%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO225+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 : n009.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 0.16s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO225+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.47 % Computer : n009.cluster.edu
% 0.16/0.47 % Model : x86_64 x86_64
% 0.16/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.47 % Memory : 8046.5625MB
% 0.16/0.47 % OS : Linux 6.8.0-71-generic
% 0.16/0.47 % CPULimit : 300
% 0.16/0.47 % WCLimit : 300
% 0.16/0.47 % DateTime : Sun Sep 20 13:58:58 UTC 2026
% 0.16/0.48 % CPUTime :
% 0.16/0.51 % Drodi V4.1.1
% 0.16/0.52 % Refutation found
% 0.16/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.52 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.52 fof(f1,axiom,(
% 0.16/0.52 (! [X] : ~ distinct_points(X,X) )),
% 0.16/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.52 fof(f4,axiom,(
% 0.16/0.52 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.16/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.52 fof(f7,axiom,(
% 0.16/0.52 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.16/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.52 fof(f8,axiom,(
% 0.16/0.52 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.16/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.52 fof(f34,axiom,(
% 0.16/0.52 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 0.16/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.52 fof(f36,conjecture,(
% 0.16/0.52 (! [A,B] :( ( point(A)& point(B)& distinct_points(A,B) )=> (? [X] :( line(X)=> ( incident_point_and_line(A,X)& incident_point_and_line(B,X) ) ) )) )),
% 0.16/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.52 fof(f37,negated_conjecture,(
% 0.16/0.52 ~((! [A,B] :( ( point(A)& point(B)& distinct_points(A,B) )=> (? [X] :( line(X)=> ( incident_point_and_line(A,X)& incident_point_and_line(B,X) ) ) )) ))),
% 0.16/0.52 inference(negated_conjecture,[status(cth)],[f36])).
% 0.16/0.52 fof(f38,plain,(
% 0.16/0.52 ![X0]: (~distinct_points(X0,X0))),
% 0.16/0.52 inference(cnf_transformation,[status(thm)],[f1])).
% 0.16/0.52 fof(f41,plain,(
% 0.16/0.52 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.16/0.52 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.16/0.52 fof(f42,plain,(
% 0.16/0.52 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.16/0.52 inference(miniscoping,[status(thm)],[f41])).
% 0.16/0.52 fof(f43,plain,(
% 0.16/0.52 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.16/0.52 inference(cnf_transformation,[status(thm)],[f42])).
% 0.16/0.52 fof(f50,plain,(
% 0.16/0.52 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.16/0.52 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.16/0.52 fof(f51,plain,(
% 0.16/0.52 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.16/0.52 inference(cnf_transformation,[status(thm)],[f50])).
% 0.16/0.52 fof(f52,plain,(
% 0.16/0.52 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.16/0.52 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.16/0.52 fof(f53,plain,(
% 0.16/0.52 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.16/0.52 inference(cnf_transformation,[status(thm)],[f52])).
% 0.16/0.52 fof(f119,plain,(
% 0.16/0.52 ![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)))),
% 0.16/0.52 inference(NNF_transformation,[status(thm)],[f34])).
% 0.16/0.52 fof(f120,plain,(
% 0.16/0.52 (![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)))),
% 0.16/0.52 inference(miniscoping,[status(thm)],[f119])).
% 0.16/0.52 fof(f122,plain,(
% 0.16/0.52 ![X0,X1]: (incident_point_and_line(X0,X1)|apart_point_and_line(X0,X1))),
% 0.16/0.52 inference(cnf_transformation,[status(thm)],[f120])).
% 0.16/0.52 fof(f127,plain,(
% 0.16/0.52 (?[A,B]: (((point(A)&point(B))&distinct_points(A,B))&(![X]: (line(X)&(~incident_point_and_line(A,X)|~incident_point_and_line(B,X))))))),
% 0.16/0.52 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.16/0.52 fof(f128,plain,(
% 0.16/0.52 ?[A,B]: (((point(A)&point(B))&distinct_points(A,B))&((![X]: line(X))&(![X]: (~incident_point_and_line(A,X)|~incident_point_and_line(B,X)))))),
% 0.16/0.52 inference(miniscoping,[status(thm)],[f127])).
% 0.16/0.52 fof(f129,plain,(
% 0.16/0.52 (((point(sK0_skl)&point(sK1_skl))&distinct_points(sK0_skl,sK1_skl))&((![X]: line(X))&(![X]: (~incident_point_and_line(sK0_skl,X)|~incident_point_and_line(sK1_skl,X)))))),
% 0.16/0.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f128])).
% 0.16/0.52 fof(f132,plain,(
% 0.16/0.52 distinct_points(sK0_skl,sK1_skl)),
% 0.16/0.52 inference(cnf_transformation,[status(thm)],[f129])).
% 0.16/0.52 fof(f134,plain,(
% 0.16/0.52 ![X0]: (~incident_point_and_line(sK0_skl,X0)|~incident_point_and_line(sK1_skl,X0))),
% 0.16/0.52 inference(cnf_transformation,[status(thm)],[f129])).
% 0.16/0.52 fof(f146,plain,(
% 0.16/0.52 ![X0]: (~incident_point_and_line(sK0_skl,X0)|apart_point_and_line(sK1_skl,X0))),
% 0.16/0.52 inference(resolution,[status(thm)],[f134,f122])).
% 0.16/0.52 fof(f147,plain,(
% 0.16/0.52 ![X0]: (apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0))),
% 0.16/0.52 inference(resolution,[status(thm)],[f146,f122])).
% 0.16/0.52 fof(f148,plain,(
% 0.16/0.52 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.16/0.52 inference(resolution,[status(thm)],[f43,f132])).
% 0.16/0.52 fof(f153,plain,(
% 0.16/0.52 ![X0]: (~distinct_points(sK1_skl,X0)|apart_point_and_line(sK0_skl,line_connecting(sK1_skl,X0)))),
% 0.16/0.52 inference(resolution,[status(thm)],[f51,f147])).
% 0.16/0.52 fof(f154,plain,(
% 0.16/0.52 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.16/0.52 inference(resolution,[status(thm)],[f148,f43])).
% 0.16/0.52 fof(f158,plain,(
% 0.16/0.52 distinct_points(sK1_skl,sK0_skl)),
% 0.16/0.52 inference(resolution,[status(thm)],[f154,f38])).
% 0.16/0.52 fof(f166,definition,(
% 0.16/0.52 sQ0_spl <=> (distinct_points(sK1_skl,sK0_skl))),
% 0.16/0.52 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.16/0.52 fof(f168,plain,(
% 0.16/0.52 ~distinct_points(sK1_skl,sK0_skl)|sQ0_spl),
% 0.16/0.52 inference(component_clause,[status(thm)],[f166])).
% 0.16/0.52 fof(f218,plain,(
% 0.16/0.52 ~distinct_points(sK1_skl,sK0_skl)|~distinct_points(sK1_skl,sK0_skl)),
% 0.16/0.52 inference(resolution,[status(thm)],[f53,f153])).
% 0.16/0.52 fof(f220,plain,(
% 0.16/0.52 ~sQ0_spl),
% 0.16/0.52 inference(split_clause,[status(thm)],[f218,f166])).
% 0.16/0.52 fof(f222,plain,(
% 0.16/0.52 $false|sQ0_spl),
% 0.16/0.52 inference(forward_subsumption_resolution,[status(thm)],[f168,f158])).
% 0.16/0.52 fof(f223,plain,(
% 0.16/0.52 sQ0_spl),
% 0.16/0.52 inference(contradiction_clause,[status(thm)],[f222])).
% 0.16/0.52 fof(f224,plain,(
% 0.16/0.52 $false),
% 0.16/0.52 inference(sat_refutation,[status(thm)],[f220,f223])).
% 0.16/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.21/0.56 % Elapsed time: 0.068661 seconds
% 0.21/0.56 % CPU time: 0.078654 seconds
% 0.21/0.56 % Total memory used: 3.032 MB
% 0.21/0.56 % Net memory used: 3.002 MB
%------------------------------------------------------------------------------