%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO212+1 : 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 : 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 12:26:07 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO212+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 13:28:06 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.40 fof(f3,axiom,(
% 0.13/0.40 (! [X] : ~ convergent_lines(X,X) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f6,axiom,(
% 0.13/0.40 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f18,axiom,(
% 0.13/0.40 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f19,axiom,(
% 0.13/0.40 (! [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) ) ) ) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f23,conjecture,(
% 0.13/0.40 (! [L,M,N] :( unorthogonal_lines(L,M)=> ( convergent_lines(L,N)| unorthogonal_lines(M,N) ) ) )),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f24,negated_conjecture,(
% 0.13/0.40 ~((! [L,M,N] :( unorthogonal_lines(L,M)=> ( convergent_lines(L,N)| unorthogonal_lines(M,N) ) ) ))),
% 0.13/0.40 inference(negated_conjecture,[status(cth)],[f23])).
% 0.13/0.40 fof(f27,plain,(
% 0.13/0.40 ![X0]: (~convergent_lines(X0,X0))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.40 fof(f34,plain,(
% 0.13/0.40 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.13/0.40 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.40 fof(f35,plain,(
% 0.13/0.40 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.13/0.40 inference(miniscoping,[status(thm)],[f34])).
% 0.13/0.40 fof(f36,plain,(
% 0.13/0.40 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f35])).
% 0.13/0.40 fof(f61,plain,(
% 0.13/0.40 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f18])).
% 0.13/0.40 fof(f62,plain,(
% 0.13/0.40 ![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))))),
% 0.13/0.40 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.13/0.40 fof(f63,definition,(
% 0.13/0.40 ![L,N]: (sP0_prd(N,L)<=>(convergent_lines(L,N)&unorthogonal_lines(L,N)))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.13/0.40 fof(f64,plain,(
% 0.13/0.40 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 0.13/0.40 inference(formula_renaming,[status(thm)],[f62,f63])).
% 0.13/0.40 fof(f65,plain,(
% 0.13/0.40 ![L,M]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(![N]: (sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N)))))),
% 0.13/0.40 inference(miniscoping,[status(thm)],[f64])).
% 0.13/0.40 fof(f67,plain,(
% 0.13/0.40 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~unorthogonal_lines(X0,X1)|sP0_prd(X2,X0)|unorthogonal_lines(X1,X2))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f65])).
% 0.13/0.40 fof(f73,plain,(
% 0.13/0.40 (?[L,M,N]: (unorthogonal_lines(L,M)&(~convergent_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.13/0.40 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.13/0.40 fof(f74,plain,(
% 0.13/0.40 ?[L,M]: (unorthogonal_lines(L,M)&(?[N]: (~convergent_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.13/0.40 inference(miniscoping,[status(thm)],[f73])).
% 0.13/0.40 fof(f75,plain,(
% 0.13/0.40 (unorthogonal_lines(sK0_skl,sK1_skl)&(~convergent_lines(sK0_skl,sK2_skl)&~unorthogonal_lines(sK1_skl,sK2_skl)))),
% 0.13/0.40 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)],[f74])).
% 0.13/0.40 fof(f76,plain,(
% 0.13/0.40 unorthogonal_lines(sK0_skl,sK1_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f75])).
% 0.13/0.40 fof(f77,plain,(
% 0.13/0.40 ~convergent_lines(sK0_skl,sK2_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f75])).
% 0.13/0.40 fof(f78,plain,(
% 0.13/0.40 ~unorthogonal_lines(sK1_skl,sK2_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f75])).
% 0.13/0.40 fof(f79,plain,(
% 0.13/0.40 ![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))))),
% 0.13/0.40 inference(NNF_transformation,[status(thm)],[f63])).
% 0.13/0.40 fof(f80,plain,(
% 0.13/0.40 (![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))))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f79])).
% 0.13/0.41 fof(f81,plain,(
% 0.13/0.41 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f80])).
% 0.13/0.41 fof(f84,plain,(
% 0.13/0.41 convergent_lines(sK1_skl,sK2_skl)),
% 0.13/0.41 inference(resolution,[status(thm)],[f61,f78])).
% 0.13/0.41 fof(f85,plain,(
% 0.13/0.41 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK2_skl,X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f36,f84])).
% 0.13/0.41 fof(f86,plain,(
% 0.13/0.41 ![X0,X1]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK2_skl,X1)|convergent_lines(X0,X1))),
% 0.13/0.41 inference(resolution,[status(thm)],[f85,f36])).
% 0.13/0.41 fof(f89,plain,(
% 0.13/0.41 ![X0,X1,X2]: (convergent_lines(sK2_skl,X0)|convergent_lines(X1,X0)|convergent_lines(sK1_skl,X2)|convergent_lines(X1,X2))),
% 0.13/0.41 inference(resolution,[status(thm)],[f86,f36])).
% 0.13/0.41 fof(f116,definition,(
% 0.13/0.41 sQ5_spl <=> (convergent_lines(sK2_skl,sK2_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f117,plain,(
% 0.13/0.41 convergent_lines(sK2_skl,sK2_skl)|~sQ5_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f116])).
% 0.13/0.41 fof(f126,plain,(
% 0.13/0.41 ![X0]: (convergent_lines(sK2_skl,sK2_skl)|convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f89,f77])).
% 0.13/0.41 fof(f139,definition,(
% 0.13/0.41 ![X0]: (sQ6_spl <=> (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0)))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f140,plain,(
% 0.13/0.41 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0)|~sQ6_spl)),
% 0.13/0.41 inference(component_clause,[status(thm)],[f139])).
% 0.13/0.41 fof(f142,plain,(
% 0.13/0.41 sQ5_spl|sQ6_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f126,f116,f139])).
% 0.13/0.41 fof(f154,plain,(
% 0.13/0.41 $false|~sQ5_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f117,f27])).
% 0.13/0.41 fof(f155,plain,(
% 0.13/0.41 ~sQ5_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f154])).
% 0.13/0.41 fof(f215,plain,(
% 0.13/0.41 convergent_lines(sK0_skl,sK1_skl)|~sQ6_spl),
% 0.13/0.41 inference(resolution,[status(thm)],[f140,f27])).
% 0.13/0.41 fof(f305,definition,(
% 0.13/0.41 sQ17_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f307,plain,(
% 0.13/0.41 ~convergent_lines(sK0_skl,sK1_skl)|sQ17_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f305])).
% 0.13/0.41 fof(f351,plain,(
% 0.13/0.41 $false|~sQ6_spl|sQ17_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f307,f215])).
% 0.13/0.41 fof(f352,plain,(
% 0.13/0.41 ~sQ6_spl|sQ17_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f351])).
% 0.13/0.41 fof(f353,plain,(
% 0.13/0.41 ![X0]: (~convergent_lines(sK0_skl,sK1_skl)|sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f67,f76])).
% 0.13/0.41 fof(f355,definition,(
% 0.13/0.41 ![X0]: (sQ20_spl <=> (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f356,plain,(
% 0.13/0.41 ![X0]: (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)|~sQ20_spl)),
% 0.13/0.41 inference(component_clause,[status(thm)],[f355])).
% 0.13/0.41 fof(f358,plain,(
% 0.13/0.41 ~sQ17_spl|sQ20_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f353,f305,f355])).
% 0.13/0.41 fof(f383,plain,(
% 0.13/0.41 sP0_prd(sK2_skl,sK0_skl)|~sQ20_spl),
% 0.13/0.41 inference(resolution,[status(thm)],[f356,f78])).
% 0.13/0.41 fof(f399,plain,(
% 0.13/0.41 convergent_lines(sK0_skl,sK2_skl)|~sQ20_spl),
% 0.13/0.41 inference(resolution,[status(thm)],[f383,f81])).
% 0.13/0.41 fof(f400,plain,(
% 0.13/0.41 $false|~sQ20_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f399,f77])).
% 0.13/0.41 fof(f401,plain,(
% 0.13/0.41 ~sQ20_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f400])).
% 0.13/0.41 fof(f402,plain,(
% 0.13/0.41 $false),
% 0.13/0.41 inference(sat_refutation,[status(thm)],[f142,f155,f352,f358,f401])).
% 0.13/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.43 % Elapsed time: 0.060785 seconds
% 0.13/0.43 % CPU time: 0.254611 seconds
% 0.13/0.43 % Total memory used: 19.591 MB
% 0.13/0.43 % Net memory used: 18.978 MB
%------------------------------------------------------------------------------