%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO223+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 : n018.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 12:26:10 PM UTC 2026
% Result : Theorem 5.65s 1.12s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO223+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 13:51:58 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 5.65/1.12 % Refutation found
% 5.65/1.12 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.65/1.12 % SZS output start CNFRefutation for theBenchmark
% 5.65/1.12 fof(f3,axiom,(
% 5.65/1.12 (! [X] : ~ convergent_lines(X,X) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f6,axiom,(
% 5.65/1.12 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f15,axiom,(
% 5.65/1.12 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f16,axiom,(
% 5.65/1.12 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f19,axiom,(
% 5.65/1.12 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f20,axiom,(
% 5.65/1.12 (! [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) ) ) ) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f21,axiom,(
% 5.65/1.12 (! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f25,axiom,(
% 5.65/1.12 (! [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) ) ) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f26,axiom,(
% 5.65/1.12 (! [L,M,N] :( ( ~ unorthogonal_lines(L,M)& ~ unorthogonal_lines(L,N) )=> ~ convergent_lines(M,N) ) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f32,axiom,(
% 5.65/1.12 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f36,conjecture,(
% 5.65/1.12 (! [A,L] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)) )),
% 5.65/1.12 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 5.65/1.12 fof(f37,negated_conjecture,(
% 5.65/1.12 ~((! [A,L] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)) ))),
% 5.65/1.12 inference(negated_conjecture,[status(cth)],[f36])).
% 5.65/1.12 fof(f40,plain,(
% 5.65/1.12 ![X0]: (~convergent_lines(X0,X0))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f3])).
% 5.65/1.12 fof(f47,plain,(
% 5.65/1.12 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 5.65/1.12 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 5.65/1.12 fof(f48,plain,(
% 5.65/1.12 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 5.65/1.12 inference(miniscoping,[status(thm)],[f47])).
% 5.65/1.12 fof(f49,plain,(
% 5.65/1.12 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f48])).
% 5.65/1.12 fof(f69,plain,(
% 5.65/1.12 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 5.65/1.12 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 5.65/1.12 fof(f70,plain,(
% 5.65/1.12 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f69])).
% 5.65/1.12 fof(f71,plain,(
% 5.65/1.12 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f16])).
% 5.65/1.12 fof(f76,plain,(
% 5.65/1.12 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f19])).
% 5.65/1.12 fof(f77,plain,(
% 5.65/1.12 ![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))))),
% 5.65/1.12 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 5.65/1.12 fof(f78,definition,(
% 5.65/1.12 ![L,N]: (sP0_prd(N,L)<=>(convergent_lines(L,N)&unorthogonal_lines(L,N)))),
% 5.65/1.12 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 5.65/1.12 fof(f79,plain,(
% 5.65/1.12 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 5.65/1.12 inference(formula_renaming,[status(thm)],[f77,f78])).
% 5.65/1.12 fof(f80,plain,(
% 5.65/1.12 ![L,M]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(![N]: (sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N)))))),
% 5.65/1.12 inference(miniscoping,[status(thm)],[f79])).
% 5.65/1.12 fof(f81,plain,(
% 5.65/1.12 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~unorthogonal_lines(X0,X1)|sP0_prd(X2,X0)|convergent_lines(X1,X2))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f80])).
% 5.65/1.12 fof(f82,plain,(
% 5.65/1.12 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~unorthogonal_lines(X0,X1)|sP0_prd(X2,X0)|unorthogonal_lines(X1,X2))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f80])).
% 5.65/1.12 fof(f83,plain,(
% 5.65/1.12 ![X0,X1]: (~unorthogonal_lines(orthogonal_through_point(X0,X1),X0))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f21])).
% 5.65/1.12 fof(f90,plain,(
% 5.65/1.12 ![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)))),
% 5.65/1.12 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 5.65/1.12 fof(f91,definition,(
% 5.65/1.12 ![L,M]: (sP1_prd(M,L)<=>(convergent_lines(L,M)&unorthogonal_lines(L,M)))),
% 5.65/1.12 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 5.65/1.12 fof(f92,plain,(
% 5.65/1.12 ![L,M,N]: ((sP1_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N)))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 5.65/1.12 inference(formula_renaming,[status(thm)],[f90,f91])).
% 5.65/1.12 fof(f93,plain,(
% 5.65/1.12 ![M,N]: ((![L]: (sP1_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N))))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 5.65/1.12 inference(miniscoping,[status(thm)],[f92])).
% 5.65/1.12 fof(f94,plain,(
% 5.65/1.12 ![X0,X1,X2]: (sP1_prd(X0,X1)|convergent_lines(X1,X2)|~convergent_lines(X0,X2)|~unorthogonal_lines(X0,X2))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f93])).
% 5.65/1.12 fof(f96,plain,(
% 5.65/1.12 ![L,M,N]: ((unorthogonal_lines(L,M)|unorthogonal_lines(L,N))|~convergent_lines(M,N))),
% 5.65/1.12 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 5.65/1.12 fof(f97,plain,(
% 5.65/1.12 ![M,N]: ((![L]: (unorthogonal_lines(L,M)|unorthogonal_lines(L,N)))|~convergent_lines(M,N))),
% 5.65/1.12 inference(miniscoping,[status(thm)],[f96])).
% 5.65/1.12 fof(f98,plain,(
% 5.65/1.12 ![X0,X1,X2]: (unorthogonal_lines(X0,X1)|unorthogonal_lines(X0,X2)|~convergent_lines(X1,X2))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f97])).
% 5.65/1.12 fof(f111,plain,(
% 5.65/1.12 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 5.65/1.12 inference(NNF_transformation,[status(thm)],[f32])).
% 5.65/1.12 fof(f112,plain,(
% 5.65/1.12 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 5.65/1.12 inference(miniscoping,[status(thm)],[f111])).
% 5.65/1.12 fof(f114,plain,(
% 5.65/1.12 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f112])).
% 5.65/1.12 fof(f127,plain,(
% 5.65/1.12 (?[A,L]: ~equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)))),
% 5.65/1.12 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 5.65/1.12 fof(f128,plain,(
% 5.65/1.12 ~equal_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 5.65/1.12 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(L,sK1_skl)],[f127])).
% 5.65/1.12 fof(f129,plain,(
% 5.65/1.12 ~equal_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f128])).
% 5.65/1.12 fof(f130,plain,(
% 5.65/1.12 ![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))))),
% 5.65/1.12 inference(NNF_transformation,[status(thm)],[f78])).
% 5.65/1.12 fof(f131,plain,(
% 5.65/1.12 (![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))))),
% 5.65/1.12 inference(miniscoping,[status(thm)],[f130])).
% 5.65/1.12 fof(f133,plain,(
% 5.65/1.12 ![X0,X1]: (~sP0_prd(X0,X1)|unorthogonal_lines(X1,X0))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f131])).
% 5.65/1.12 fof(f135,plain,(
% 5.65/1.12 ![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))))),
% 5.65/1.12 inference(NNF_transformation,[status(thm)],[f91])).
% 5.65/1.12 fof(f136,plain,(
% 5.65/1.12 (![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))))),
% 5.65/1.12 inference(miniscoping,[status(thm)],[f135])).
% 5.65/1.12 fof(f138,plain,(
% 5.65/1.12 ![X0,X1]: (~sP1_prd(X0,X1)|unorthogonal_lines(X1,X0))),
% 5.65/1.12 inference(cnf_transformation,[status(thm)],[f136])).
% 5.65/1.12 fof(f140,plain,(
% 5.65/1.12 distinct_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 5.65/1.12 inference(resolution,[status(thm)],[f114,f129])).
% 5.65/1.12 fof(f142,plain,(
% 5.65/1.12 convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 5.65/1.12 inference(resolution,[status(thm)],[f70,f140])).
% 5.65/1.12 fof(f143,plain,(
% 5.65/1.12 ![X0,X1]: (convergent_lines(orthogonal_through_point(X0,X1),X0))),
% 5.65/1.12 inference(resolution,[status(thm)],[f76,f83])).
% 5.65/1.12 fof(f149,plain,(
% 5.65/1.12 ![X0,X1,X2]: (convergent_lines(orthogonal_through_point(X0,X1),X2)|convergent_lines(X0,X2))),
% 5.65/1.12 inference(resolution,[status(thm)],[f49,f143])).
% 5.65/1.12 fof(f150,plain,(
% 5.65/1.12 ![X0]: (convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0))),
% 5.65/1.12 inference(resolution,[status(thm)],[f49,f142])).
% 5.65/1.12 fof(f154,plain,(
% 5.65/1.12 ![X0,X1]: (convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1)|convergent_lines(X0,X1))),
% 5.65/1.12 inference(resolution,[status(thm)],[f150,f49])).
% 5.65/1.12 fof(f197,plain,(
% 5.65/1.12 ![X0]: (convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)|convergent_lines(sK1_skl,X0))),
% 5.65/1.12 inference(resolution,[status(thm)],[f154,f71])).
% 5.65/1.12 fof(f224,plain,(
% 5.65/1.12 ![X0,X1]: (convergent_lines(X0,orthogonal_through_point(X0,X1)))),
% 5.65/1.12 inference(resolution,[status(thm)],[f149,f40])).
% 5.65/1.12 fof(f335,plain,(
% 5.65/1.12 ![X0,X1,X2]: (unorthogonal_lines(X0,orthogonal_through_point(X1,X2))|unorthogonal_lines(X0,X1))),
% 5.65/1.12 inference(resolution,[status(thm)],[f98,f143])).
% 5.65/1.12 fof(f365,plain,(
% 5.65/1.12 ![X0,X1,X2,X3]: (~convergent_lines(X0,orthogonal_through_point(X1,X2))|sP0_prd(X3,X0)|convergent_lines(orthogonal_through_point(X1,X2),X3)|unorthogonal_lines(X0,X1))),
% 5.65/1.12 inference(resolution,[status(thm)],[f81,f335])).
% 5.65/1.12 fof(f390,plain,(
% 5.65/1.12 convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 5.65/1.12 inference(resolution,[status(thm)],[f197,f40])).
% 5.65/1.12 fof(f771,plain,(
% 5.65/1.12 ![X0]: (sP0_prd(X0,sK1_skl)|convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)|unorthogonal_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl)))),
% 5.65/1.12 inference(resolution,[status(thm)],[f365,f390])).
% 5.65/1.12 fof(f814,definition,(
% 5.65/1.12 ![X0]: (sQ18_spl <=> (sP0_prd(X0,sK1_skl)|convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)))),
% 5.65/1.12 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 5.65/1.12 fof(f815,plain,(
% 5.65/1.12 ![X0]: (sP0_prd(X0,sK1_skl)|convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)|~sQ18_spl)),
% 5.65/1.12 inference(component_clause,[status(thm)],[f814])).
% 5.65/1.12 fof(f817,definition,(
% 5.65/1.12 sQ19_spl <=> (unorthogonal_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl)))),
% 5.65/1.12 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 5.65/1.12 fof(f818,plain,(
% 5.65/1.12 unorthogonal_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl))|~sQ19_spl),
% 5.65/1.12 inference(component_clause,[status(thm)],[f817])).
% 5.65/1.12 fof(f820,plain,(
% 5.65/1.12 sQ18_spl|sQ19_spl),
% 5.65/1.12 inference(split_clause,[status(thm)],[f771,f814,f817])).
% 5.65/1.12 fof(f871,definition,(
% 5.65/1.12 ![X0]: (sQ22_spl <=> (sP0_prd(X0,sK1_skl)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)))),
% 5.65/1.12 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 5.65/1.12 fof(f872,plain,(
% 5.65/1.12 ![X0]: (sP0_prd(X0,sK1_skl)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)|~sQ22_spl)),
% 5.65/1.12 inference(component_clause,[status(thm)],[f871])).
% 5.65/1.12 fof(f880,plain,(
% 5.65/1.12 ![X0]: (sP1_prd(sK1_skl,X0)|convergent_lines(X0,orthogonal_through_point(sK1_skl,sK0_skl))|~convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl))|~sQ19_spl)),
% 5.65/1.13 inference(resolution,[status(thm)],[f818,f94])).
% 5.65/1.13 fof(f886,definition,(
% 5.65/1.13 sQ25_spl <=> (convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl)))),
% 5.65/1.13 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 5.65/1.13 fof(f888,plain,(
% 5.65/1.13 ~convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl))|sQ25_spl),
% 5.65/1.13 inference(component_clause,[status(thm)],[f886])).
% 5.65/1.13 fof(f890,definition,(
% 5.65/1.13 ![X0]: (sQ26_spl <=> (sP1_prd(sK1_skl,X0)|convergent_lines(X0,orthogonal_through_point(sK1_skl,sK0_skl))))),
% 5.65/1.13 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 5.65/1.13 fof(f891,plain,(
% 5.65/1.13 ![X0]: (sP1_prd(sK1_skl,X0)|convergent_lines(X0,orthogonal_through_point(sK1_skl,sK0_skl))|~sQ26_spl)),
% 5.65/1.13 inference(component_clause,[status(thm)],[f890])).
% 5.65/1.13 fof(f893,plain,(
% 5.65/1.13 sQ26_spl|~sQ25_spl|~sQ19_spl),
% 5.65/1.13 inference(split_clause,[status(thm)],[f880,f890,f886,f817])).
% 5.65/1.13 fof(f902,plain,(
% 5.65/1.13 $false|sQ25_spl),
% 5.65/1.13 inference(forward_subsumption_resolution,[status(thm)],[f888,f224])).
% 5.65/1.13 fof(f903,plain,(
% 5.65/1.13 sQ25_spl),
% 5.65/1.13 inference(contradiction_clause,[status(thm)],[f902])).
% 5.65/1.13 fof(f1482,plain,(
% 5.65/1.13 sP0_prd(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),sK1_skl)|~sQ18_spl),
% 5.65/1.13 inference(resolution,[status(thm)],[f815,f40])).
% 5.65/1.13 fof(f1483,plain,(
% 5.65/1.13 unorthogonal_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|~sQ18_spl),
% 5.65/1.13 inference(resolution,[status(thm)],[f1482,f133])).
% 5.65/1.13 fof(f1487,plain,(
% 5.65/1.13 ![X0]: (~convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|sP0_prd(X0,sK1_skl)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)|~sQ18_spl)),
% 5.65/1.13 inference(resolution,[status(thm)],[f1483,f82])).
% 5.65/1.13 fof(f1489,definition,(
% 5.65/1.13 sQ51_spl <=> (convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl)))),
% 5.65/1.13 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 5.65/1.13 fof(f1491,plain,(
% 5.65/1.13 ~convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|sQ51_spl),
% 5.65/1.13 inference(component_clause,[status(thm)],[f1489])).
% 5.65/1.13 fof(f1494,plain,(
% 5.65/1.13 ~sQ51_spl|sQ22_spl|~sQ18_spl),
% 5.65/1.13 inference(split_clause,[status(thm)],[f1487,f1489,f871,f814])).
% 5.65/1.13 fof(f1496,plain,(
% 5.65/1.13 sP0_prd(orthogonal_through_point(sK1_skl,sK0_skl),sK1_skl)|~sQ22_spl),
% 5.65/1.13 inference(resolution,[status(thm)],[f872,f83])).
% 5.65/1.13 fof(f1505,plain,(
% 5.65/1.13 unorthogonal_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl))|~sQ22_spl),
% 5.65/1.13 inference(resolution,[status(thm)],[f1496,f133])).
% 5.65/1.13 fof(f1507,plain,(
% 5.65/1.13 sQ19_spl|~sQ22_spl),
% 5.65/1.13 inference(split_clause,[status(thm)],[f1505,f817,f871])).
% 5.65/1.13 fof(f1508,plain,(
% 5.65/1.13 $false|sQ51_spl),
% 5.65/1.13 inference(forward_subsumption_resolution,[status(thm)],[f1491,f390])).
% 5.65/1.13 fof(f1509,plain,(
% 5.65/1.13 sQ51_spl),
% 5.65/1.13 inference(contradiction_clause,[status(thm)],[f1508])).
% 5.65/1.13 fof(f1575,plain,(
% 5.65/1.13 sP1_prd(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl))|~sQ26_spl),
% 5.65/1.13 inference(resolution,[status(thm)],[f891,f40])).
% 5.65/1.13 fof(f1576,plain,(
% 5.65/1.13 unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),sK1_skl)|~sQ26_spl),
% 5.65/1.13 inference(resolution,[status(thm)],[f1575,f138])).
% 5.65/1.13 fof(f1578,plain,(
% 5.65/1.13 $false|~sQ26_spl),
% 5.65/1.13 inference(forward_subsumption_resolution,[status(thm)],[f1576,f83])).
% 5.65/1.13 fof(f1579,plain,(
% 5.65/1.13 ~sQ26_spl),
% 5.65/1.13 inference(contradiction_clause,[status(thm)],[f1578])).
% 5.65/1.13 fof(f1580,plain,(
% 5.65/1.13 $false),
% 5.65/1.13 inference(sat_refutation,[status(thm)],[f820,f893,f903,f1494,f1507,f1509,f1579])).
% 5.65/1.13 % SZS output end CNFRefutation for theBenchmark.p
% 5.65/1.15 % Elapsed time: 0.788741 seconds
% 5.65/1.15 % CPU time: 5.975828 seconds
% 5.65/1.15 % Total memory used: 65.691 MB
% 5.65/1.15 % Net memory used: 55.194 MB
%------------------------------------------------------------------------------