%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 40.68s 5.58s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.33 % Computer : n013.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Sun Sep 20 13:54:05 UTC 2026
% 0.09/0.33 % CPUTime :
% 0.09/0.34 % Drodi V4.1.1
% 40.68/5.58 % Refutation found
% 40.68/5.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 40.68/5.58 % SZS output start CNFRefutation for theBenchmark
% 40.68/5.58 fof(f2,axiom,(
% 40.68/5.58 (! [X] : ~ distinct_lines(X,X) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f3,axiom,(
% 40.68/5.58 (! [X] : ~ convergent_lines(X,X) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f5,axiom,(
% 40.68/5.58 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f6,axiom,(
% 40.68/5.58 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f15,axiom,(
% 40.68/5.58 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f16,axiom,(
% 40.68/5.58 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f18,axiom,(
% 40.68/5.58 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f19,axiom,(
% 40.68/5.58 (! [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) ) ) ) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f20,axiom,(
% 40.68/5.58 (! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f21,axiom,(
% 40.68/5.58 (! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f22,axiom,(
% 40.68/5.58 (! [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) ) ) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f23,conjecture,(
% 40.68/5.58 (! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)) )),
% 40.68/5.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 40.68/5.58 fof(f24,negated_conjecture,(
% 40.68/5.58 ~((! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)) ))),
% 40.68/5.58 inference(negated_conjecture,[status(cth)],[f23])).
% 40.68/5.58 fof(f26,plain,(
% 40.68/5.58 ![X0]: (~distinct_lines(X0,X0))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f2])).
% 40.68/5.58 fof(f27,plain,(
% 40.68/5.58 ![X0]: (~convergent_lines(X0,X0))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f3])).
% 40.68/5.58 fof(f31,plain,(
% 40.68/5.58 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 40.68/5.58 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 40.68/5.58 fof(f32,plain,(
% 40.68/5.58 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 40.68/5.58 inference(miniscoping,[status(thm)],[f31])).
% 40.68/5.58 fof(f33,plain,(
% 40.68/5.58 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f32])).
% 40.68/5.58 fof(f34,plain,(
% 40.68/5.58 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 40.68/5.58 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 40.68/5.58 fof(f35,plain,(
% 40.68/5.58 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 40.68/5.58 inference(miniscoping,[status(thm)],[f34])).
% 40.68/5.58 fof(f36,plain,(
% 40.68/5.58 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f35])).
% 40.68/5.58 fof(f56,plain,(
% 40.68/5.58 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f15])).
% 40.68/5.58 fof(f57,plain,(
% 40.68/5.58 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f16])).
% 40.68/5.58 fof(f61,plain,(
% 40.68/5.58 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f18])).
% 40.68/5.58 fof(f62,plain,(
% 40.68/5.58 ![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))))),
% 40.68/5.58 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 40.68/5.58 fof(f63,definition,(
% 40.68/5.58 ![L,N]: (sP0_prd(N,L)<=>(convergent_lines(L,N)&unorthogonal_lines(L,N)))),
% 40.68/5.58 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 40.68/5.58 fof(f64,plain,(
% 40.68/5.58 ![L,M,N]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N))))),
% 40.68/5.58 inference(formula_renaming,[status(thm)],[f62,f63])).
% 40.68/5.58 fof(f65,plain,(
% 40.68/5.58 ![L,M]: ((~convergent_lines(L,M)|~unorthogonal_lines(L,M))|(![N]: (sP0_prd(N,L)|(convergent_lines(M,N)&unorthogonal_lines(M,N)))))),
% 40.68/5.58 inference(miniscoping,[status(thm)],[f64])).
% 40.68/5.58 fof(f67,plain,(
% 40.68/5.58 ![X0,X1,X2]: (~convergent_lines(X0,X1)|~unorthogonal_lines(X0,X1)|sP0_prd(X2,X0)|unorthogonal_lines(X1,X2))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f65])).
% 40.68/5.58 fof(f68,plain,(
% 40.68/5.58 ![X0,X1]: (~unorthogonal_lines(orthogonal_through_point(X0,X1),X0))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f20])).
% 40.68/5.58 fof(f69,plain,(
% 40.68/5.58 ![X0,X1]: (~apart_point_and_line(X0,orthogonal_through_point(X1,X0)))),
% 40.68/5.58 inference(cnf_transformation,[status(thm)],[f21])).
% 40.68/5.59 fof(f70,plain,(
% 40.68/5.59 ![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)))),
% 40.68/5.59 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 40.68/5.59 fof(f71,plain,(
% 40.68/5.59 ![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))))),
% 40.68/5.59 inference(miniscoping,[status(thm)],[f70])).
% 40.68/5.59 fof(f72,plain,(
% 40.68/5.59 ![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))),
% 40.68/5.59 inference(cnf_transformation,[status(thm)],[f71])).
% 40.68/5.59 fof(f73,plain,(
% 40.68/5.59 (?[A,L]: distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)))),
% 40.68/5.59 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 40.68/5.59 fof(f74,plain,(
% 40.68/5.59 distinct_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 40.68/5.59 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(L,sK1_skl)],[f73])).
% 40.68/5.59 fof(f75,plain,(
% 40.68/5.59 distinct_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))),
% 40.68/5.59 inference(cnf_transformation,[status(thm)],[f74])).
% 40.68/5.59 fof(f76,plain,(
% 40.68/5.59 ![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))))),
% 40.68/5.59 inference(NNF_transformation,[status(thm)],[f63])).
% 40.68/5.59 fof(f77,plain,(
% 40.68/5.59 (![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))))),
% 40.68/5.59 inference(miniscoping,[status(thm)],[f76])).
% 40.68/5.59 fof(f78,plain,(
% 40.68/5.59 ![X0,X1]: (~sP0_prd(X0,X1)|convergent_lines(X1,X0))),
% 40.68/5.59 inference(cnf_transformation,[status(thm)],[f77])).
% 40.68/5.59 fof(f81,plain,(
% 40.68/5.59 ![X0]: (distinct_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0))),
% 40.68/5.59 inference(resolution,[status(thm)],[f33,f75])).
% 40.68/5.59 fof(f98,definition,(
% 40.68/5.59 ![X0]: (sQ1_spl <=> (distinct_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|distinct_lines(parallel_through_point(sK1_skl,sK0_skl),X0)))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f99,plain,(
% 40.68/5.59 ![X0]: (distinct_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|distinct_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|~sQ1_spl)),
% 40.68/5.59 inference(component_clause,[status(thm)],[f98])).
% 40.68/5.59 fof(f265,definition,(
% 40.68/5.59 ![X0]: (sQ10_spl <=> (apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f266,plain,(
% 40.68/5.59 ![X0]: (apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|~sQ10_spl)),
% 40.68/5.59 inference(component_clause,[status(thm)],[f265])).
% 40.68/5.59 fof(f273,definition,(
% 40.68/5.59 ![X0]: (sQ12_spl <=> (apart_point_and_line(X0,parallel_through_point(sK1_skl,sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f274,plain,(
% 40.68/5.59 ![X0]: (apart_point_and_line(X0,parallel_through_point(sK1_skl,sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|~sQ12_spl)),
% 40.68/5.59 inference(component_clause,[status(thm)],[f273])).
% 40.68/5.59 fof(f299,plain,(
% 40.68/5.59 apart_point_and_line(sK0_skl,parallel_through_point(sK1_skl,sK0_skl))|~sQ12_spl),
% 40.68/5.59 inference(resolution,[status(thm)],[f274,f69])).
% 40.68/5.59 fof(f301,plain,(
% 40.68/5.59 $false|~sQ12_spl),
% 40.68/5.59 inference(forward_subsumption_resolution,[status(thm)],[f299,f57])).
% 40.68/5.59 fof(f302,plain,(
% 40.68/5.59 ~sQ12_spl),
% 40.68/5.59 inference(contradiction_clause,[status(thm)],[f301])).
% 40.68/5.59 fof(f456,definition,(
% 40.68/5.59 ![X0]: (sQ24_spl <=> (apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f457,plain,(
% 40.68/5.59 ![X0]: (apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|~sQ24_spl)),
% 40.68/5.59 inference(component_clause,[status(thm)],[f456])).
% 40.68/5.59 fof(f637,plain,(
% 40.68/5.59 ![X0,X1]: (convergent_lines(orthogonal_through_point(X0,X1),X0))),
% 40.68/5.59 inference(resolution,[status(thm)],[f61,f68])).
% 40.68/5.59 fof(f688,plain,(
% 40.68/5.59 ![X0,X1,X2]: (apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|apart_point_and_line(X0,X1)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X2)|unorthogonal_lines(X1,X2)|distinct_lines(parallel_through_point(sK1_skl,sK0_skl),X1))),
% 40.68/5.59 inference(resolution,[status(thm)],[f72,f81])).
% 40.68/5.59 fof(f832,definition,(
% 40.68/5.59 sQ41_spl <=> (convergent_lines(sK1_skl,sK1_skl))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f833,plain,(
% 40.68/5.59 convergent_lines(sK1_skl,sK1_skl)|~sQ41_spl),
% 40.68/5.59 inference(component_clause,[status(thm)],[f832])).
% 40.68/5.59 fof(f1193,plain,(
% 40.68/5.59 ![X0,X1,X2,X3,X4]: (apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|apart_point_and_line(X0,X1)|unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X2)|unorthogonal_lines(X1,X2)|apart_point_and_line(X3,parallel_through_point(sK1_skl,sK0_skl))|apart_point_and_line(X3,X1)|unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),X4)|unorthogonal_lines(X1,X4))),
% 40.68/5.59 inference(resolution,[status(thm)],[f688,f72])).
% 40.68/5.59 fof(f1398,plain,(
% 40.68/5.59 ![X0,X1,X2]: (convergent_lines(orthogonal_through_point(X0,X1),X2)|convergent_lines(X0,X2))),
% 40.68/5.59 inference(resolution,[status(thm)],[f637,f36])).
% 40.68/5.59 fof(f1539,definition,(
% 40.68/5.59 sQ99_spl <=> (convergent_lines(parallel_through_point(sK1_skl,sK0_skl),sK1_skl))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f1540,plain,(
% 40.68/5.59 convergent_lines(parallel_through_point(sK1_skl,sK0_skl),sK1_skl)|~sQ99_spl),
% 40.68/5.59 inference(component_clause,[status(thm)],[f1539])).
% 40.68/5.59 fof(f1560,plain,(
% 40.68/5.59 ![X0,X1,X2,X3]: (convergent_lines(X0,X1)|convergent_lines(orthogonal_through_point(X0,X2),X3)|convergent_lines(X1,X3))),
% 40.68/5.59 inference(resolution,[status(thm)],[f1398,f36])).
% 40.68/5.59 fof(f1562,plain,(
% 40.68/5.59 ![X0,X1]: (convergent_lines(X0,orthogonal_through_point(X0,X1)))),
% 40.68/5.59 inference(resolution,[status(thm)],[f1398,f27])).
% 40.68/5.59 fof(f1757,plain,(
% 40.68/5.59 ![X0,X1,X2]: (convergent_lines(X0,X1)|convergent_lines(X1,orthogonal_through_point(X0,X2)))),
% 40.68/5.59 inference(resolution,[status(thm)],[f1560,f27])).
% 40.68/5.59 fof(f2074,definition,(
% 40.68/5.59 ![X0]: (sQ139_spl <=> (convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f2075,plain,(
% 40.68/5.59 ![X0]: (convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl),X0)|~sQ139_spl)),
% 40.68/5.59 inference(component_clause,[status(thm)],[f2074])).
% 40.68/5.59 fof(f4098,plain,(
% 40.68/5.59 ![X0]: (apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|~sQ10_spl)),
% 40.68/5.59 inference(duplicate_literals_removal,[status(thm)],[f266])).
% 40.68/5.59 fof(f5029,plain,(
% 40.68/5.59 ![X0,X1]: (apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|apart_point_and_line(X0,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|apart_point_and_line(X1,parallel_through_point(sK1_skl,sK0_skl))|apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(sK1_skl,sK0_skl),sK0_skl))|unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)))),
% 40.68/5.59 inference(resolution,[status(thm)],[f1193,f68])).
% 40.68/5.59 fof(f5096,definition,(
% 40.68/5.59 sQ275_spl <=> (unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f5097,plain,(
% 40.68/5.59 unorthogonal_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl))|~sQ275_spl),
% 40.68/5.59 inference(component_clause,[status(thm)],[f5096])).
% 40.68/5.59 fof(f5099,plain,(
% 40.68/5.59 sQ10_spl|sQ12_spl|sQ275_spl),
% 40.68/5.59 inference(split_clause,[status(thm)],[f5029,f265,f273,f5096])).
% 40.68/5.59 fof(f5697,plain,(
% 40.68/5.59 $false|~sQ10_spl),
% 40.68/5.59 inference(resolution,[status(thm)],[f4098,f69])).
% 40.68/5.59 fof(f5702,plain,(
% 40.68/5.59 ~sQ10_spl),
% 40.68/5.59 inference(contradiction_clause,[status(thm)],[f5697])).
% 40.68/5.59 fof(f6665,plain,(
% 40.68/5.59 ![X0]: (~convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl))|sP0_prd(X0,parallel_through_point(sK1_skl,sK0_skl))|unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)|~sQ275_spl)),
% 40.68/5.59 inference(resolution,[status(thm)],[f5097,f67])).
% 40.68/5.59 fof(f6668,definition,(
% 40.68/5.59 sQ304_spl <=> (convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl)))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f6670,plain,(
% 40.68/5.59 ~convergent_lines(parallel_through_point(sK1_skl,sK0_skl),orthogonal_through_point(sK1_skl,sK0_skl))|sQ304_spl),
% 40.68/5.59 inference(component_clause,[status(thm)],[f6668])).
% 40.68/5.59 fof(f6671,definition,(
% 40.68/5.59 ![X0]: (sQ305_spl <=> (sP0_prd(X0,parallel_through_point(sK1_skl,sK0_skl))|unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f6672,plain,(
% 40.68/5.59 ![X0]: (sP0_prd(X0,parallel_through_point(sK1_skl,sK0_skl))|unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)|~sQ305_spl)),
% 40.68/5.59 inference(component_clause,[status(thm)],[f6671])).
% 40.68/5.59 fof(f6674,plain,(
% 40.68/5.59 ~sQ304_spl|sQ305_spl|~sQ275_spl),
% 40.68/5.59 inference(split_clause,[status(thm)],[f6665,f6668,f6671,f5096])).
% 40.68/5.59 fof(f9063,plain,(
% 40.68/5.59 convergent_lines(sK1_skl,parallel_through_point(sK1_skl,sK0_skl))|sQ304_spl),
% 40.68/5.59 inference(resolution,[status(thm)],[f6670,f1757])).
% 40.68/5.59 fof(f11073,plain,(
% 40.68/5.59 $false|~sQ99_spl),
% 40.68/5.59 inference(forward_subsumption_resolution,[status(thm)],[f1540,f56])).
% 40.68/5.59 fof(f11074,plain,(
% 40.68/5.59 ~sQ99_spl),
% 40.68/5.59 inference(contradiction_clause,[status(thm)],[f11073])).
% 40.68/5.59 fof(f12715,plain,(
% 40.68/5.59 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|sQ304_spl)),
% 40.68/5.59 inference(resolution,[status(thm)],[f9063,f36])).
% 40.68/5.59 fof(f12743,plain,(
% 40.68/5.59 convergent_lines(sK1_skl,sK1_skl)|sQ304_spl),
% 40.68/5.59 inference(resolution,[status(thm)],[f12715,f56])).
% 40.68/5.59 fof(f12759,plain,(
% 40.68/5.59 $false|sQ304_spl),
% 40.68/5.59 inference(forward_subsumption_resolution,[status(thm)],[f12743,f27])).
% 40.68/5.59 fof(f12760,plain,(
% 40.68/5.59 sQ304_spl),
% 40.68/5.59 inference(contradiction_clause,[status(thm)],[f12759])).
% 40.68/5.59 fof(f12778,plain,(
% 40.68/5.59 ![X0]: (unorthogonal_lines(orthogonal_through_point(sK1_skl,sK0_skl),X0)|convergent_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|~sQ305_spl)),
% 40.68/5.59 inference(resolution,[status(thm)],[f6672,f78])).
% 40.68/5.59 fof(f14360,definition,(
% 40.68/5.59 sQ492_spl <=> (convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl)))),
% 40.68/5.59 introduced(definition,[new_symbols(definition,[sQ492_spl])],[split_symbol_definition])).
% 40.68/5.59 fof(f14362,plain,(
% 40.68/5.59 ~convergent_lines(sK1_skl,orthogonal_through_point(sK1_skl,sK0_skl))|sQ492_spl),
% 40.68/5.59 inference(component_clause,[status(thm)],[f14360])).
% 40.68/5.59 fof(f14375,plain,(
% 40.68/5.59 $false|sQ492_spl),
% 40.68/5.59 inference(forward_subsumption_resolution,[status(thm)],[f14362,f1562])).
% 40.68/5.59 fof(f14376,plain,(
% 40.68/5.59 sQ492_spl),
% 40.68/5.59 inference(contradiction_clause,[status(thm)],[f14375])).
% 40.68/5.59 fof(f14389,plain,(
% 40.68/5.59 $false|~sQ139_spl),
% 40.68/5.59 inference(resolution,[status(thm)],[f2075,f27])).
% 40.68/5.59 fof(f14394,plain,(
% 40.68/5.59 ~sQ139_spl),
% 40.68/5.59 inference(contradiction_clause,[status(thm)],[f14389])).
% 40.68/5.59 fof(f14434,plain,(
% 40.68/5.59 $false|~sQ41_spl),
% 40.68/5.59 inference(forward_subsumption_resolution,[status(thm)],[f833,f27])).
% 40.68/5.59 fof(f14435,plain,(
% 40.68/5.59 ~sQ41_spl),
% 40.68/5.59 inference(contradiction_clause,[status(thm)],[f14434])).
% 40.68/5.59 fof(f14438,plain,(
% 40.68/5.59 ![X0]: (distinct_lines(parallel_through_point(sK1_skl,sK0_skl),X0)|~sQ1_spl)),
% 40.68/5.59 inference(duplicate_literals_removal,[status(thm)],[f99])).
% 40.68/5.59 fof(f14443,plain,(
% 40.68/5.59 $false|~sQ24_spl),
% 40.68/5.59 inference(resolution,[status(thm)],[f457,f69])).
% 40.68/5.59 fof(f14448,plain,(
% 40.68/5.59 ~sQ24_spl),
% 40.68/5.59 inference(contradiction_clause,[status(thm)],[f14443])).
% 40.68/5.59 fof(f14453,plain,(
% 40.68/5.59 $false|~sQ1_spl),
% 40.68/5.59 inference(resolution,[status(thm)],[f14438,f26])).
% 40.68/5.59 fof(f14455,plain,(
% 40.68/5.59 ~sQ1_spl),
% 40.68/5.59 inference(contradiction_clause,[status(thm)],[f14453])).
% 40.68/5.59 fof(f14841,plain,(
% 40.68/5.59 convergent_lines(parallel_through_point(sK1_skl,sK0_skl),sK1_skl)|~sQ305_spl),
% 40.68/5.59 inference(resolution,[status(thm)],[f12778,f68])).
% 40.68/5.59 fof(f14845,plain,(
% 40.68/5.59 sQ99_spl|~sQ305_spl),
% 40.68/5.59 inference(split_clause,[status(thm)],[f14841,f1539,f6671])).
% 40.68/5.59 fof(f14846,plain,(
% 40.68/5.59 $false),
% 40.68/5.59 inference(sat_refutation,[status(thm)],[f302,f5099,f5702,f6674,f11074,f12760,f14376,f14394,f14435,f14448,f14455,f14845])).
% 40.68/5.59 % SZS output end CNFRefutation for theBenchmark.p
% 40.68/5.61 % Elapsed time: 5.265178 seconds
% 40.68/5.61 % CPU time: 41.474888 seconds
% 40.68/5.61 % Total memory used: 170.130 MB
% 40.68/5.61 % Net memory used: 129.195 MB
%------------------------------------------------------------------------------