%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO225+1 : 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 : n016.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 0.17s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO225+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.48 % Computer : n016.cluster.edu
% 0.17/0.48 % Model : x86_64 x86_64
% 0.17/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.48 % Memory : 8046.5625MB
% 0.17/0.48 % OS : Linux 6.8.0-71-generic
% 0.17/0.48 % CPULimit : 300
% 0.17/0.48 % WCLimit : 300
% 0.17/0.48 % DateTime : Sun Sep 20 14:02:06 UTC 2026
% 0.17/0.49 % CPUTime :
% 0.17/0.51 % Drodi V4.1.1
% 0.17/0.52 % Refutation found
% 0.17/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.52 fof(f1,axiom,(
% 0.17/0.52 (! [X] : ~ distinct_points(X,X) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f4,axiom,(
% 0.17/0.52 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f7,axiom,(
% 0.17/0.52 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f8,axiom,(
% 0.17/0.52 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f12,axiom,(
% 0.17/0.52 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f19,conjecture,(
% 0.17/0.52 (! [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) ) ) )) )),
% 0.17/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.52 fof(f20,negated_conjecture,(
% 0.17/0.52 ~((! [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) ) ) )) ))),
% 0.17/0.52 inference(negated_conjecture,[status(cth)],[f19])).
% 0.17/0.52 fof(f21,plain,(
% 0.17/0.52 ![X0]: (~distinct_points(X0,X0))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f1])).
% 0.17/0.52 fof(f24,plain,(
% 0.17/0.52 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.17/0.52 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.17/0.52 fof(f25,plain,(
% 0.17/0.52 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.17/0.52 inference(miniscoping,[status(thm)],[f24])).
% 0.17/0.52 fof(f26,plain,(
% 0.17/0.52 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f25])).
% 0.17/0.52 fof(f33,plain,(
% 0.17/0.52 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.17/0.52 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.17/0.52 fof(f34,plain,(
% 0.17/0.52 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f33])).
% 0.17/0.52 fof(f35,plain,(
% 0.17/0.52 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.17/0.52 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.17/0.52 fof(f36,plain,(
% 0.17/0.52 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f35])).
% 0.17/0.52 fof(f43,plain,(
% 0.17/0.52 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 0.17/0.52 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.17/0.52 fof(f44,plain,(
% 0.17/0.52 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 0.17/0.52 inference(miniscoping,[status(thm)],[f43])).
% 0.17/0.52 fof(f45,plain,(
% 0.17/0.52 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f44])).
% 0.17/0.52 fof(f60,plain,(
% 0.17/0.52 (?[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))))))),
% 0.17/0.52 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.17/0.52 fof(f61,plain,(
% 0.17/0.52 ?[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)))))),
% 0.17/0.52 inference(miniscoping,[status(thm)],[f60])).
% 0.17/0.52 fof(f62,plain,(
% 0.17/0.52 (((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)))))),
% 0.17/0.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f61])).
% 0.17/0.52 fof(f65,plain,(
% 0.17/0.52 distinct_points(sK0_skl,sK1_skl)),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f62])).
% 0.17/0.52 fof(f67,plain,(
% 0.17/0.52 ![X0]: (apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK1_skl,X0))),
% 0.17/0.52 inference(cnf_transformation,[status(thm)],[f62])).
% 0.17/0.52 fof(f70,plain,(
% 0.17/0.52 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.17/0.52 inference(resolution,[status(thm)],[f26,f65])).
% 0.17/0.52 fof(f72,plain,(
% 0.17/0.52 distinct_points(sK1_skl,sK0_skl)),
% 0.17/0.52 inference(resolution,[status(thm)],[f70,f21])).
% 0.17/0.52 fof(f74,plain,(
% 0.17/0.52 ![X0,X1]: (distinct_points(sK0_skl,X0)|apart_point_and_line(X0,X1)|apart_point_and_line(sK1_skl,X1))),
% 0.17/0.52 inference(resolution,[status(thm)],[f45,f67])).
% 0.17/0.52 fof(f80,definition,(
% 0.17/0.52 sQ0_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.17/0.52 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.17/0.52 fof(f87,plain,(
% 0.17/0.52 ![X0]: (~distinct_points(sK1_skl,X0)|distinct_points(sK0_skl,sK1_skl))),
% 0.17/0.52 inference(resolution,[status(thm)],[f34,f74])).
% 0.17/0.52 fof(f89,plain,(
% 0.17/0.52 ![X0]: (~distinct_points(sK0_skl,X0)|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,X0)))),
% 0.17/0.52 inference(resolution,[status(thm)],[f34,f67])).
% 0.17/0.52 fof(f92,definition,(
% 0.17/0.52 ![X0]: (sQ2_spl <=> (~distinct_points(sK1_skl,X0)))),
% 0.17/0.52 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.17/0.52 fof(f93,plain,(
% 0.17/0.52 ![X0]: (~distinct_points(sK1_skl,X0)|~sQ2_spl)),
% 0.17/0.52 inference(component_clause,[status(thm)],[f92])).
% 0.17/0.52 fof(f95,plain,(
% 0.17/0.52 sQ2_spl|sQ0_spl),
% 0.17/0.52 inference(split_clause,[status(thm)],[f87,f92,f80])).
% 0.17/0.52 fof(f117,plain,(
% 0.17/0.52 ~distinct_points(sK0_skl,sK1_skl)|~distinct_points(sK0_skl,sK1_skl)),
% 0.17/0.52 inference(resolution,[status(thm)],[f89,f36])).
% 0.17/0.52 fof(f120,plain,(
% 0.17/0.52 ~sQ0_spl),
% 0.17/0.52 inference(split_clause,[status(thm)],[f117,f80])).
% 0.17/0.52 fof(f122,plain,(
% 0.17/0.52 $false|~sQ2_spl),
% 0.17/0.52 inference(backward_subsumption_resolution,[status(thm)],[f72,f93])).
% 0.17/0.52 fof(f127,plain,(
% 0.17/0.52 ~sQ2_spl),
% 0.17/0.52 inference(contradiction_clause,[status(thm)],[f122])).
% 0.17/0.52 fof(f128,plain,(
% 0.17/0.52 $false),
% 0.17/0.52 inference(sat_refutation,[status(thm)],[f95,f120,f127])).
% 0.17/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.22/0.57 % Elapsed time: 0.067711 seconds
% 0.22/0.57 % CPU time: 0.060419 seconds
% 0.22/0.57 % Total memory used: 1.692 MB
% 0.22/0.57 % Net memory used: 1.652 MB
%------------------------------------------------------------------------------