%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO205+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 : n014.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 12:26:05 PM UTC 2026
% Result : Theorem 10.45s 2.03s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO205+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n014.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sun Sep 20 13:26:35 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.58 % Drodi V4.1.1
% 10.45/2.03 % Refutation found
% 10.45/2.03 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.45/2.03 % SZS output start CNFRefutation for theBenchmark
% 10.45/2.03 fof(f2,axiom,(
% 10.45/2.03 (! [X] : ~ distinct_lines(X,X) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f3,axiom,(
% 10.45/2.03 (! [X] : ~ convergent_lines(X,X) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f5,axiom,(
% 10.45/2.03 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f6,axiom,(
% 10.45/2.03 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f11,axiom,(
% 10.45/2.03 (! [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) ) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f13,axiom,(
% 10.45/2.03 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f14,axiom,(
% 10.45/2.03 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f15,axiom,(
% 10.45/2.03 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f16,axiom,(
% 10.45/2.03 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f17,axiom,(
% 10.45/2.03 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f19,axiom,(
% 10.45/2.03 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f21,axiom,(
% 10.45/2.03 (! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f31,axiom,(
% 10.45/2.03 (! [X,Y] :( equal_points(X,Y)<=> ~ distinct_points(X,Y) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f32,axiom,(
% 10.45/2.03 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f34,axiom,(
% 10.45/2.03 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f36,conjecture,(
% 10.45/2.03 (! [X,Y,Z] :( ( convergent_lines(X,Y)& equal_lines(Y,Z) )=> ( convergent_lines(X,Z)& equal_points(intersection_point(X,Y),intersection_point(X,Z)) ) ) )),
% 10.45/2.03 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 10.45/2.03 fof(f37,negated_conjecture,(
% 10.45/2.03 ~((! [X,Y,Z] :( ( convergent_lines(X,Y)& equal_lines(Y,Z) )=> ( convergent_lines(X,Z)& equal_points(intersection_point(X,Y),intersection_point(X,Z)) ) ) ))),
% 10.45/2.03 inference(negated_conjecture,[status(cth)],[f36])).
% 10.45/2.03 fof(f39,plain,(
% 10.45/2.03 ![X0]: (~distinct_lines(X0,X0))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f2])).
% 10.45/2.03 fof(f40,plain,(
% 10.45/2.03 ![X0]: (~convergent_lines(X0,X0))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f3])).
% 10.45/2.03 fof(f44,plain,(
% 10.45/2.03 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 10.45/2.03 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 10.45/2.03 fof(f45,plain,(
% 10.45/2.03 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 10.45/2.03 inference(miniscoping,[status(thm)],[f44])).
% 10.45/2.03 fof(f46,plain,(
% 10.45/2.03 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f45])).
% 10.45/2.03 fof(f47,plain,(
% 10.45/2.03 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 10.45/2.03 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 10.45/2.03 fof(f48,plain,(
% 10.45/2.03 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 10.45/2.03 inference(miniscoping,[status(thm)],[f47])).
% 10.45/2.03 fof(f49,plain,(
% 10.45/2.03 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f48])).
% 10.45/2.03 fof(f58,plain,(
% 10.45/2.03 ![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)))),
% 10.45/2.03 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 10.45/2.03 fof(f59,plain,(
% 10.45/2.03 ![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))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f58])).
% 10.45/2.03 fof(f63,plain,(
% 10.45/2.03 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 10.45/2.03 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 10.45/2.03 fof(f64,plain,(
% 10.45/2.03 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 10.45/2.03 inference(miniscoping,[status(thm)],[f63])).
% 10.45/2.03 fof(f65,plain,(
% 10.45/2.03 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f64])).
% 10.45/2.03 fof(f66,plain,(
% 10.45/2.03 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 10.45/2.03 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 10.45/2.03 fof(f67,plain,(
% 10.45/2.03 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 10.45/2.03 inference(miniscoping,[status(thm)],[f66])).
% 10.45/2.03 fof(f68,plain,(
% 10.45/2.03 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f67])).
% 10.45/2.03 fof(f69,plain,(
% 10.45/2.03 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 10.45/2.03 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 10.45/2.03 fof(f70,plain,(
% 10.45/2.03 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f69])).
% 10.45/2.03 fof(f71,plain,(
% 10.45/2.03 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f16])).
% 10.45/2.03 fof(f72,plain,(
% 10.45/2.03 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f17])).
% 10.45/2.03 fof(f76,plain,(
% 10.45/2.03 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f19])).
% 10.45/2.03 fof(f83,plain,(
% 10.45/2.03 ![X0,X1]: (~unorthogonal_lines(orthogonal_through_point(X0,X1),X0))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f21])).
% 10.45/2.03 fof(f107,plain,(
% 10.45/2.03 ![X,Y]: ((~equal_points(X,Y)|~distinct_points(X,Y))&(equal_points(X,Y)|distinct_points(X,Y)))),
% 10.45/2.03 inference(NNF_transformation,[status(thm)],[f31])).
% 10.45/2.03 fof(f108,plain,(
% 10.45/2.03 (![X,Y]: (~equal_points(X,Y)|~distinct_points(X,Y)))&(![X,Y]: (equal_points(X,Y)|distinct_points(X,Y)))),
% 10.45/2.03 inference(miniscoping,[status(thm)],[f107])).
% 10.45/2.03 fof(f110,plain,(
% 10.45/2.03 ![X0,X1]: (equal_points(X0,X1)|distinct_points(X0,X1))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f108])).
% 10.45/2.03 fof(f111,plain,(
% 10.45/2.03 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 10.45/2.03 inference(NNF_transformation,[status(thm)],[f32])).
% 10.45/2.03 fof(f112,plain,(
% 10.45/2.03 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 10.45/2.03 inference(miniscoping,[status(thm)],[f111])).
% 10.45/2.03 fof(f113,plain,(
% 10.45/2.03 ![X0,X1]: (~equal_lines(X0,X1)|~distinct_lines(X0,X1))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f112])).
% 10.45/2.03 fof(f114,plain,(
% 10.45/2.03 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f112])).
% 10.45/2.03 fof(f119,plain,(
% 10.45/2.03 ![X,Y]: ((~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y))&(incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 10.45/2.03 inference(NNF_transformation,[status(thm)],[f34])).
% 10.45/2.03 fof(f120,plain,(
% 10.45/2.03 (![X,Y]: (~incident_point_and_line(X,Y)|~apart_point_and_line(X,Y)))&(![X,Y]: (incident_point_and_line(X,Y)|apart_point_and_line(X,Y)))),
% 10.45/2.03 inference(miniscoping,[status(thm)],[f119])).
% 10.45/2.03 fof(f121,plain,(
% 10.45/2.03 ![X0,X1]: (~incident_point_and_line(X0,X1)|~apart_point_and_line(X0,X1))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f120])).
% 10.45/2.03 fof(f122,plain,(
% 10.45/2.03 ![X0,X1]: (incident_point_and_line(X0,X1)|apart_point_and_line(X0,X1))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f120])).
% 10.45/2.03 fof(f127,plain,(
% 10.45/2.03 (?[X,Y,Z]: ((convergent_lines(X,Y)&equal_lines(Y,Z))&(~convergent_lines(X,Z)|~equal_points(intersection_point(X,Y),intersection_point(X,Z)))))),
% 10.45/2.03 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 10.45/2.03 fof(f128,plain,(
% 10.45/2.03 ((convergent_lines(sK0_skl,sK1_skl)&equal_lines(sK1_skl,sK2_skl))&(~convergent_lines(sK0_skl,sK2_skl)|~equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))))),
% 10.45/2.03 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl)],[f127])).
% 10.45/2.03 fof(f129,plain,(
% 10.45/2.03 convergent_lines(sK0_skl,sK1_skl)),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f128])).
% 10.45/2.03 fof(f130,plain,(
% 10.45/2.03 equal_lines(sK1_skl,sK2_skl)),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f128])).
% 10.45/2.03 fof(f131,plain,(
% 10.45/2.03 ~convergent_lines(sK0_skl,sK2_skl)|~equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))),
% 10.45/2.03 inference(cnf_transformation,[status(thm)],[f128])).
% 10.45/2.03 fof(f142,definition,(
% 10.45/2.03 sQ0_spl <=> (convergent_lines(sK0_skl,sK2_skl))),
% 10.45/2.03 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 10.45/2.03 fof(f145,definition,(
% 10.45/2.03 sQ1_spl <=> (equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))),
% 10.45/2.03 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 10.45/2.03 fof(f147,plain,(
% 10.45/2.03 ~equal_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))|sQ1_spl),
% 10.45/2.03 inference(component_clause,[status(thm)],[f145])).
% 10.45/2.03 fof(f148,plain,(
% 10.45/2.03 ~sQ0_spl|~sQ1_spl),
% 10.45/2.03 inference(split_clause,[status(thm)],[f131,f142,f145])).
% 10.45/2.03 fof(f149,plain,(
% 10.45/2.03 ![X0]: (convergent_lines(sK0_skl,X0)|convergent_lines(sK1_skl,X0))),
% 10.45/2.03 inference(resolution,[status(thm)],[f49,f129])).
% 10.45/2.03 fof(f187,definition,(
% 10.45/2.03 sQ6_spl <=> (convergent_lines(sK1_skl,sK1_skl))),
% 10.45/2.03 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 10.45/2.03 fof(f188,plain,(
% 10.45/2.03 convergent_lines(sK1_skl,sK1_skl)|~sQ6_spl),
% 10.45/2.03 inference(component_clause,[status(thm)],[f187])).
% 10.45/2.03 fof(f261,plain,(
% 10.45/2.03 ![X0,X1,X2]: (distinct_lines(X0,X1)|distinct_lines(X2,X1)|equal_lines(X0,X2))),
% 10.45/2.03 inference(resolution,[status(thm)],[f46,f114])).
% 10.45/2.03 fof(f263,plain,(
% 10.45/2.03 ![X0,X1,X2]: (distinct_lines(X0,X1)|apart_point_and_line(X2,X1)|incident_point_and_line(X2,X0))),
% 10.45/2.03 inference(resolution,[status(thm)],[f65,f122])).
% 10.45/2.03 fof(f280,plain,(
% 10.45/2.03 ![X0,X1]: (distinct_lines(X0,X1)|convergent_lines(sK0_skl,X1)|convergent_lines(sK1_skl,X0))),
% 10.45/2.03 inference(resolution,[status(thm)],[f68,f149])).
% 10.45/2.03 fof(f292,plain,(
% 10.45/2.03 ![X0,X1,X2]: (distinct_lines(X0,X1)|convergent_lines(X2,X1)|unorthogonal_lines(X2,X0))),
% 10.45/2.03 inference(resolution,[status(thm)],[f68,f76])).
% 10.45/2.03 fof(f357,plain,(
% 10.45/2.03 ![X0,X1,X2,X3]: (~distinct_lines(X0,X1)|apart_point_and_line(X2,X0)|apart_point_and_line(X2,X1)|apart_point_and_line(X3,X0)|apart_point_and_line(X3,X1)|equal_points(X2,X3))),
% 10.45/2.03 inference(resolution,[status(thm)],[f59,f110])).
% 10.45/2.03 fof(f409,plain,(
% 10.45/2.03 ~distinct_lines(sK1_skl,sK2_skl)),
% 10.45/2.03 inference(resolution,[status(thm)],[f113,f130])).
% 10.45/2.03 fof(f414,plain,(
% 10.45/2.03 ![X0,X1]: (distinct_lines(X0,X1)|equal_lines(X1,X0))),
% 10.45/2.03 inference(resolution,[status(thm)],[f261,f39])).
% 10.45/2.03 fof(f444,plain,(
% 10.45/2.03 ![X0,X1,X2]: (distinct_lines(X0,parallel_through_point(X1,X2))|incident_point_and_line(X2,X0))),
% 10.45/2.03 inference(resolution,[status(thm)],[f263,f72])).
% 10.45/2.03 fof(f470,plain,(
% 10.45/2.03 ![X0,X1]: (convergent_lines(X0,X1)|equal_lines(X1,X0))),
% 10.45/2.03 inference(resolution,[status(thm)],[f70,f414])).
% 10.45/2.03 fof(f562,plain,(
% 10.45/2.03 convergent_lines(sK0_skl,sK2_skl)|convergent_lines(sK1_skl,sK1_skl)),
% 10.45/2.03 inference(resolution,[status(thm)],[f409,f280])).
% 10.45/2.03 fof(f564,plain,(
% 10.45/2.03 sQ0_spl|sQ6_spl),
% 10.45/2.03 inference(split_clause,[status(thm)],[f562,f142,f187])).
% 10.45/2.03 fof(f565,plain,(
% 10.45/2.03 $false|~sQ6_spl),
% 10.45/2.03 inference(forward_subsumption_resolution,[status(thm)],[f188,f40])).
% 10.45/2.03 fof(f566,plain,(
% 10.45/2.03 ~sQ6_spl),
% 10.45/2.03 inference(contradiction_clause,[status(thm)],[f565])).
% 10.45/2.03 fof(f652,plain,(
% 10.45/2.03 ![X0,X1]: (equal_lines(X0,parallel_through_point(X0,X1)))),
% 10.45/2.03 inference(resolution,[status(thm)],[f470,f71])).
% 10.45/2.03 fof(f675,plain,(
% 10.45/2.03 ![X0,X1]: (~distinct_lines(X0,parallel_through_point(X0,X1)))),
% 10.45/2.03 inference(resolution,[status(thm)],[f652,f113])).
% 10.45/2.04 fof(f680,plain,(
% 10.45/2.04 ![X0,X1]: (incident_point_and_line(X0,X1))),
% 10.45/2.04 inference(resolution,[status(thm)],[f675,f444])).
% 10.45/2.04 fof(f691,plain,(
% 10.45/2.04 ![X0,X1]: (~apart_point_and_line(X0,X1))),
% 10.45/2.04 inference(backward_subsumption_resolution,[status(thm)],[f121,f680])).
% 10.45/2.04 fof(f692,plain,(
% 10.45/2.04 ![X0,X1,X2,X3]: (~distinct_lines(X0,X1)|apart_point_and_line(X2,X0)|apart_point_and_line(X2,X1)|apart_point_and_line(X3,X0)|equal_points(X2,X3))),
% 10.45/2.04 inference(backward_subsumption_resolution,[status(thm)],[f357,f691])).
% 10.45/2.04 fof(f707,plain,(
% 10.45/2.04 ![X0,X1,X2,X3]: (~distinct_lines(X0,X1)|apart_point_and_line(X2,X1)|apart_point_and_line(X3,X0)|equal_points(X2,X3))),
% 10.45/2.04 inference(forward_subsumption_resolution,[status(thm)],[f692,f691])).
% 10.45/2.04 fof(f1457,plain,(
% 10.45/2.04 ![X0,X1,X2]: (distinct_lines(X0,X1)|convergent_lines(orthogonal_through_point(X0,X2),X1))),
% 10.45/2.04 inference(resolution,[status(thm)],[f292,f83])).
% 10.45/2.04 fof(f2930,plain,(
% 10.45/2.04 ![X0,X1]: (distinct_lines(X0,orthogonal_through_point(X0,X1)))),
% 10.45/2.04 inference(resolution,[status(thm)],[f1457,f40])).
% 10.45/2.04 fof(f2931,plain,(
% 10.45/2.04 ![X0,X1,X2,X3]: (apart_point_and_line(X0,orthogonal_through_point(X1,X2))|apart_point_and_line(X3,X1)|equal_points(X0,X3))),
% 10.45/2.04 inference(resolution,[status(thm)],[f2930,f707])).
% 10.45/2.04 fof(f2935,plain,(
% 10.45/2.04 ![X0,X1,X2]: (apart_point_and_line(X0,X1)|equal_points(X2,X0))),
% 10.45/2.04 inference(forward_subsumption_resolution,[status(thm)],[f2931,f691])).
% 10.45/2.04 fof(f2937,plain,(
% 10.45/2.04 ![X0]: (apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0)|sQ1_spl)),
% 10.45/2.04 inference(resolution,[status(thm)],[f2935,f147])).
% 10.45/2.04 fof(f2941,plain,(
% 10.45/2.04 $false|sQ1_spl),
% 10.45/2.04 inference(forward_subsumption_resolution,[status(thm)],[f2937,f691])).
% 10.45/2.04 fof(f2942,plain,(
% 10.45/2.04 sQ1_spl),
% 10.45/2.04 inference(contradiction_clause,[status(thm)],[f2941])).
% 10.45/2.04 fof(f2943,plain,(
% 10.45/2.04 $false),
% 10.45/2.04 inference(sat_refutation,[status(thm)],[f148,f564,f566,f2942])).
% 10.45/2.04 % SZS output end CNFRefutation for theBenchmark.p
% 9.55/2.07 % Elapsed time: 1.479158 seconds
% 9.55/2.07 % CPU time: 11.546888 seconds
% 9.55/2.07 % Total memory used: 70.415 MB
% 9.55/2.07 % Net memory used: 58.653 MB
%------------------------------------------------------------------------------