%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO218+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 : n016.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 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO218+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
% 0.08/0.35 % Computer : n016.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 13:47:23 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f6,axiom,(
% 0.13/0.39 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f15,axiom,(
% 0.13/0.39 (! [L,M] :~ ( ~ convergent_lines(L,M)& ~ unorthogonal_lines(L,M) ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f16,axiom,(
% 0.13/0.39 (! [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) ) ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f17,axiom,(
% 0.13/0.39 (! [L,M,N] :( ( ~ unorthogonal_lines(L,M)& ~ unorthogonal_lines(L,N) )=> ~ convergent_lines(M,N) ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f18,conjecture,(
% 0.13/0.39 (! [L,M,N] :( ( ~ convergent_lines(L,M)& ~ unorthogonal_lines(L,N) )=> ~ unorthogonal_lines(M,N) ) )),
% 0.13/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f19,negated_conjecture,(
% 0.13/0.39 ~((! [L,M,N] :( ( ~ convergent_lines(L,M)& ~ unorthogonal_lines(L,N) )=> ~ unorthogonal_lines(M,N) ) ))),
% 0.13/0.39 inference(negated_conjecture,[status(cth)],[f18])).
% 0.13/0.39 fof(f29,plain,(
% 0.13/0.39 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.39 fof(f30,plain,(
% 0.13/0.39 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f29])).
% 0.13/0.39 fof(f31,plain,(
% 0.13/0.39 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f30])).
% 0.13/0.39 fof(f51,plain,(
% 0.13/0.39 ![L,M]: (convergent_lines(L,M)|unorthogonal_lines(L,M))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.13/0.39 fof(f52,plain,(
% 0.13/0.39 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f51])).
% 0.13/0.39 fof(f53,plain,(
% 0.13/0.39 ![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)))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.13/0.39 fof(f54,definition,(
% 0.13/0.39 ![L,M]: (sP0_prd(M,L)<=>(convergent_lines(L,M)&unorthogonal_lines(L,M)))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.13/0.39 fof(f55,plain,(
% 0.13/0.39 ![L,M,N]: ((sP0_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N)))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.13/0.39 inference(formula_renaming,[status(thm)],[f53,f54])).
% 0.13/0.39 fof(f56,plain,(
% 0.13/0.39 ![M,N]: ((![L]: (sP0_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N))))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f55])).
% 0.13/0.39 fof(f58,plain,(
% 0.13/0.39 ![X0,X1,X2]: (sP0_prd(X0,X1)|unorthogonal_lines(X1,X2)|~convergent_lines(X0,X2)|~unorthogonal_lines(X0,X2))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f56])).
% 0.13/0.39 fof(f59,plain,(
% 0.13/0.39 ![L,M,N]: ((unorthogonal_lines(L,M)|unorthogonal_lines(L,N))|~convergent_lines(M,N))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.13/0.39 fof(f60,plain,(
% 0.13/0.39 ![M,N]: ((![L]: (unorthogonal_lines(L,M)|unorthogonal_lines(L,N)))|~convergent_lines(M,N))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f59])).
% 0.13/0.39 fof(f61,plain,(
% 0.13/0.39 ![X0,X1,X2]: (unorthogonal_lines(X0,X1)|unorthogonal_lines(X0,X2)|~convergent_lines(X1,X2))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f60])).
% 0.13/0.39 fof(f62,plain,(
% 0.13/0.39 (?[L,M,N]: ((~convergent_lines(L,M)&~unorthogonal_lines(L,N))&unorthogonal_lines(M,N)))),
% 0.13/0.39 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.13/0.39 fof(f63,plain,(
% 0.13/0.39 ?[M,N]: ((?[L]: (~convergent_lines(L,M)&~unorthogonal_lines(L,N)))&unorthogonal_lines(M,N))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f62])).
% 0.13/0.39 fof(f64,plain,(
% 0.13/0.39 ((~convergent_lines(sK2_skl,sK0_skl)&~unorthogonal_lines(sK2_skl,sK1_skl))&unorthogonal_lines(sK0_skl,sK1_skl))),
% 0.13/0.39 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)],[f63])).
% 0.13/0.40 fof(f65,plain,(
% 0.13/0.40 ~convergent_lines(sK2_skl,sK0_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f64])).
% 0.13/0.40 fof(f66,plain,(
% 0.13/0.40 ~unorthogonal_lines(sK2_skl,sK1_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f64])).
% 0.13/0.40 fof(f67,plain,(
% 0.13/0.40 unorthogonal_lines(sK0_skl,sK1_skl)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f64])).
% 0.13/0.40 fof(f68,plain,(
% 0.13/0.40 ![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))))),
% 0.13/0.40 inference(NNF_transformation,[status(thm)],[f54])).
% 0.13/0.40 fof(f69,plain,(
% 0.13/0.40 (![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))))),
% 0.13/0.40 inference(miniscoping,[status(thm)],[f68])).
% 0.13/0.40 fof(f70,plain,(
% 0.13/0.40 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f69])).
% 0.13/0.40 fof(f73,plain,(
% 0.13/0.40 convergent_lines(sK2_skl,sK1_skl)),
% 0.13/0.40 inference(resolution,[status(thm)],[f52,f66])).
% 0.13/0.40 fof(f74,plain,(
% 0.13/0.40 ![X0]: (convergent_lines(sK2_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.13/0.40 inference(resolution,[status(thm)],[f31,f73])).
% 0.13/0.40 fof(f75,plain,(
% 0.13/0.40 convergent_lines(sK1_skl,sK0_skl)),
% 0.13/0.40 inference(resolution,[status(thm)],[f74,f65])).
% 0.13/0.40 fof(f78,plain,(
% 0.13/0.40 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.13/0.40 inference(resolution,[status(thm)],[f75,f31])).
% 0.13/0.40 fof(f84,plain,(
% 0.13/0.40 ![X0,X1]: (convergent_lines(sK0_skl,X0)|unorthogonal_lines(X1,sK1_skl)|unorthogonal_lines(X1,X0))),
% 0.13/0.40 inference(resolution,[status(thm)],[f78,f61])).
% 0.13/0.40 fof(f130,definition,(
% 0.13/0.40 sQ6_spl <=> (convergent_lines(sK2_skl,sK0_skl))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f131,plain,(
% 0.13/0.40 convergent_lines(sK2_skl,sK0_skl)|~sQ6_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f130])).
% 0.13/0.40 fof(f157,plain,(
% 0.13/0.40 convergent_lines(sK0_skl,sK1_skl)|unorthogonal_lines(sK2_skl,sK1_skl)),
% 0.13/0.40 inference(resolution,[status(thm)],[f84,f66])).
% 0.13/0.40 fof(f158,definition,(
% 0.13/0.40 sQ9_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f161,definition,(
% 0.13/0.40 sQ10_spl <=> (unorthogonal_lines(sK2_skl,sK1_skl))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f162,plain,(
% 0.13/0.40 unorthogonal_lines(sK2_skl,sK1_skl)|~sQ10_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f161])).
% 0.13/0.40 fof(f164,plain,(
% 0.13/0.40 sQ9_spl|sQ10_spl),
% 0.13/0.40 inference(split_clause,[status(thm)],[f157,f158,f161])).
% 0.13/0.40 fof(f236,plain,(
% 0.13/0.40 $false|~sQ10_spl),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f162,f66])).
% 0.13/0.40 fof(f237,plain,(
% 0.13/0.40 ~sQ10_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f236])).
% 0.13/0.40 fof(f388,plain,(
% 0.13/0.40 ![X0]: (sP0_prd(sK0_skl,X0)|unorthogonal_lines(X0,sK1_skl)|~convergent_lines(sK0_skl,sK1_skl))),
% 0.13/0.40 inference(resolution,[status(thm)],[f58,f67])).
% 0.13/0.40 fof(f408,definition,(
% 0.13/0.40 ![X0]: (sQ31_spl <=> (sP0_prd(sK0_skl,X0)|unorthogonal_lines(X0,sK1_skl)))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f409,plain,(
% 0.13/0.40 ![X0]: (sP0_prd(sK0_skl,X0)|unorthogonal_lines(X0,sK1_skl)|~sQ31_spl)),
% 0.13/0.40 inference(component_clause,[status(thm)],[f408])).
% 0.13/0.40 fof(f411,plain,(
% 0.13/0.40 sQ31_spl|~sQ9_spl),
% 0.13/0.40 inference(split_clause,[status(thm)],[f388,f408,f158])).
% 0.13/0.40 fof(f471,plain,(
% 0.13/0.40 sP0_prd(sK0_skl,sK2_skl)|~sQ31_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f409,f66])).
% 0.13/0.40 fof(f490,plain,(
% 0.13/0.40 convergent_lines(sK2_skl,sK0_skl)|~sQ31_spl),
% 0.13/0.40 inference(resolution,[status(thm)],[f471,f70])).
% 0.13/0.40 fof(f491,plain,(
% 0.13/0.40 sQ6_spl|~sQ31_spl),
% 0.13/0.40 inference(split_clause,[status(thm)],[f490,f130,f408])).
% 0.13/0.40 fof(f492,plain,(
% 0.13/0.40 $false|~sQ6_spl),
% 0.13/0.40 inference(forward_subsumption_resolution,[status(thm)],[f131,f65])).
% 0.13/0.40 fof(f493,plain,(
% 0.13/0.40 ~sQ6_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f492])).
% 0.13/0.40 fof(f494,plain,(
% 0.13/0.40 $false),
% 0.13/0.40 inference(sat_refutation,[status(thm)],[f164,f237,f411,f491,f493])).
% 0.13/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.41 % Elapsed time: 0.051311 seconds
% 0.13/0.41 % CPU time: 0.152721 seconds
% 0.13/0.41 % Total memory used: 18.107 MB
% 0.13/0.41 % Net memory used: 17.708 MB
%------------------------------------------------------------------------------