%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO201+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 : n004.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 12:26:04 PM UTC 2026
% Result : Theorem 0.15s 5.60s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO201+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sun Sep 20 13:27:40 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.40 % Drodi V4.1.1
% 0.15/5.60 % Refutation found
% 0.15/5.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.60 % SZS output start CNFRefutation for theBenchmark
% 0.15/5.60 fof(f3,axiom,(
% 0.15/5.60 (! [X] : ~ convergent_lines(X,X) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f6,axiom,(
% 0.15/5.60 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f9,axiom,(
% 0.15/5.60 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f10,axiom,(
% 0.15/5.60 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f11,axiom,(
% 0.15/5.60 (! [X,Y,U,V] :( ( distinct_points(X,Y)& distinct_lines(U,V) )=> ( apart_point_and_line(X,U)| apart_point_and_line(X,V)| apart_point_and_line(Y,U)| apart_point_and_line(Y,V) ) ) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f14,axiom,(
% 0.15/5.60 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f16,axiom,(
% 0.15/5.60 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f20,axiom,(
% 0.15/5.60 (! [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) ) ) ) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f25,axiom,(
% 0.15/5.60 (! [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) ) ) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f31,axiom,(
% 0.15/5.60 (! [X,Y] :( equal_points(X,Y)<=> ~ distinct_points(X,Y) ) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f36,conjecture,(
% 0.15/5.60 (! [X,Y] :( convergent_lines(X,Y)=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ) )),
% 0.15/5.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/5.60 fof(f37,negated_conjecture,(
% 0.15/5.60 ~((! [X,Y] :( convergent_lines(X,Y)=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ) ))),
% 0.15/5.60 inference(negated_conjecture,[status(cth)],[f36])).
% 0.15/5.60 fof(f40,plain,(
% 0.15/5.60 ![X0]: (~convergent_lines(X0,X0))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f3])).
% 0.15/5.60 fof(f47,plain,(
% 0.15/5.60 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 0.15/5.60 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.15/5.60 fof(f48,plain,(
% 0.15/5.60 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 0.15/5.60 inference(miniscoping,[status(thm)],[f47])).
% 0.15/5.60 fof(f49,plain,(
% 0.15/5.60 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f48])).
% 0.15/5.60 fof(f54,plain,(
% 0.15/5.60 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 0.15/5.60 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.15/5.60 fof(f55,plain,(
% 0.15/5.60 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f54])).
% 0.15/5.60 fof(f56,plain,(
% 0.15/5.60 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 0.15/5.60 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.15/5.60 fof(f57,plain,(
% 0.15/5.60 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f56])).
% 0.15/5.60 fof(f58,plain,(
% 0.15/5.60 ![X,Y,U,V]: ((~distinct_points(X,Y)|~distinct_lines(U,V))|(((apart_point_and_line(X,U)|apart_point_and_line(X,V))|apart_point_and_line(Y,U))|apart_point_and_line(Y,V)))),
% 0.15/5.60 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.15/5.60 fof(f59,plain,(
% 0.15/5.60 ![X0,X1,X2,X3]: (~distinct_points(X0,X1)|~distinct_lines(X2,X3)|apart_point_and_line(X0,X2)|apart_point_and_line(X0,X3)|apart_point_and_line(X1,X2)|apart_point_and_line(X1,X3))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f58])).
% 0.15/5.60 fof(f66,plain,(
% 0.15/5.60 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 0.15/5.60 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.15/5.60 fof(f67,plain,(
% 0.15/5.60 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 0.15/5.60 inference(miniscoping,[status(thm)],[f66])).
% 0.15/5.60 fof(f68,plain,(
% 0.15/5.60 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f67])).
% 0.15/5.60 fof(f71,plain,(
% 0.15/5.60 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f16])).
% 0.15/5.60 fof(f77,plain,(
% 0.15/5.60 ![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))))),
% 0.15/5.60 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.15/5.60 fof(f78,definition,(
% 0.15/5.60 ![L,N]: (sP0_prd(N,L)<=>(convergent_lines(L,N)&unorthogonal_lines(L,N)))),
% 0.15/5.60 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.15/5.60 fof(f90,plain,(
% 0.15/5.60 ![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)))),
% 0.15/5.60 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.15/5.60 fof(f91,definition,(
% 0.15/5.60 ![L,M]: (sP1_prd(M,L)<=>(convergent_lines(L,M)&unorthogonal_lines(L,M)))),
% 0.15/5.60 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.15/5.60 fof(f107,plain,(
% 0.15/5.60 ![X,Y]: ((~equal_points(X,Y)|~distinct_points(X,Y))&(equal_points(X,Y)|distinct_points(X,Y)))),
% 0.15/5.60 inference(NNF_transformation,[status(thm)],[f31])).
% 0.15/5.60 fof(f108,plain,(
% 0.15/5.60 (![X,Y]: (~equal_points(X,Y)|~distinct_points(X,Y)))&(![X,Y]: (equal_points(X,Y)|distinct_points(X,Y)))),
% 0.15/5.60 inference(miniscoping,[status(thm)],[f107])).
% 0.15/5.60 fof(f110,plain,(
% 0.15/5.60 ![X0,X1]: (equal_points(X0,X1)|distinct_points(X0,X1))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f108])).
% 0.15/5.60 fof(f127,plain,(
% 0.15/5.60 (?[X,Y]: (convergent_lines(X,Y)&~equal_points(intersection_point(X,Y),intersection_point(Y,X))))),
% 0.15/5.60 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.15/5.60 fof(f128,plain,(
% 0.15/5.60 (convergent_lines(sK0_skl,sK1_skl)&~equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl)))),
% 0.15/5.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f127])).
% 0.15/5.60 fof(f129,plain,(
% 0.15/5.60 convergent_lines(sK0_skl,sK1_skl)),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f128])).
% 0.15/5.60 fof(f130,plain,(
% 0.15/5.60 ~equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f128])).
% 0.15/5.60 fof(f131,plain,(
% 0.15/5.60 ![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))))),
% 0.15/5.60 inference(NNF_transformation,[status(thm)],[f78])).
% 0.15/5.60 fof(f132,plain,(
% 0.15/5.60 (![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))))),
% 0.15/5.60 inference(miniscoping,[status(thm)],[f131])).
% 0.15/5.60 fof(f133,plain,(
% 0.15/5.60 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f132])).
% 0.15/5.60 fof(f136,plain,(
% 0.15/5.60 ![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))))),
% 0.15/5.60 inference(NNF_transformation,[status(thm)],[f91])).
% 0.15/5.60 fof(f137,plain,(
% 0.15/5.60 (![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))))),
% 0.15/5.60 inference(miniscoping,[status(thm)],[f136])).
% 0.15/5.60 fof(f138,plain,(
% 0.15/5.60 ![X0,X1]: (~sP1_prd(X0,X1)|convergent_lines(X1,X0))),
% 0.15/5.60 inference(cnf_transformation,[status(thm)],[f137])).
% 0.15/5.60 fof(f141,plain,(
% 0.15/5.60 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK1_skl,sK0_skl))),
% 0.15/5.60 inference(resolution,[status(thm)],[f110,f130])).
% 0.15/5.60 fof(f143,plain,(
% 0.15/5.60 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 0.15/5.60 inference(resolution,[status(thm)],[f49,f129])).
% 0.15/5.60 fof(f156,plain,(
% 0.15/5.60 ![X0,X1,X2,X3]: (~distinct_points(intersection_point(X0,X1),X2)|~distinct_lines(X1,X3)|apart_point_and_line(intersection_point(X0,X1),X3)|apart_point_and_line(X2,X1)|apart_point_and_line(X2,X3)|~convergent_lines(X0,X1))),
% 0.15/5.60 inference(resolution,[status(thm)],[f59,f57])).
% 0.15/5.60 fof(f197,plain,(
% 0.15/5.60 ![X0,X1]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X1)|convergent_lines(X0,X1))),
% 0.15/5.60 inference(resolution,[status(thm)],[f143,f49])).
% 0.15/5.60 fof(f207,plain,(
% 0.15/5.60 convergent_lines(sK1_skl,sK0_skl)),
% 0.15/5.60 inference(resolution,[status(thm)],[f197,f40])).
% 0.15/5.60 fof(f219,definition,(
% 0.15/5.60 sQ4_spl <=> (convergent_lines(sK1_skl,sK0_skl))),
% 0.15/5.60 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.15/5.60 fof(f221,plain,(
% 0.15/5.60 ~convergent_lines(sK1_skl,sK0_skl)|sQ4_spl),
% 0.15/5.60 inference(component_clause,[status(thm)],[f219])).
% 0.15/5.60 fof(f230,definition,(
% 0.15/5.60 ![X0]: (sQ7_spl <=> (convergent_lines(sK0_skl,X0)|convergent_lines(sK0_skl,X0)))),
% 0.15/5.60 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.15/5.60 fof(f231,plain,(
% 0.15/5.60 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK0_skl,X0)|~sQ7_spl)),
% 0.15/5.60 inference(component_clause,[status(thm)],[f230])).
% 0.15/5.60 fof(f234,definition,(
% 0.15/5.60 sQ8_spl <=> (convergent_lines(sK0_skl,sK1_skl))),
% 0.15/5.60 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.15/5.60 fof(f236,plain,(
% 0.15/5.60 ~convergent_lines(sK0_skl,sK1_skl)|sQ8_spl),
% 0.15/5.60 inference(component_clause,[status(thm)],[f234])).
% 0.15/5.60 fof(f249,plain,(
% 0.15/5.60 ![X0]: (~distinct_lines(sK1_skl,X0)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0)|~convergent_lines(sK0_skl,sK1_skl))),
% 0.15/5.60 inference(resolution,[status(thm)],[f156,f141])).
% 0.15/5.60 fof(f250,definition,(
% 0.15/5.60 ![X0]: (sQ12_spl <=> (~distinct_lines(sK1_skl,X0)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0)))),
% 0.15/5.60 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.15/5.60 fof(f251,plain,(
% 0.15/5.60 ![X0]: (~distinct_lines(sK1_skl,X0)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X0)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),X0)|~sQ12_spl)),
% 0.15/5.60 inference(component_clause,[status(thm)],[f250])).
% 0.15/5.60 fof(f253,definition,(
% 0.15/5.60 sQ13_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl))),
% 0.15/5.60 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.15/5.60 fof(f254,plain,(
% 0.15/5.60 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK1_skl)|~sQ13_spl),
% 0.15/5.60 inference(component_clause,[status(thm)],[f253])).
% 0.15/5.60 fof(f256,plain,(
% 0.15/5.60 sQ12_spl|sQ13_spl|~sQ8_spl),
% 0.15/5.60 inference(split_clause,[status(thm)],[f249,f250,f253,f234])).
% 0.15/5.60 fof(f261,definition,(
% 0.15/5.60 sQ15_spl <=> (apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl))),
% 0.15/5.60 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.15/5.60 fof(f262,plain,(
% 0.15/5.60 apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|~sQ15_spl),
% 0.15/5.60 inference(component_clause,[status(thm)],[f261])).
% 0.15/5.60 fof(f298,plain,(
% 0.15/5.60 ![X0]: (distinct_lines(sK1_skl,X0)|convergent_lines(sK0_skl,X0))),
% 0.15/5.60 inference(resolution,[status(thm)],[f68,f129])).
% 0.15/5.60 fof(f336,plain,(
% 0.15/5.60 distinct_lines(sK1_skl,sK0_skl)),
% 0.15/5.60 inference(resolution,[status(thm)],[f298,f40])).
% 0.15/5.60 fof(f352,definition,(
% 0.15/5.60 sQ23_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 0.15/5.60 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.15/5.60 fof(f353,plain,(
% 0.15/5.60 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ23_spl),
% 0.15/5.60 inference(component_clause,[status(thm)],[f352])).
% 0.15/5.60 fof(f361,plain,(
% 0.15/5.60 ![X0]: (convergent_lines(sK0_skl,X0)|~sQ7_spl)),
% 0.15/5.60 inference(duplicate_literals_removal,[status(thm)],[f231])).
% 0.15/5.60 fof(f421,plain,(
% 0.15/5.60 ~convergent_lines(sK1_skl,sK0_skl)|~sQ13_spl),
% 0.15/5.60 inference(resolution,[status(thm)],[f254,f55])).
% 0.15/5.60 fof(f424,plain,(
% 0.15/5.60 $false|~sQ13_spl),
% 0.15/5.60 inference(forward_subsumption_resolution,[status(thm)],[f421,f207])).
% 0.15/5.60 fof(f425,plain,(
% 0.15/5.60 ~sQ13_spl),
% 0.15/5.60 inference(contradiction_clause,[status(thm)],[f424])).
% 0.15/5.61 fof(f426,plain,(
% 0.15/5.61 $false|sQ8_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f236,f129])).
% 0.15/5.61 fof(f427,plain,(
% 0.15/5.61 sQ8_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f426])).
% 0.15/5.61 fof(f538,plain,(
% 0.15/5.61 $false|sQ4_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f221,f207])).
% 0.15/5.61 fof(f539,plain,(
% 0.15/5.61 sQ4_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f538])).
% 0.15/5.61 fof(f544,plain,(
% 0.15/5.61 $false|~sQ7_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f361,f40])).
% 0.15/5.61 fof(f549,plain,(
% 0.15/5.61 ~sQ7_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f544])).
% 0.15/5.61 fof(f723,definition,(
% 0.15/5.61 sQ55_spl <=> (sP1_prd(sK0_skl,sK0_skl))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f724,plain,(
% 0.15/5.61 sP1_prd(sK0_skl,sK0_skl)|~sQ55_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f723])).
% 0.15/5.61 fof(f730,definition,(
% 0.15/5.61 sQ57_spl <=> (sP0_prd(sK0_skl,sK0_skl))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f731,plain,(
% 0.15/5.61 sP0_prd(sK0_skl,sK0_skl)|~sQ57_spl),
% 0.15/5.61 inference(component_clause,[status(thm)],[f730])).
% 0.15/5.61 fof(f746,definition,(
% 0.15/5.61 ![X0]: (sQ61_spl <=> (sP1_prd(sK0_skl,X0)|convergent_lines(X0,sK0_skl)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f747,plain,(
% 0.15/5.61 ![X0]: (sP1_prd(sK0_skl,X0)|convergent_lines(X0,sK0_skl)|~sQ61_spl)),
% 0.15/5.61 inference(component_clause,[status(thm)],[f746])).
% 0.15/5.61 fof(f754,definition,(
% 0.15/5.61 ![X0]: (sQ63_spl <=> (sP0_prd(X0,sK0_skl)|convergent_lines(sK0_skl,X0)))),
% 0.15/5.61 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 0.15/5.61 fof(f755,plain,(
% 0.15/5.61 ![X0]: (sP0_prd(X0,sK0_skl)|convergent_lines(sK0_skl,X0)|~sQ63_spl)),
% 0.15/5.61 inference(component_clause,[status(thm)],[f754])).
% 0.15/5.61 fof(f758,plain,(
% 0.15/5.61 ![X0]: (convergent_lines(sK0_skl,X0)|~sQ63_spl)),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f755,f133])).
% 0.15/5.61 fof(f767,plain,(
% 0.15/5.61 ![X0]: (convergent_lines(X0,sK0_skl)|~sQ61_spl)),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f747,f138])).
% 0.15/5.61 fof(f784,plain,(
% 0.15/5.61 $false|~sQ63_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f758,f40])).
% 0.15/5.61 fof(f786,plain,(
% 0.15/5.61 ~sQ63_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f784])).
% 0.15/5.61 fof(f789,plain,(
% 0.15/5.61 $false|~sQ61_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f767,f71])).
% 0.15/5.61 fof(f797,plain,(
% 0.15/5.61 ~sQ61_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f789])).
% 0.15/5.61 fof(f825,plain,(
% 0.15/5.61 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK1_skl,sK0_skl),sK0_skl)|~sQ12_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f251,f336])).
% 0.15/5.61 fof(f826,plain,(
% 0.15/5.61 sQ23_spl|sQ15_spl|~sQ12_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f825,f352,f261,f250])).
% 0.15/5.61 fof(f828,plain,(
% 0.15/5.61 convergent_lines(sK0_skl,sK0_skl)|~sQ57_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f731,f133])).
% 0.15/5.61 fof(f829,plain,(
% 0.15/5.61 $false|~sQ57_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f828,f40])).
% 0.15/5.61 fof(f830,plain,(
% 0.15/5.61 ~sQ57_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f829])).
% 0.15/5.61 fof(f832,plain,(
% 0.15/5.61 convergent_lines(sK0_skl,sK0_skl)|~sQ55_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f724,f138])).
% 0.15/5.61 fof(f833,plain,(
% 0.15/5.61 $false|~sQ55_spl),
% 0.15/5.61 inference(forward_subsumption_resolution,[status(thm)],[f832,f40])).
% 0.15/5.61 fof(f834,plain,(
% 0.15/5.61 ~sQ55_spl),
% 0.15/5.61 inference(contradiction_clause,[status(thm)],[f833])).
% 0.15/5.61 fof(f858,plain,(
% 0.15/5.61 ~convergent_lines(sK0_skl,sK1_skl)|~sQ23_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f353,f55])).
% 0.15/5.61 fof(f861,plain,(
% 0.15/5.61 ~sQ8_spl|~sQ23_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f858,f234,f352])).
% 0.15/5.61 fof(f888,plain,(
% 0.15/5.61 ~convergent_lines(sK1_skl,sK0_skl)|~sQ15_spl),
% 0.15/5.61 inference(resolution,[status(thm)],[f262,f57])).
% 0.15/5.61 fof(f891,plain,(
% 0.15/5.61 ~sQ4_spl|~sQ15_spl),
% 0.15/5.61 inference(split_clause,[status(thm)],[f888,f219,f261])).
% 0.15/5.61 fof(f894,plain,(
% 0.15/5.61 $false),
% 0.15/5.61 inference(sat_refutation,[status(thm)],[f256,f425,f427,f539,f549,f786,f797,f826,f830,f834,f861,f891])).
% 0.15/5.61 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/5.62 % Elapsed time: 0.222619 seconds
% 0.15/5.62 % CPU time: 1.541861 seconds
% 0.15/5.62 % Total memory used: 34.334 MB
% 0.15/5.62 % Net memory used: 30.970 MB
%------------------------------------------------------------------------------