%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO218+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 : n001.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 12:26:08 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO218+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
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 13:49:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.41 fof(f6,axiom,(
% 0.09/0.41 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f13,axiom,(
% 0.09/0.41 (! [L,M] :~ ( ~ convergent_lines(L,M)& ~ unorthogonal_lines(L,M) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f14,axiom,(
% 0.09/0.41 (! [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) ) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f15,axiom,(
% 0.09/0.41 (! [L,M,N] :( ( ~ unorthogonal_lines(L,M)& ~ unorthogonal_lines(L,N) )=> ~ convergent_lines(M,N) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f16,conjecture,(
% 0.09/0.41 (! [L,M,N] :( ( ~ convergent_lines(L,M)& ~ unorthogonal_lines(L,N) )=> ~ unorthogonal_lines(M,N) ) )),
% 0.09/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f17,negated_conjecture,(
% 0.09/0.41 ~((! [L,M,N] :( ( ~ convergent_lines(L,M)& ~ unorthogonal_lines(L,N) )=> ~ unorthogonal_lines(M,N) ) ))),
% 0.09/0.41 inference(negated_conjecture,[status(cth)],[f16])).
% 0.09/0.41 fof(f27,plain,(
% 0.09/0.41 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.09/0.41 fof(f28,plain,(
% 0.09/0.41 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f27])).
% 0.09/0.41 fof(f29,plain,(
% 0.09/0.41 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f28])).
% 0.09/0.41 fof(f48,plain,(
% 0.09/0.41 ![L,M]: (convergent_lines(L,M)|unorthogonal_lines(L,M))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.09/0.41 fof(f49,plain,(
% 0.09/0.41 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f48])).
% 0.09/0.41 fof(f50,plain,(
% 0.09/0.41 ![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)))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.09/0.41 fof(f51,definition,(
% 0.09/0.41 ![L,M]: (sP0_prd(M,L)<=>(convergent_lines(L,M)&unorthogonal_lines(L,M)))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/0.41 fof(f52,plain,(
% 0.09/0.41 ![L,M,N]: ((sP0_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N)))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.09/0.41 inference(formula_renaming,[status(thm)],[f50,f51])).
% 0.09/0.41 fof(f53,plain,(
% 0.09/0.41 ![M,N]: ((![L]: (sP0_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N))))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f52])).
% 0.09/0.41 fof(f55,plain,(
% 0.09/0.41 ![X0,X1,X2]: (sP0_prd(X0,X1)|unorthogonal_lines(X1,X2)|~convergent_lines(X0,X2)|~unorthogonal_lines(X0,X2))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f53])).
% 0.09/0.41 fof(f56,plain,(
% 0.09/0.41 ![L,M,N]: ((unorthogonal_lines(L,M)|unorthogonal_lines(L,N))|~convergent_lines(M,N))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.09/0.41 fof(f57,plain,(
% 0.09/0.41 ![M,N]: ((![L]: (unorthogonal_lines(L,M)|unorthogonal_lines(L,N)))|~convergent_lines(M,N))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f56])).
% 0.09/0.41 fof(f58,plain,(
% 0.09/0.41 ![X0,X1,X2]: (unorthogonal_lines(X0,X1)|unorthogonal_lines(X0,X2)|~convergent_lines(X1,X2))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f57])).
% 0.09/0.41 fof(f59,plain,(
% 0.09/0.41 (?[L,M,N]: ((~convergent_lines(L,M)&~unorthogonal_lines(L,N))&unorthogonal_lines(M,N)))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.09/0.41 fof(f60,plain,(
% 0.09/0.41 ?[M,N]: ((?[L]: (~convergent_lines(L,M)&~unorthogonal_lines(L,N)))&unorthogonal_lines(M,N))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f59])).
% 0.09/0.41 fof(f61,plain,(
% 0.09/0.41 ((~convergent_lines(sK2_skl,sK0_skl)&~unorthogonal_lines(sK2_skl,sK1_skl))&unorthogonal_lines(sK0_skl,sK1_skl))),
% 0.09/0.41 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)],[f60])).
% 0.09/0.41 fof(f62,plain,(
% 0.09/0.41 ~convergent_lines(sK2_skl,sK0_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f61])).
% 0.09/0.41 fof(f63,plain,(
% 0.09/0.41 ~unorthogonal_lines(sK2_skl,sK1_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f61])).
% 0.09/0.41 fof(f64,plain,(
% 0.09/0.41 unorthogonal_lines(sK0_skl,sK1_skl)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f61])).
% 0.09/0.41 fof(f65,plain,(
% 0.09/0.41 ![L,M]: ((~sP0_prd(M,L)|(convergent_lines(L,M)&unorthogonal_lines(L,M)))&(sP0_prd(M,L)|(~convergent_lines(L,M)|~unorthogonal_lines(L,M))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f51])).
% 0.09/0.41 fof(f66,plain,(
% 0.09/0.41 (![L,M]: (~sP0_prd(M,L)|(convergent_lines(L,M)&unorthogonal_lines(L,M))))&(![L,M]: (sP0_prd(M,L)|(~convergent_lines(L,M)|~unorthogonal_lines(L,M))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f65])).
% 0.09/0.41 fof(f67,plain,(
% 0.09/0.41 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f66])).
% 0.09/0.41 fof(f70,plain,(
% 0.09/0.41 convergent_lines(sK2_skl,sK1_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f49,f63])).
% 0.09/0.41 fof(f71,plain,(
% 0.09/0.41 ![X0]: (convergent_lines(sK2_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.09/0.41 inference(resolution,[status(thm)],[f29,f70])).
% 0.09/0.41 fof(f72,plain,(
% 0.09/0.41 convergent_lines(sK1_skl,sK0_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f71,f62])).
% 0.09/0.41 fof(f75,plain,(
% 0.09/0.41 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.09/0.41 inference(resolution,[status(thm)],[f72,f29])).
% 0.09/0.41 fof(f86,plain,(
% 0.09/0.41 ![X0,X1]: (convergent_lines(sK0_skl,X0)|unorthogonal_lines(X1,sK1_skl)|unorthogonal_lines(X1,X0))),
% 0.09/0.41 inference(resolution,[status(thm)],[f75,f58])).
% 0.09/0.41 fof(f149,definition,(
% 0.09/0.41 sQ8_spl <=> (convergent_lines(sK2_skl,sK0_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f150,plain,(
% 0.09/0.41 convergent_lines(sK2_skl,sK0_skl)|~sQ8_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f149])).
% 0.09/0.41 fof(f255,definition,(
% 0.09/0.41 sQ14_spl <=> (unorthogonal_lines(sK2_skl,sK1_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f256,plain,(
% 0.09/0.41 unorthogonal_lines(sK2_skl,sK1_skl)|~sQ14_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f255])).
% 0.09/0.41 fof(f352,plain,(
% 0.09/0.41 $false|~sQ8_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f150,f62])).
% 0.09/0.41 fof(f353,plain,(
% 0.09/0.41 ~sQ8_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f352])).
% 0.09/0.41 fof(f382,definition,(
% 0.09/0.41 sQ26_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f414,plain,(
% 0.09/0.41 convergent_lines(sK0_skl,sK1_skl)|unorthogonal_lines(sK2_skl,sK1_skl)),
% 0.09/0.41 inference(resolution,[status(thm)],[f86,f63])).
% 0.09/0.41 fof(f417,plain,(
% 0.09/0.41 sQ26_spl|sQ14_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f414,f382,f255])).
% 0.09/0.41 fof(f418,plain,(
% 0.09/0.41 $false|~sQ14_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f256,f63])).
% 0.09/0.41 fof(f419,plain,(
% 0.09/0.41 ~sQ14_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f418])).
% 0.09/0.41 fof(f464,plain,(
% 0.09/0.41 ![X0]: (sP0_prd(sK0_skl,X0)|unorthogonal_lines(X0,sK1_skl)|~convergent_lines(sK0_skl,sK1_skl))),
% 0.09/0.41 inference(resolution,[status(thm)],[f55,f64])).
% 0.09/0.41 fof(f488,definition,(
% 0.09/0.41 ![X0]: (sQ36_spl <=> (sP0_prd(sK0_skl,X0)|unorthogonal_lines(X0,sK1_skl)))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f489,plain,(
% 0.09/0.41 ![X0]: (sP0_prd(sK0_skl,X0)|unorthogonal_lines(X0,sK1_skl)|~sQ36_spl)),
% 0.09/0.41 inference(component_clause,[status(thm)],[f488])).
% 0.09/0.41 fof(f491,plain,(
% 0.09/0.41 sQ36_spl|~sQ26_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f464,f488,f382])).
% 0.09/0.41 fof(f514,plain,(
% 0.09/0.41 sP0_prd(sK0_skl,sK2_skl)|~sQ36_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f489,f63])).
% 0.09/0.41 fof(f537,plain,(
% 0.09/0.41 convergent_lines(sK2_skl,sK0_skl)|~sQ36_spl),
% 0.09/0.41 inference(resolution,[status(thm)],[f514,f67])).
% 0.09/0.41 fof(f538,plain,(
% 0.09/0.41 sQ8_spl|~sQ36_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f537,f149,f488])).
% 0.09/0.41 fof(f539,plain,(
% 0.09/0.41 $false),
% 0.09/0.41 inference(sat_refutation,[status(thm)],[f353,f417,f419,f491,f538])).
% 0.09/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.44 % Elapsed time: 0.048700 seconds
% 0.09/0.44 % CPU time: 0.190162 seconds
% 0.09/0.44 % Total memory used: 18.885 MB
% 0.09/0.44 % Net memory used: 18.348 MB
%------------------------------------------------------------------------------