%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO222+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.05s 10.59s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO222+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.50 % Computer : n020.cluster.edu
% 0.17/10.50 % Model : x86_64 x86_64
% 0.17/10.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.50 % Memory : 8046.5625MB
% 0.17/10.50 % OS : Linux 6.8.0-71-generic
% 0.05/10.50 % CPULimit : 300
% 0.05/10.50 % WCLimit : 300
% 0.05/10.50 % DateTime : Sun Sep 20 13:53:44 UTC 2026
% 0.05/10.50 % CPUTime :
% 0.05/10.51 % Drodi V4.1.1
% 0.05/10.59 % Refutation found
% 0.05/10.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.05/10.59 % SZS output start CNFRefutation for theBenchmark
% 0.05/10.59 fof(f3,axiom,(
% 0.05/10.59 (! [X] : ~ convergent_lines(X,X) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f6,axiom,(
% 0.05/10.59 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f13,axiom,(
% 0.05/10.59 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f14,axiom,(
% 0.05/10.59 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f15,axiom,(
% 0.05/10.59 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f16,axiom,(
% 0.05/10.59 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f17,axiom,(
% 0.05/10.59 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f19,axiom,(
% 0.05/10.59 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f21,axiom,(
% 0.05/10.59 (! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f22,axiom,(
% 0.05/10.59 (! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f23,axiom,(
% 0.05/10.59 (! [A,L,M,N] :( distinct_lines(L,M)=> ( apart_point_and_line(A,L)| apart_point_and_line(A,M)| unorthogonal_lines(L,N)| unorthogonal_lines(M,N) ) ) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f25,axiom,(
% 0.05/10.59 (! [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) ) ) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f33,axiom,(
% 0.05/10.59 (! [X,Y] :( parallel_lines(X,Y)<=> ~ convergent_lines(X,Y) ) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f36,conjecture,(
% 0.05/10.59 (! [A,L] : parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)) )),
% 0.05/10.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.05/10.59 fof(f37,negated_conjecture,(
% 0.05/10.59 ~((! [A,L] : parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)) ))),
% 0.05/10.59 inference(negated_conjecture,[status(cth)],[f36])).
% 0.05/10.59 fof(f40,plain,(
% 0.05/10.59 ![X0]: (~convergent_lines(X0,X0))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f3])).
% 0.05/10.59 fof(f47,plain,(
% 0.05/10.59 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.05/10.59 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.05/10.59 fof(f48,plain,(
% 0.05/10.59 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.05/10.59 inference(miniscoping,[status(thm)],[f47])).
% 0.05/10.59 fof(f49,plain,(
% 0.05/10.59 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f48])).
% 0.05/10.59 fof(f63,plain,(
% 0.05/10.59 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.05/10.59 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.05/10.59 fof(f64,plain,(
% 0.05/10.59 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.05/10.59 inference(miniscoping,[status(thm)],[f63])).
% 0.05/10.59 fof(f65,plain,(
% 0.05/10.59 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f64])).
% 0.05/10.59 fof(f66,plain,(
% 0.05/10.59 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.05/10.59 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.05/10.59 fof(f67,plain,(
% 0.05/10.59 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.05/10.59 inference(miniscoping,[status(thm)],[f66])).
% 0.05/10.59 fof(f68,plain,(
% 0.05/10.59 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f67])).
% 0.05/10.59 fof(f69,plain,(
% 0.05/10.59 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 0.05/10.59 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.05/10.59 fof(f70,plain,(
% 0.05/10.59 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f69])).
% 0.05/10.59 fof(f71,plain,(
% 0.05/10.59 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f16])).
% 0.05/10.59 fof(f72,plain,(
% 0.05/10.59 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f17])).
% 0.05/10.59 fof(f76,plain,(
% 0.05/10.59 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f19])).
% 0.05/10.59 fof(f83,plain,(
% 0.05/10.59 ![X0,X1]: (~unorthogonal_lines(orthogonal_through_point(X0,X1),X0))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f21])).
% 0.05/10.59 fof(f84,plain,(
% 0.05/10.59 ![X0,X1]: (~apart_point_and_line(X0,orthogonal_through_point(X1,X0)))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f22])).
% 0.05/10.59 fof(f85,plain,(
% 0.05/10.59 ![A,L,M,N]: (~distinct_lines(L,M)|(((apart_point_and_line(A,L)|apart_point_and_line(A,M))|unorthogonal_lines(L,N))|unorthogonal_lines(M,N)))),
% 0.05/10.59 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.05/10.59 fof(f86,plain,(
% 0.05/10.59 ![L,M]: (~distinct_lines(L,M)|(![N]: (((![A]: (apart_point_and_line(A,L)|apart_point_and_line(A,M)))|unorthogonal_lines(L,N))|unorthogonal_lines(M,N))))),
% 0.05/10.59 inference(miniscoping,[status(thm)],[f85])).
% 0.05/10.59 fof(f87,plain,(
% 0.05/10.59 ![X0,X1,X2,X3]: (~distinct_lines(X0,X1)|apart_point_and_line(X2,X0)|apart_point_and_line(X2,X1)|unorthogonal_lines(X0,X3)|unorthogonal_lines(X1,X3))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f86])).
% 0.05/10.59 fof(f90,plain,(
% 0.05/10.59 ![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)))),
% 0.05/10.59 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.05/10.59 fof(f91,definition,(
% 0.05/10.59 ![L,M]: (sP1_prd(M,L)<=>(convergent_lines(L,M)&unorthogonal_lines(L,M)))),
% 0.05/10.59 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.05/10.59 fof(f92,plain,(
% 0.05/10.59 ![L,M,N]: ((sP1_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N)))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.05/10.59 inference(formula_renaming,[status(thm)],[f90,f91])).
% 0.05/10.59 fof(f93,plain,(
% 0.05/10.59 ![M,N]: ((![L]: (sP1_prd(M,L)|(convergent_lines(L,N)&unorthogonal_lines(L,N))))|(~convergent_lines(M,N)|~unorthogonal_lines(M,N)))),
% 0.05/10.59 inference(miniscoping,[status(thm)],[f92])).
% 0.05/10.59 fof(f94,plain,(
% 0.05/10.59 ![X0,X1,X2]: (sP1_prd(X0,X1)|convergent_lines(X1,X2)|~convergent_lines(X0,X2)|~unorthogonal_lines(X0,X2))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f93])).
% 0.05/10.59 fof(f115,plain,(
% 0.05/10.59 ![X,Y]: ((~parallel_lines(X,Y)|~convergent_lines(X,Y))&(parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 0.05/10.59 inference(NNF_transformation,[status(thm)],[f33])).
% 0.05/10.59 fof(f116,plain,(
% 0.05/10.59 (![X,Y]: (~parallel_lines(X,Y)|~convergent_lines(X,Y)))&(![X,Y]: (parallel_lines(X,Y)|convergent_lines(X,Y)))),
% 0.05/10.59 inference(miniscoping,[status(thm)],[f115])).
% 0.05/10.59 fof(f118,plain,(
% 0.05/10.59 ![X0,X1]: (parallel_lines(X0,X1)|convergent_lines(X0,X1))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f116])).
% 0.05/10.59 fof(f127,plain,(
% 0.05/10.59 (?[A,L]: ~parallel_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)))),
% 0.05/10.59 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.05/10.59 fof(f128,plain,(
% 0.05/10.59 ~parallel_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 0.05/10.59 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(L,sK1_skl)],[f127])).
% 0.05/10.59 fof(f129,plain,(
% 0.05/10.59 ~parallel_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f128])).
% 0.05/10.59 fof(f135,plain,(
% 0.05/10.59 ![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))))),
% 0.05/10.59 inference(NNF_transformation,[status(thm)],[f91])).
% 0.05/10.59 fof(f136,plain,(
% 0.05/10.59 (![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))))),
% 0.05/10.59 inference(miniscoping,[status(thm)],[f135])).
% 0.05/10.59 fof(f138,plain,(
% 0.05/10.59 ![X0,X1]: (~sP1_prd(X0,X1)|unorthogonal_lines(X1,X0))),
% 0.05/10.59 inference(cnf_transformation,[status(thm)],[f136])).
% 0.05/10.59 fof(f140,plain,(
% 0.05/10.59 convergent_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 0.05/10.59 inference(resolution,[status(thm)],[f118,f129])).
% 0.05/10.59 fof(f142,plain,(
% 0.05/10.59 ![X0,X1]: (convergent_lines(orthogonal_through_point(X0,X1),X0))),
% 0.05/10.59 inference(resolution,[status(thm)],[f76,f83])).
% 0.05/10.59 fof(f144,plain,(
% 0.05/10.59 ![X0,X1,X2]: (convergent_lines(orthogonal_through_point(X0,X1),X2)|convergent_lines(X0,X2))),
% 0.05/10.59 inference(resolution,[status(thm)],[f49,f142])).
% 0.05/10.59 fof(f145,plain,(
% 0.05/10.59 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0))),
% 0.05/10.59 inference(resolution,[status(thm)],[f49,f140])).
% 0.05/10.59 fof(f146,plain,(
% 0.05/10.59 ![X0,X1]: (convergent_lines(sK1_skl,X0)|convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1)|convergent_lines(X0,X1))),
% 0.05/10.59 inference(resolution,[status(thm)],[f145,f49])).
% 0.05/10.59 fof(f150,plain,(
% 0.05/10.59 convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),sK1_skl)),
% 0.05/10.59 inference(resolution,[status(thm)],[f146,f40])).
% 0.05/10.59 fof(f199,plain,(
% 0.05/10.59 ![X0,X1]: (convergent_lines(X0,orthogonal_through_point(X0,X1)))),
% 0.05/10.59 inference(resolution,[status(thm)],[f144,f40])).
% 0.05/10.59 fof(f290,plain,(
% 0.05/10.59 ![X0]: (distinct_lines(sK1_skl,X0)|convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0))),
% 0.05/10.59 inference(resolution,[status(thm)],[f68,f150])).
% 0.05/10.59 fof(f387,plain,(
% 0.05/10.59 distinct_lines(sK1_skl,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 0.05/10.59 inference(resolution,[status(thm)],[f290,f40])).
% 0.05/10.59 fof(f471,plain,(
% 0.05/10.59 ![X0,X1]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|unorthogonal_lines(sK1_skl,X1)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1))),
% 0.05/10.59 inference(resolution,[status(thm)],[f87,f387])).
% 0.05/10.59 fof(f481,definition,(
% 0.05/10.59 ![X0]: (sQ12_spl <=> (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))))),
% 0.05/10.59 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.05/10.59 fof(f482,plain,(
% 0.05/10.59 ![X0]: (apart_point_and_line(X0,sK1_skl)|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|~sQ12_spl)),
% 0.05/10.59 inference(component_clause,[status(thm)],[f481])).
% 0.05/10.59 fof(f484,definition,(
% 0.05/10.59 ![X1]: (sQ13_spl <=> (unorthogonal_lines(sK1_skl,X1)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X1)))),
% 0.05/10.59 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.05/10.59 fof(f485,plain,(
% 0.05/10.59 ![X0]: (unorthogonal_lines(sK1_skl,X0)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)|~sQ13_spl)),
% 0.05/10.59 inference(component_clause,[status(thm)],[f484])).
% 0.05/10.59 fof(f487,plain,(
% 0.05/10.59 sQ12_spl|sQ13_spl),
% 0.05/10.59 inference(split_clause,[status(thm)],[f471,f481,f484])).
% 0.05/10.59 fof(f710,plain,(
% 0.05/10.59 apart_point_and_line(sK0_skl,sK1_skl)|~sQ12_spl),
% 0.05/10.59 inference(resolution,[status(thm)],[f482,f84])).
% 0.05/10.59 fof(f713,plain,(
% 0.05/10.59 ![X0]: (distinct_lines(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|~sQ12_spl)),
% 0.05/10.59 inference(resolution,[status(thm)],[f710,f65])).
% 0.05/10.59 fof(f717,plain,(
% 0.05/10.59 ![X0]: (distinct_lines(sK1_skl,parallel_through_point(X0,sK0_skl))|~sQ12_spl)),
% 0.05/10.59 inference(resolution,[status(thm)],[f713,f72])).
% 0.05/10.59 fof(f723,plain,(
% 0.05/10.59 ![X0]: (convergent_lines(sK1_skl,parallel_through_point(X0,sK0_skl))|~sQ12_spl)),
% 0.05/10.59 inference(resolution,[status(thm)],[f717,f70])).
% 0.05/10.59 fof(f731,plain,(
% 0.05/10.59 ![X0,X1]: (convergent_lines(sK1_skl,X0)|convergent_lines(parallel_through_point(X1,sK0_skl),X0)|~sQ12_spl)),
% 0.05/10.59 inference(resolution,[status(thm)],[f723,f49])).
% 0.05/10.59 fof(f841,plain,(
% 0.05/10.59 ![X0]: (convergent_lines(sK1_skl,X0)|~sQ12_spl)),
% 0.05/10.60 inference(resolution,[status(thm)],[f731,f71])).
% 0.05/10.60 fof(f851,plain,(
% 0.05/10.60 $false|~sQ12_spl),
% 0.05/10.60 inference(resolution,[status(thm)],[f841,f40])).
% 0.05/10.60 fof(f852,plain,(
% 0.05/10.60 ~sQ12_spl),
% 0.05/10.60 inference(contradiction_clause,[status(thm)],[f851])).
% 0.05/10.60 fof(f895,plain,(
% 0.05/10.60 unorthogonal_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl))|~sQ13_spl),
% 0.05/10.60 inference(resolution,[status(thm)],[f485,f83])).
% 0.05/10.60 fof(f903,plain,(
% 0.05/10.60 ![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))|~sQ13_spl)),
% 0.05/10.60 inference(resolution,[status(thm)],[f895,f94])).
% 0.05/10.60 fof(f911,definition,(
% 0.05/10.60 sQ24_spl <=> (convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl)))),
% 0.05/10.60 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.05/10.60 fof(f913,plain,(
% 0.05/10.60 ~convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl))|sQ24_spl),
% 0.05/10.60 inference(component_clause,[status(thm)],[f911])).
% 0.05/10.60 fof(f915,definition,(
% 0.05/10.60 ![X0]: (sQ25_spl <=> (sP1_prd(sK1_skl,X0)|convergent_lines(X0,orthogonal_through_point(sK1_skl,sK0_skl))))),
% 0.05/10.60 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.05/10.60 fof(f916,plain,(
% 0.05/10.60 ![X0]: (sP1_prd(sK1_skl,X0)|convergent_lines(X0,orthogonal_through_point(sK1_skl,sK0_skl))|~sQ25_spl)),
% 0.05/10.60 inference(component_clause,[status(thm)],[f915])).
% 0.05/10.60 fof(f918,plain,(
% 0.05/10.60 sQ25_spl|~sQ24_spl|~sQ13_spl),
% 0.05/10.60 inference(split_clause,[status(thm)],[f903,f915,f911,f484])).
% 0.05/10.60 fof(f935,plain,(
% 0.05/10.60 $false|sQ24_spl),
% 0.05/10.60 inference(forward_subsumption_resolution,[status(thm)],[f913,f199])).
% 0.05/10.60 fof(f936,plain,(
% 0.05/10.60 sQ24_spl),
% 0.05/10.60 inference(contradiction_clause,[status(thm)],[f935])).
% 0.05/10.60 fof(f1020,plain,(
% 0.05/10.60 sP1_prd(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl))|~sQ25_spl),
% 0.05/10.60 inference(resolution,[status(thm)],[f916,f40])).
% 0.05/10.60 fof(f1023,plain,(
% 0.05/10.60 unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),sK1_skl)|~sQ25_spl),
% 0.05/10.60 inference(resolution,[status(thm)],[f1020,f138])).
% 0.05/10.60 fof(f1025,plain,(
% 0.05/10.60 $false|~sQ25_spl),
% 0.05/10.60 inference(forward_subsumption_resolution,[status(thm)],[f1023,f83])).
% 0.05/10.60 fof(f1026,plain,(
% 0.05/10.60 ~sQ25_spl),
% 0.05/10.60 inference(contradiction_clause,[status(thm)],[f1025])).
% 0.05/10.60 fof(f1027,plain,(
% 0.05/10.60 $false),
% 0.05/10.60 inference(sat_refutation,[status(thm)],[f487,f852,f918,f936,f1026])).
% 0.05/10.60 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/10.63 % Elapsed time: 0.122237 seconds
% 0.21/10.63 % CPU time: 0.454627 seconds
% 0.21/10.63 % Total memory used: 15.202 MB
% 0.21/10.63 % Net memory used: 14.479 MB
%------------------------------------------------------------------------------