%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO213+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 : 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 12:26:07 PM UTC 2026
% Result : Theorem 0.16s 10.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO213+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
% 0.11/10.39 % Computer : n001.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Sun Sep 20 13:40:39 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.16/10.40 % Drodi V4.1.1
% 0.16/10.43 % Refutation found
% 0.16/10.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/10.43 % SZS output start CNFRefutation for theBenchmark
% 0.16/10.43 fof(f2,axiom,(
% 0.16/10.43 (! [X] : ~ distinct_lines(X,X) )),
% 0.16/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/10.43 fof(f3,axiom,(
% 0.16/10.43 (! [X] : ~ convergent_lines(X,X) )),
% 0.16/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/10.43 fof(f5,axiom,(
% 0.16/10.43 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 0.16/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/10.43 fof(f6,axiom,(
% 0.16/10.43 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.16/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/10.43 fof(f14,axiom,(
% 0.16/10.43 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.16/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/10.43 fof(f18,axiom,(
% 0.16/10.43 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 0.16/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/10.43 fof(f19,axiom,(
% 0.16/10.43 (! [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) ) ) ) )),
% 0.16/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/10.43 fof(f23,conjecture,(
% 0.16/10.43 (! [L,M,N] :( unorthogonal_lines(L,M)=> ( distinct_lines(L,N)| unorthogonal_lines(M,N) ) ) )),
% 0.16/10.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/10.43 fof(f24,negated_conjecture,(
% 0.16/10.43 ~((! [L,M,N] :( unorthogonal_lines(L,M)=> ( distinct_lines(L,N)| unorthogonal_lines(M,N) ) ) ))),
% 0.16/10.43 inference(negated_conjecture,[status(cth)],[f23])).
% 0.16/10.43 fof(f26,plain,(
% 0.16/10.43 ![X0]: (~distinct_lines(X0,X0))),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f2])).
% 0.16/10.43 fof(f27,plain,(
% 0.16/10.43 ![X0]: (~convergent_lines(X0,X0))),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f3])).
% 0.16/10.43 fof(f31,plain,(
% 0.16/10.43 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 0.16/10.43 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.16/10.43 fof(f32,plain,(
% 0.16/10.43 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 0.16/10.43 inference(miniscoping,[status(thm)],[f31])).
% 0.16/10.43 fof(f33,plain,(
% 0.16/10.43 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f32])).
% 0.16/10.43 fof(f34,plain,(
% 0.16/10.43 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.16/10.43 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.16/10.43 fof(f35,plain,(
% 0.16/10.43 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.16/10.43 inference(miniscoping,[status(thm)],[f34])).
% 0.16/10.43 fof(f36,plain,(
% 0.16/10.43 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f35])).
% 0.16/10.43 fof(f53,plain,(
% 0.16/10.43 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.16/10.43 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.16/10.43 fof(f54,plain,(
% 0.16/10.43 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.16/10.43 inference(miniscoping,[status(thm)],[f53])).
% 0.16/10.43 fof(f55,plain,(
% 0.16/10.43 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f54])).
% 0.16/10.43 fof(f61,plain,(
% 0.16/10.43 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f18])).
% 0.16/10.43 fof(f62,plain,(
% 0.16/10.43 ![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))))),
% 0.16/10.43 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.16/10.43 fof(f63,definition,(
% 0.16/10.43 ![L,N]: (sP0_prd(N,L)<=>(convergent_lines(L,N)&unorthogonal_lines(L,N)))),
% 0.16/10.43 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.16/10.43 fof(f64,plain,(
% 0.16/10.43 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 0.16/10.43 inference(formula_renaming,[status(thm)],[f62,f63])).
% 0.16/10.43 fof(f65,plain,(
% 0.16/10.43 ![L,M]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(![N]: (sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N)))))),
% 0.16/10.43 inference(miniscoping,[status(thm)],[f64])).
% 0.16/10.43 fof(f67,plain,(
% 0.16/10.43 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~unorthogonal_lines(X0,X1)|sP0_prd(X2,X0)|unorthogonal_lines(X1,X2))),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f65])).
% 0.16/10.43 fof(f73,plain,(
% 0.16/10.43 (?[L,M,N]: (unorthogonal_lines(L,M)&(~distinct_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.16/10.43 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.16/10.43 fof(f74,plain,(
% 0.16/10.43 ?[L,M]: (unorthogonal_lines(L,M)&(?[N]: (~distinct_lines(L,N)&~unorthogonal_lines(M,N))))),
% 0.16/10.43 inference(miniscoping,[status(thm)],[f73])).
% 0.16/10.43 fof(f75,plain,(
% 0.16/10.43 (unorthogonal_lines(sK0_skl,sK1_skl)&(~distinct_lines(sK0_skl,sK2_skl)&~unorthogonal_lines(sK1_skl,sK2_skl)))),
% 0.16/10.43 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])).
% 0.16/10.43 fof(f76,plain,(
% 0.16/10.43 unorthogonal_lines(sK0_skl,sK1_skl)),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f75])).
% 0.16/10.43 fof(f77,plain,(
% 0.16/10.43 ~distinct_lines(sK0_skl,sK2_skl)),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f75])).
% 0.16/10.43 fof(f78,plain,(
% 0.16/10.43 ~unorthogonal_lines(sK1_skl,sK2_skl)),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f75])).
% 0.16/10.43 fof(f79,plain,(
% 0.16/10.43 ![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))))),
% 0.16/10.43 inference(NNF_transformation,[status(thm)],[f63])).
% 0.16/10.43 fof(f80,plain,(
% 0.16/10.43 (![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))))),
% 0.16/10.43 inference(miniscoping,[status(thm)],[f79])).
% 0.16/10.43 fof(f81,plain,(
% 0.16/10.43 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.16/10.43 inference(cnf_transformation,[status(thm)],[f80])).
% 0.16/10.43 fof(f84,plain,(
% 0.16/10.43 convergent_lines(sK1_skl,sK2_skl)),
% 0.16/10.43 inference(resolution,[status(thm)],[f61,f78])).
% 0.16/10.43 fof(f85,plain,(
% 0.16/10.43 ![X0]: (distinct_lines(sK2_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.16/10.43 inference(resolution,[status(thm)],[f55,f84])).
% 0.16/10.43 fof(f106,plain,(
% 0.16/10.43 ![X0,X1]: (convergent_lines(sK1_skl,X0)|convergent_lines(X1,X0)|distinct_lines(sK2_skl,X1))),
% 0.16/10.43 inference(resolution,[status(thm)],[f36,f85])).
% 0.16/10.43 fof(f180,plain,(
% 0.16/10.43 ![X0]: (convergent_lines(X0,sK1_skl)|distinct_lines(sK2_skl,X0))),
% 0.16/10.43 inference(resolution,[status(thm)],[f106,f27])).
% 0.16/10.43 fof(f221,definition,(
% 0.16/10.43 sQ13_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.16/10.43 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.16/10.43 fof(f223,plain,(
% 0.16/10.43 ~convergent_lines(sK0_skl,sK1_skl)|sQ13_spl),
% 0.16/10.43 inference(component_clause,[status(thm)],[f221])).
% 0.16/10.43 fof(f231,plain,(
% 0.16/10.43 ![X0]: (~convergent_lines(sK0_skl,sK1_skl)|sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0))),
% 0.16/10.43 inference(resolution,[status(thm)],[f67,f76])).
% 0.16/10.43 fof(f233,definition,(
% 0.16/10.43 ![X0]: (sQ15_spl <=> (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)))),
% 0.16/10.43 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.16/10.43 fof(f234,plain,(
% 0.16/10.43 ![X0]: (sP0_prd(X0,sK0_skl)|unorthogonal_lines(sK1_skl,X0)|~sQ15_spl)),
% 0.16/10.43 inference(component_clause,[status(thm)],[f233])).
% 0.16/10.43 fof(f236,plain,(
% 0.16/10.43 ~sQ13_spl|sQ15_spl),
% 0.16/10.43 inference(split_clause,[status(thm)],[f231,f221,f233])).
% 0.16/10.43 fof(f237,plain,(
% 0.16/10.43 distinct_lines(sK2_skl,sK0_skl)|sQ13_spl),
% 0.16/10.43 inference(resolution,[status(thm)],[f223,f180])).
% 0.16/10.43 fof(f245,plain,(
% 0.16/10.43 ![X0]: (distinct_lines(sK2_skl,X0)|distinct_lines(sK0_skl,X0)|sQ13_spl)),
% 0.16/10.43 inference(resolution,[status(thm)],[f237,f33])).
% 0.16/10.43 fof(f281,plain,(
% 0.16/10.43 sP0_prd(sK2_skl,sK0_skl)|~sQ15_spl),
% 0.16/10.43 inference(resolution,[status(thm)],[f234,f78])).
% 0.16/10.43 fof(f289,plain,(
% 0.16/10.43 convergent_lines(sK0_skl,sK2_skl)|~sQ15_spl),
% 0.16/10.43 inference(resolution,[status(thm)],[f281,f81])).
% 0.16/10.43 fof(f333,plain,(
% 0.16/10.43 ![X0]: (distinct_lines(sK2_skl,X0)|convergent_lines(sK0_skl,X0)|~sQ15_spl)),
% 0.16/10.43 inference(resolution,[status(thm)],[f289,f55])).
% 0.16/10.43 fof(f400,plain,(
% 0.16/10.43 distinct_lines(sK2_skl,sK0_skl)|~sQ15_spl),
% 0.16/10.43 inference(resolution,[status(thm)],[f333,f27])).
% 0.16/10.43 fof(f404,plain,(
% 0.16/10.43 ![X0]: (distinct_lines(sK2_skl,X0)|distinct_lines(sK0_skl,X0)|~sQ15_spl)),
% 0.16/10.43 inference(resolution,[status(thm)],[f400,f33])).
% 0.16/10.43 fof(f459,plain,(
% 0.16/10.43 distinct_lines(sK0_skl,sK2_skl)|~sQ15_spl),
% 0.16/10.43 inference(resolution,[status(thm)],[f404,f26])).
% 0.16/10.43 fof(f460,plain,(
% 0.16/10.43 $false|~sQ15_spl),
% 0.16/10.43 inference(forward_subsumption_resolution,[status(thm)],[f459,f77])).
% 0.16/10.43 fof(f461,plain,(
% 0.16/10.43 ~sQ15_spl),
% 0.16/10.43 inference(contradiction_clause,[status(thm)],[f460])).
% 0.16/10.43 fof(f473,plain,(
% 0.16/10.43 distinct_lines(sK0_skl,sK2_skl)|sQ13_spl),
% 0.16/10.43 inference(resolution,[status(thm)],[f245,f26])).
% 0.16/10.43 fof(f474,plain,(
% 0.16/10.43 $false|sQ13_spl),
% 0.16/10.43 inference(forward_subsumption_resolution,[status(thm)],[f473,f77])).
% 0.16/10.43 fof(f475,plain,(
% 0.16/10.43 sQ13_spl),
% 0.16/10.43 inference(contradiction_clause,[status(thm)],[f474])).
% 0.16/10.43 fof(f476,plain,(
% 0.16/10.43 $false),
% 0.16/10.43 inference(sat_refutation,[status(thm)],[f236,f461,f475])).
% 0.16/10.43 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/10.45 % Elapsed time: 0.045581 seconds
% 0.16/10.45 % CPU time: 0.177314 seconds
% 0.16/10.45 % Total memory used: 14.952 MB
% 0.16/10.45 % Net memory used: 14.604 MB
%------------------------------------------------------------------------------