%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO218+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 : n012.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 12:26:09 PM UTC 2026
% Result : Theorem 0.07s 0.35s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO218+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 20 13:37:22 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.07/0.35 % Refutation found
% 0.07/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.35 % SZS output start CNFRefutation for theBenchmark
% 0.07/0.35 fof(f3,axiom,(
% 0.07/0.35 (! [X] : ~ convergent_lines(X,X) )),
% 0.07/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.35 fof(f6,axiom,(
% 0.07/0.35 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.07/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.35 fof(f19,axiom,(
% 0.07/0.35 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 0.07/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.35 fof(f25,axiom,(
% 0.07/0.35 (! [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) ) ) )),
% 0.07/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.35 fof(f33,axiom,(
% 0.07/0.35 (! [X,Y] :( parallel_lines(X,Y)<=> ~ convergent_lines(X,Y) ) )),
% 0.07/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.35 fof(f35,axiom,(
% 0.07/0.35 (! [X,Y] :( orthogonal_lines(X,Y)<=> ~ unorthogonal_lines(X,Y) ) )),
% 0.07/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.35 fof(f36,conjecture,(
% 0.07/0.35 (! [L,M,N] :( ( parallel_lines(L,M)& orthogonal_lines(L,N) )=> orthogonal_lines(M,N) ) )),
% 0.07/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.07/0.35 fof(f37,negated_conjecture,(
% 0.07/0.35 ~((! [L,M,N] :( ( parallel_lines(L,M)& orthogonal_lines(L,N) )=> orthogonal_lines(M,N) ) ))),
% 0.07/0.35 inference(negated_conjecture,[status(cth)],[f36])).
% 0.07/0.35 fof(f40,plain,(
% 0.07/0.35 ![X0]: (~convergent_lines(X0,X0))),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f3])).
% 0.07/0.35 fof(f47,plain,(
% 0.07/0.35 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.07/0.35 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.07/0.35 fof(f48,plain,(
% 0.07/0.35 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.07/0.35 inference(miniscoping,[status(thm)],[f47])).
% 0.07/0.35 fof(f49,plain,(
% 0.07/0.35 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f48])).
% 0.07/0.35 fof(f76,plain,(
% 0.07/0.35 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f19])).
% 0.07/0.35 fof(f90,plain,(
% 0.07/0.35 ![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)))),
% 0.07/0.35 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.07/0.35 fof(f91,definition,(
% 0.07/0.35 ![L,M]: (sP1_prd(M,L)<=>(convergent_lines(L,M)&unorthogonal_lines(L,M)))),
% 0.07/0.35 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.07/0.35 fof(f92,plain,(
% 0.07/0.35 ![L,M,N]: ((sP1_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N)))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.07/0.35 inference(formula_renaming,[status(thm)],[f90,f91])).
% 0.07/0.35 fof(f93,plain,(
% 0.07/0.35 ![M,N]: ((![L]: (sP1_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N))))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.07/0.35 inference(miniscoping,[status(thm)],[f92])).
% 0.07/0.35 fof(f95,plain,(
% 0.07/0.35 ![X0,X1,X2]: (sP1_prd(X0,X1)|unorthogonal_lines(X1,X2)|~convergent_lines(X0,X2)|~unorthogonal_lines(X0,X2))),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f93])).
% 0.07/0.35 fof(f115,plain,(
% 0.07/0.35 ![X,Y]: ((~parallel_lines(X,Y)|~convergent_lines(X,Y))&(parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 0.07/0.35 inference(NNF_transformation,[status(thm)],[f33])).
% 0.07/0.35 fof(f116,plain,(
% 0.07/0.35 (![X,Y]: (~parallel_lines(X,Y)|~convergent_lines(X,Y)))&(![X,Y]: (parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 0.07/0.35 inference(miniscoping,[status(thm)],[f115])).
% 0.07/0.35 fof(f117,plain,(
% 0.07/0.35 ![X0,X1]: (~parallel_lines(X0,X1)|~convergent_lines(X0,X1))),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f116])).
% 0.07/0.35 fof(f123,plain,(
% 0.07/0.35 ![X,Y]: ((~orthogonal_lines(X,Y)|~unorthogonal_lines(X,Y))&(orthogonal_lines(X,Y)|unorthogonal_lines(X,Y)))),
% 0.07/0.35 inference(NNF_transformation,[status(thm)],[f35])).
% 0.07/0.35 fof(f124,plain,(
% 0.07/0.35 (![X,Y]: (~orthogonal_lines(X,Y)|~unorthogonal_lines(X,Y)))&(![X,Y]: (orthogonal_lines(X,Y)|unorthogonal_lines(X,Y)))),
% 0.07/0.35 inference(miniscoping,[status(thm)],[f123])).
% 0.07/0.35 fof(f125,plain,(
% 0.07/0.35 ![X0,X1]: (~orthogonal_lines(X0,X1)|~unorthogonal_lines(X0,X1))),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f124])).
% 0.07/0.35 fof(f126,plain,(
% 0.07/0.35 ![X0,X1]: (orthogonal_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f124])).
% 0.07/0.35 fof(f127,plain,(
% 0.07/0.35 (?[L,M,N]: ((parallel_lines(L,M)&orthogonal_lines(L,N))&~orthogonal_lines(M,N)))),
% 0.07/0.35 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.07/0.35 fof(f128,plain,(
% 0.07/0.35 ?[M,N]: ((?[L]: (parallel_lines(L,M)&orthogonal_lines(L,N)))&~orthogonal_lines(M,N))),
% 0.07/0.35 inference(miniscoping,[status(thm)],[f127])).
% 0.07/0.35 fof(f129,plain,(
% 0.07/0.35 ((parallel_lines(sK2_skl,sK0_skl)&orthogonal_lines(sK2_skl,sK1_skl))&~orthogonal_lines(sK0_skl,sK1_skl))),
% 0.07/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(M,sK0_skl),skolemize(N,sK1_skl),skolemize(L,sK2_skl)],[f128])).
% 0.07/0.35 fof(f130,plain,(
% 0.07/0.35 parallel_lines(sK2_skl,sK0_skl)),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f129])).
% 0.07/0.35 fof(f131,plain,(
% 0.07/0.35 orthogonal_lines(sK2_skl,sK1_skl)),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f129])).
% 0.07/0.35 fof(f132,plain,(
% 0.07/0.35 ~orthogonal_lines(sK0_skl,sK1_skl)),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f129])).
% 0.07/0.35 fof(f138,plain,(
% 0.07/0.35 ![L,M]: ((~sP1_prd(M,L)|(convergent_lines(L,M)&unorthogonal_lines(L,M)))&(sP1_prd(M,L)|(~convergent_lines(L,M)|~unorthogonal_lines(L,M))))),
% 0.07/0.35 inference(NNF_transformation,[status(thm)],[f91])).
% 0.07/0.35 fof(f139,plain,(
% 0.07/0.35 (![L,M]: (~sP1_prd(M,L)|(convergent_lines(L,M)&unorthogonal_lines(L,M))))&(![L,M]: (sP1_prd(M,L)|(~convergent_lines(L,M)|~unorthogonal_lines(L,M))))),
% 0.07/0.35 inference(miniscoping,[status(thm)],[f138])).
% 0.07/0.35 fof(f140,plain,(
% 0.07/0.35 ![X0,X1]: (~sP1_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.07/0.35 inference(cnf_transformation,[status(thm)],[f139])).
% 0.07/0.35 fof(f143,plain,(
% 0.07/0.35 unorthogonal_lines(sK0_skl,sK1_skl)),
% 0.07/0.35 inference(resolution,[status(thm)],[f126,f132])).
% 0.07/0.35 fof(f146,plain,(
% 0.07/0.35 ![X0,X1]: (convergent_lines(X0,X1)|~orthogonal_lines(X0,X1))),
% 0.07/0.35 inference(resolution,[status(thm)],[f76,f125])).
% 0.07/0.35 fof(f150,plain,(
% 0.07/0.35 convergent_lines(sK2_skl,sK1_skl)),
% 0.07/0.35 inference(resolution,[status(thm)],[f146,f131])).
% 0.07/0.35 fof(f152,plain,(
% 0.07/0.35 ![X0]: (convergent_lines(sK2_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.07/0.35 inference(resolution,[status(thm)],[f150,f49])).
% 0.07/0.35 fof(f157,plain,(
% 0.07/0.35 ![X0]: (convergent_lines(sK1_skl,X0)|~parallel_lines(sK2_skl,X0))),
% 0.07/0.35 inference(resolution,[status(thm)],[f152,f117])).
% 0.07/0.35 fof(f161,plain,(
% 0.07/0.35 convergent_lines(sK1_skl,sK0_skl)),
% 0.07/0.35 inference(resolution,[status(thm)],[f157,f130])).
% 0.07/0.35 fof(f163,plain,(
% 0.07/0.35 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.07/0.35 inference(resolution,[status(thm)],[f161,f49])).
% 0.07/0.35 fof(f167,plain,(
% 0.07/0.35 convergent_lines(sK0_skl,sK1_skl)),
% 0.07/0.35 inference(resolution,[status(thm)],[f163,f40])).
% 0.07/0.35 fof(f388,definition,(
% 0.07/0.35 sQ15_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.07/0.35 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.07/0.35 fof(f390,plain,(
% 0.07/0.35 ~convergent_lines(sK0_skl,sK1_skl)|sQ15_spl),
% 0.07/0.35 inference(component_clause,[status(thm)],[f388])).
% 0.07/0.35 fof(f597,plain,(
% 0.07/0.35 $false|sQ15_spl),
% 0.07/0.35 inference(forward_subsumption_resolution,[status(thm)],[f390,f167])).
% 0.07/0.35 fof(f598,plain,(
% 0.07/0.35 sQ15_spl),
% 0.07/0.35 inference(contradiction_clause,[status(thm)],[f597])).
% 0.07/0.35 fof(f698,plain,(
% 0.07/0.35 ![X0]: (sP1_prd(sK0_skl,X0)|unorthogonal_lines(X0,sK1_skl)|~convergent_lines(sK0_skl,sK1_skl))),
% 0.07/0.35 inference(resolution,[status(thm)],[f95,f143])).
% 0.07/0.35 fof(f701,definition,(
% 0.07/0.35 ![X0]: (sQ36_spl <=> (sP1_prd(sK0_skl,X0)|unorthogonal_lines(X0,sK1_skl)))),
% 0.07/0.35 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.07/0.35 fof(f702,plain,(
% 0.07/0.35 ![X0]: (sP1_prd(sK0_skl,X0)|unorthogonal_lines(X0,sK1_skl)|~sQ36_spl)),
% 0.07/0.35 inference(component_clause,[status(thm)],[f701])).
% 0.07/0.35 fof(f704,plain,(
% 0.07/0.35 sQ36_spl|~sQ15_spl),
% 0.07/0.35 inference(split_clause,[status(thm)],[f698,f701,f388])).
% 0.07/0.35 fof(f763,plain,(
% 0.07/0.35 ![X0]: (sP1_prd(sK0_skl,X0)|~orthogonal_lines(X0,sK1_skl)|~sQ36_spl)),
% 0.07/0.35 inference(resolution,[status(thm)],[f702,f125])).
% 0.07/0.35 fof(f1027,plain,(
% 0.07/0.35 sP1_prd(sK0_skl,sK2_skl)|~sQ36_spl),
% 0.07/0.35 inference(resolution,[status(thm)],[f763,f131])).
% 0.07/0.35 fof(f1030,plain,(
% 0.07/0.35 convergent_lines(sK2_skl,sK0_skl)|~sQ36_spl),
% 0.07/0.35 inference(resolution,[status(thm)],[f1027,f140])).
% 0.07/0.35 fof(f1088,plain,(
% 0.07/0.35 ~parallel_lines(sK2_skl,sK0_skl)|~sQ36_spl),
% 0.07/0.35 inference(resolution,[status(thm)],[f1030,f117])).
% 0.07/0.35 fof(f1089,plain,(
% 0.07/0.35 $false|~sQ36_spl),
% 0.07/0.35 inference(forward_subsumption_resolution,[status(thm)],[f1088,f130])).
% 0.07/0.35 fof(f1090,plain,(
% 0.07/0.35 ~sQ36_spl),
% 0.07/0.35 inference(contradiction_clause,[status(thm)],[f1089])).
% 0.07/0.35 fof(f1091,plain,(
% 0.07/0.35 $false),
% 0.07/0.35 inference(sat_refutation,[status(thm)],[f598,f704,f1090])).
% 0.07/0.35 % SZS output end CNFRefutation for theBenchmark.p
% 0.07/0.36 % Elapsed time: 0.055168 seconds
% 0.07/0.36 % CPU time: 0.206868 seconds
% 0.07/0.36 % Total memory used: 21.617 MB
% 0.07/0.36 % Net memory used: 20.963 MB
%------------------------------------------------------------------------------