%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO225+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO225+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 13:51:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f1,axiom,(
% 0.10/0.40 (! [X] : ~ distinct_points(X,X) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f7,axiom,(
% 0.10/0.40 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f17,conjecture,(
% 0.10/0.40 (! [A,B] :( ( point(A)& point(B)& distinct_points(A,B) )=> (? [X] :( line(X)=> ( ~ apart_point_and_line(A,X)& ~ apart_point_and_line(B,X) ) ) )) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f18,negated_conjecture,(
% 0.10/0.40 ~((! [A,B] :( ( point(A)& point(B)& distinct_points(A,B) )=> (? [X] :( line(X)=> ( ~ apart_point_and_line(A,X)& ~ apart_point_and_line(B,X) ) ) )) ))),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f17])).
% 0.10/0.40 fof(f19,plain,(
% 0.10/0.40 ![X0]: (~distinct_points(X0,X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.40 fof(f31,plain,(
% 0.10/0.40 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.10/0.40 fof(f32,plain,(
% 0.10/0.40 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f31])).
% 0.10/0.40 fof(f33,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f32])).
% 0.10/0.40 fof(f34,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f32])).
% 0.10/0.40 fof(f57,plain,(
% 0.10/0.40 (?[A,B]: (((point(A)&point(B))&distinct_points(A,B))&(![X]: (line(X)&(apart_point_and_line(A,X)|apart_point_and_line(B,X))))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.10/0.40 fof(f58,plain,(
% 0.10/0.40 ?[A,B]: (((point(A)&point(B))&distinct_points(A,B))&((![X]: line(X))&(![X]: (apart_point_and_line(A,X)|apart_point_and_line(B,X)))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f57])).
% 0.10/0.40 fof(f59,plain,(
% 0.10/0.40 (((point(sK0_skl)&point(sK1_skl))&distinct_points(sK0_skl,sK1_skl))&((![X]: line(X))&(![X]: (apart_point_and_line(sK0_skl,X)|apart_point_and_line(sK1_skl,X)))))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f58])).
% 0.10/0.40 fof(f62,plain,(
% 0.10/0.40 distinct_points(sK0_skl,sK1_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f59])).
% 0.10/0.40 fof(f64,plain,(
% 0.10/0.40 ![X0]: (apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK1_skl,X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f59])).
% 0.10/0.40 fof(f67,plain,(
% 0.10/0.40 ![X0,X1]: (apart_point_and_line(sK0_skl,line_connecting(X0,X1))|~distinct_points(X0,X1)|distinct_points(sK1_skl,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f64,f34])).
% 0.10/0.40 fof(f71,plain,(
% 0.10/0.40 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|distinct_points(sK1_skl,sK1_skl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f67,f62])).
% 0.10/0.40 fof(f72,definition,(
% 0.10/0.40 sQ0_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f73,plain,(
% 0.10/0.40 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ0_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f72])).
% 0.10/0.40 fof(f75,definition,(
% 0.10/0.40 sQ1_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f76,plain,(
% 0.10/0.40 distinct_points(sK1_skl,sK1_skl)|~sQ1_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f75])).
% 0.10/0.40 fof(f78,plain,(
% 0.10/0.40 sQ0_spl|sQ1_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f71,f72,f75])).
% 0.10/0.40 fof(f80,plain,(
% 0.10/0.40 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ0_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f73,f33])).
% 0.10/0.40 fof(f83,definition,(
% 0.10/0.40 sQ2_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f85,plain,(
% 0.10/0.40 ~distinct_points(sK0_skl,sK1_skl)|sQ2_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f83])).
% 0.10/0.40 fof(f87,definition,(
% 0.10/0.40 sQ3_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f88,plain,(
% 0.10/0.40 distinct_points(sK0_skl,sK0_skl)|~sQ3_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f87])).
% 0.10/0.40 fof(f90,plain,(
% 0.10/0.40 ~sQ2_spl|sQ3_spl|~sQ0_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f80,f83,f87,f72])).
% 0.10/0.40 fof(f91,plain,(
% 0.10/0.40 $false|~sQ1_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f76,f19])).
% 0.10/0.40 fof(f92,plain,(
% 0.10/0.40 ~sQ1_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f91])).
% 0.10/0.40 fof(f93,plain,(
% 0.10/0.40 $false|sQ2_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f85,f62])).
% 0.10/0.40 fof(f94,plain,(
% 0.10/0.40 sQ2_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f93])).
% 0.10/0.40 fof(f95,plain,(
% 0.10/0.40 $false|~sQ3_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f88,f19])).
% 0.10/0.40 fof(f96,plain,(
% 0.10/0.40 ~sQ3_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f95])).
% 0.10/0.40 fof(f97,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(sat_refutation,[status(thm)],[f78,f90,f92,f94,f96])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.42 % Elapsed time: 0.040993 seconds
% 0.10/0.42 % CPU time: 0.109053 seconds
% 0.10/0.42 % Total memory used: 15.174 MB
% 0.10/0.42 % Net memory used: 14.874 MB
%------------------------------------------------------------------------------