,definition,(
% 0.15/10.60 ![L,N]: (sP0_prd(N,L)<=>(convergent_lines(L,N)&unorthogonal_lines(L,N)))),
% 0.15/10.60 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.15/10.60 fof(f61,plain,(
% 0.15/10.60 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 0.15/10.60 inference(formula_renaming,[status(thm)],[f59,f60])).
% 0.15/10.60 fof(f62,plain,(
% 0.15/10.60 ![L,M]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(![N]: (sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N)))))),
% 0.15/10.60 inference(miniscoping,[status(thm)],[f61])).
% 0.15/10.60 fof(f64,plain,(
% 0.15/10.60 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~unorthogonal_lines(X0,X1)|sP0_prd(X2,X0)|unorthogonal_lines(X1,X2))),
% 0.15/10.60 inference(cnf_transformation,[status(thm)],[f62])).
% 0.15/10.60 fof(f70,plain,(
% 0.15/10.60 (?[L,M,N]: (unorthogonal_lines(L,M)&(~convergent_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.15/10.60 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 0.15/10.60 fof(f71,plain,(
% 0.15/10.60 ?[L,M]: (unorthogonal_lines(L,M)&(?[N]: (~convergent_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.15/10.60 inference(miniscoping,[status(thm)],[f70])).
% 0.15/10.60 fof(f72,plain,(
% 0.15/10.60 (unorthogonal_lines(sK0_skl,sK1_skl)&(~convergent_lines(sK0_skl,sK2_skl)&~unorthogonal_lines(sK1_skl,sK2_skl)))),
% 0.15/10.60 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])).
% 0.15/10.60 fof(f73,plain,(
% 0.15/10.60 unorthogonal_lines(sK0_skl,sK1_skl)),
% 0.15/10.60 inference(cnf_transformation,[status(thm)],[f72])).
% 0.15/10.60 fof(f74,plain,(
% 0.15/10.60 ~convergent_lines(sK0_skl,sK2_skl)),
% 0.15/10.60 inference(cnf_transformation,[status(thm)],[f72])).
% 0.15/10.60 fof(f75,plain,(
% 0.15/10.60 ~unorthogonal_lines(sK1_skl,sK2_skl)),
% 0.15/10.60 inference(cnf_transformation,[status(thm)],[f72])).
% 0.15/10.60 fof(f76,plain,(
% 0.15/10.60 ![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))))),
% 0.15/10.60 inference(NNF_transformation,[status(thm)],[f60])).
% 0.15/10.60 fof(f77,plain,(
% 0.15/10.60 (![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))))),
% 0.15/10.60 inference(miniscoping,[status(thm)],[f76])).
% 0.15/10.60 fof(f78,plain,(
% 0.15/10.60 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.15/10.60 inference(cnf_transformation,[status(thm)],[f77])).
% 0.15/10.60 fof(f81,plain,(
% 0.15/10.60 convergent_lines(sK1_skl,sK2_skl)),
% 0.15/10.60 inference(resolution,[status(thm)],[f58,f75])).
% 0.15/10.60 fof(f82,plain,(
% 0.15/10.60 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK2_skl,X0))),
% 0.15/10.60 inference(resolution,[status(thm)],[f34,f81])).
% 0.15/10.60 fof(f83,plain,(
% 0.15/10.60 ![X0,X1]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK2_skl,X1)|convergent_lines(X0,X1))),
% 0.15/10.60 inference(resolution,[status(thm)],[f82,f34])).
% 0.15/10.60 fof(f86,plain,(
% 0.15/10.60 ![X0,X1,X2]: (convergent_lines(sK2_skl,X0)|convergent_lines(X1,X0)|convergent_lines(sK1_skl,X2)|convergent_lines(X1,X2))),
% 0.15/10.60 inference(resolution,[status(thm)],[f83,f34])).
% 0.15/10.60 fof(f113,definition,(
% 0.15/10.60 sQ5_spl <=> (convergent_lines(sK2_skl,sK2_skl))),
% 0.15/10.60 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.15/10.60 fof(f114,plain,(
% 0.15/10.60 convergent_lines(sK2_skl,sK2_skl)|~sQ5_spl),
% 0.15/10.60 inference(component_clause,[status(thm)],[f113])).
% 0.15/10.60 fof(f123,plain,(
% 0.15/10.60 ![X0]: (convergent_lines(sK2_skl,sK2_skl)|convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.15/10.60 inference(resolution,[status(thm)],[f86,f74])).
% 0.15/10.60 fof(f136,definition,(
% 0.15/10.60 ![X0]: (sQ6_spl <=> (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0)))),
% 0.15/10.60 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.15/10.60 fof(f137,plain,(
% 0.15/10.60 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0)|~sQ6_spl)),
% 0.15/10.60 inference(component_clause,[status(thm)],[f136])).
% 0.15/10.60 fof(f139,plain,(
% 0.15/10.60 sQ5_spl|sQ6_spl),
% 0.15/10.60 inference(split_clause,[status(thm)],[f123,f113,f136])).
% 0.15/10.60 fof(f151,plain,(
% 0.15/10.60 $false|~sQ5_spl),
% 0.15/10.60 inference(forward_subsumption_resolution,[status(thm)],[f114,f25])).
% 0.15/10.60 fof(f152,plain,(
% 0.15/10.60 ~sQ5_spl),
% 0.15/10.60 inference(contradiction_clause,[status(thm)],[f151])).
% 0.15/10.60 fof(f212,plain,(
% 0.15/10.60 convergent_lines(sK0_skl,sK1_skl)|~sQ6_spl),
% 0.15/10.60 inference(resolution,[status(thm)],[f137,f25])).
% 0.15/10.60 fof(f464,definition,(
% 0.15/10.60 sQ20_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.15/10.60 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.15/10.60 fof(f466,plain,(
% 0.15/10.60 ~convergent_lines(sK0_skl,sK1_skl)|sQ20_spl),
% 0.15/10.60 inference(component_clause,[status(thm)],[f464])).
% 0.15/10.60 fof(f521,plain,(
% 0.15/10.60 $false|~sQ6_spl|sQ20_spl),
% 0.15/10.60 inference(forward_subsumption_resolution,[status(thm)],[f466,f212])).
% 0.15/10.60 fof(f522,plain,(
% 0.15/10.60 ~sQ6_spl|sQ20_spl),
% 0.15/10.60 inference(contradiction_clause,[status(thm)],[f521])).
% 0.15/10.60 fof(f523,plain,(
% 0.15/10.60 ![X0]: (~convergent_lines(sK0_skl,sK1_skl)|sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0))),
% 0.15/10.60 inference(resolution,[status(thm)],[f64,f73])).
% 0.15/10.60 fof(f525,definition,(
% 0.15/10.60 ![X0]: (sQ24_spl <=> (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)))),
% 0.15/10.60 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.15/10.60 fof(f526,plain,(
% 0.15/10.60 ![X0]: (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)|~sQ24_spl)),
% 0.15/10.60 inference(component_clause,[status(thm)],[f525])).
% 0.15/10.60 fof(f528,plain,(
% 0.15/10.60 ~sQ20_spl|sQ24_spl),
% 0.15/10.60 inference(split_clause,[status(thm)],[f523,f464,f525])).
% 0.15/10.60 fof(f538,plain,(
% 0.15/10.60 sP0_prd(sK2_skl,sK0_skl)|~sQ24_spl),
% 0.15/10.60 inference(resolution,[status(thm)],[f526,f75])).
% 0.15/10.60 fof(f546,plain,(
% 0.15/10.60 convergent_lines(sK0_skl,sK2_skl)|~sQ24_spl),
% 0.15/10.60 inference(resolution,[status(thm)],[f538,f78])).
% 0.15/10.60 fof(f547,plain,(
% 0.15/10.60 $false|~sQ24_spl),
% 0.15/10.60 inference(forward_subsumption_resolution,[status(thm)],[f546,f74])).
% 0.15/10.60 fof(f548,plain,(
% 0.15/10.60 ~sQ24_spl),
% 0.15/10.60 inference(contradiction_clause,[status(thm)],[f547])).
% 0.15/10.60 fof(f549,plain,(
% 0.15/10.60 $false),
% 0.15/10.60 inference(sat_refutation,[status(thm)],[f139,f152,f522,f528,f548])).
% 0.15/10.60 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/10.61 % Elapsed time: 0.059144 seconds
% 0.15/10.61 % CPU time: 0.273771 seconds
% 0.15/10.61 % Total memory used: 19.797 MB
% 0.15/10.61 % Net memory used: 19.206 MB
%------------------------------------------------------------------------------