%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO189+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 : n011.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 12:26:00 PM UTC 2026
% Result : Theorem 0.19s 0.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO189+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
% 0.19/0.46 % Computer : n011.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 20 13:09:54 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.49 % Drodi V4.1.1
% 0.19/0.61 % Refutation found
% 0.19/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.61 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.61 fof(f7,axiom,(
% 0.19/0.61 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f8,axiom,(
% 0.19/0.61 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f11,axiom,(
% 0.19/0.61 (! [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) ) ) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f13,axiom,(
% 0.19/0.61 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f15,conjecture,(
% 0.19/0.61 (! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& distinct_points(Y,Z)& ~ apart_point_and_line(Z,line_connecting(X,Y)) )=> ~ apart_point_and_line(Y,line_connecting(X,Z)) ) )),
% 0.19/0.61 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.61 fof(f16,negated_conjecture,(
% 0.19/0.61 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& distinct_points(X,Z)& distinct_points(Y,Z)& ~ apart_point_and_line(Z,line_connecting(X,Y)) )=> ~ apart_point_and_line(Y,line_connecting(X,Z)) ) ))),
% 0.19/0.61 inference(negated_conjecture,[status(cth)],[f15])).
% 0.19/0.61 fof(f29,plain,(
% 0.19/0.61 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.19/0.61 fof(f30,plain,(
% 0.19/0.61 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f29])).
% 0.19/0.61 fof(f31,plain,(
% 0.19/0.61 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.19/0.61 fof(f32,plain,(
% 0.19/0.61 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f31])).
% 0.19/0.61 fof(f37,plain,(
% 0.19/0.61 ![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)))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.19/0.61 fof(f38,plain,(
% 0.19/0.61 ![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))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f37])).
% 0.19/0.61 fof(f42,plain,(
% 0.19/0.61 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.19/0.61 fof(f43,plain,(
% 0.19/0.61 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.19/0.61 inference(miniscoping,[status(thm)],[f42])).
% 0.19/0.61 fof(f44,plain,(
% 0.19/0.61 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f43])).
% 0.19/0.61 fof(f48,plain,(
% 0.19/0.61 (?[X,Y,Z]: ((((distinct_points(X,Y)&distinct_points(X,Z))&distinct_points(Y,Z))&~apart_point_and_line(Z,line_connecting(X,Y)))&apart_point_and_line(Y,line_connecting(X,Z))))),
% 0.19/0.61 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.19/0.61 fof(f49,plain,(
% 0.19/0.61 ((((distinct_points(sK0_skl,sK1_skl)&distinct_points(sK0_skl,sK2_skl))&distinct_points(sK1_skl,sK2_skl))&~apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl)))&apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.19/0.61 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)],[f48])).
% 0.19/0.61 fof(f50,plain,(
% 0.19/0.61 distinct_points(sK0_skl,sK1_skl)),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f49])).
% 0.19/0.61 fof(f51,plain,(
% 0.19/0.61 distinct_points(sK0_skl,sK2_skl)),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f49])).
% 0.19/0.61 fof(f53,plain,(
% 0.19/0.61 ~apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f49])).
% 0.19/0.61 fof(f54,plain,(
% 0.19/0.61 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))),
% 0.19/0.61 inference(cnf_transformation,[status(thm)],[f49])).
% 0.19/0.61 fof(f65,plain,(
% 0.19/0.61 ![X0]: (distinct_lines(line_connecting(sK0_skl,sK2_skl),X0)|apart_point_and_line(sK1_skl,X0))),
% 0.19/0.61 inference(resolution,[status(thm)],[f44,f54])).
% 0.19/0.61 fof(f75,definition,(
% 0.19/0.61 sQ1_spl <=> (distinct_points(sK0_skl,sK2_skl))),
% 0.19/0.61 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.19/0.61 fof(f77,plain,(
% 0.19/0.61 ~distinct_points(sK0_skl,sK2_skl)|sQ1_spl),
% 0.19/0.61 inference(component_clause,[status(thm)],[f75])).
% 0.19/0.61 fof(f83,plain,(
% 0.19/0.61 $false|sQ1_spl),
% 0.19/0.61 inference(forward_subsumption_resolution,[status(thm)],[f77,f51])).
% 0.19/0.61 fof(f84,plain,(
% 0.19/0.61 sQ1_spl),
% 0.19/0.61 inference(contradiction_clause,[status(thm)],[f83])).
% 0.19/0.61 fof(f85,plain,(
% 0.19/0.61 ![X0,X1,X2]: (apart_point_and_line(sK1_skl,X0)|~distinct_points(X1,X2)|apart_point_and_line(X1,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(X1,X0)|apart_point_and_line(X2,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(X2,X0))),
% 0.19/0.61 inference(resolution,[status(thm)],[f65,f38])).
% 0.19/0.61 fof(f214,plain,(
% 0.19/0.61 ![X0]: (apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK2_skl,X0))),
% 0.19/0.61 inference(resolution,[status(thm)],[f85,f51])).
% 0.19/0.61 fof(f241,definition,(
% 0.19/0.61 sQ15_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.19/0.61 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.19/0.61 fof(f242,plain,(
% 0.19/0.61 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|~sQ15_spl),
% 0.19/0.61 inference(component_clause,[status(thm)],[f241])).
% 0.19/0.61 fof(f245,definition,(
% 0.19/0.61 ![X0]: (sQ16_spl <=> (apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK2_skl,X0)))),
% 0.19/0.61 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.19/0.61 fof(f246,plain,(
% 0.19/0.61 ![X0]: (apart_point_and_line(sK1_skl,X0)|apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK2_skl,X0)|~sQ16_spl)),
% 0.19/0.61 inference(component_clause,[status(thm)],[f245])).
% 0.19/0.61 fof(f248,definition,(
% 0.19/0.61 sQ17_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.19/0.61 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.19/0.61 fof(f249,plain,(
% 0.19/0.61 apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK2_skl))|~sQ17_spl),
% 0.19/0.61 inference(component_clause,[status(thm)],[f248])).
% 0.19/0.61 fof(f251,plain,(
% 0.19/0.61 sQ16_spl|sQ15_spl|sQ17_spl),
% 0.19/0.61 inference(split_clause,[status(thm)],[f214,f245,f241,f248])).
% 0.19/0.61 fof(f346,plain,(
% 0.19/0.61 ~distinct_points(sK0_skl,sK2_skl)|~sQ17_spl),
% 0.19/0.61 inference(resolution,[status(thm)],[f249,f32])).
% 0.19/0.61 fof(f349,plain,(
% 0.19/0.61 ~sQ1_spl|~sQ17_spl),
% 0.19/0.61 inference(split_clause,[status(thm)],[f346,f75,f248])).
% 0.19/0.61 fof(f350,plain,(
% 0.19/0.61 ~distinct_points(sK0_skl,sK2_skl)|~sQ15_spl),
% 0.19/0.61 inference(resolution,[status(thm)],[f242,f30])).
% 0.19/0.61 fof(f353,plain,(
% 0.19/0.61 ~sQ1_spl|~sQ15_spl),
% 0.19/0.61 inference(split_clause,[status(thm)],[f350,f75,f241])).
% 0.19/0.61 fof(f834,plain,(
% 0.19/0.61 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ16_spl),
% 0.19/0.61 inference(resolution,[status(thm)],[f246,f53])).
% 0.19/0.61 fof(f840,definition,(
% 0.19/0.61 sQ62_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.19/0.61 introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition])).
% 0.19/0.61 fof(f841,plain,(
% 0.19/0.61 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ62_spl),
% 0.19/0.61 inference(component_clause,[status(thm)],[f840])).
% 0.19/0.61 fof(f843,definition,(
% 0.19/0.61 sQ63_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.19/0.61 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 0.19/0.61 fof(f844,plain,(
% 0.19/0.61 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ63_spl),
% 0.19/0.61 inference(component_clause,[status(thm)],[f843])).
% 0.19/0.61 fof(f846,plain,(
% 0.19/0.61 sQ62_spl|sQ63_spl|~sQ16_spl),
% 0.19/0.61 inference(split_clause,[status(thm)],[f834,f840,f843,f245])).
% 0.19/0.61 fof(f847,plain,(
% 0.19/0.61 ~distinct_points(sK0_skl,sK1_skl)|~sQ62_spl),
% 0.19/0.61 inference(resolution,[status(thm)],[f841,f32])).
% 0.19/0.63 fof(f850,plain,(
% 0.19/0.63 $false|~sQ62_spl),
% 0.19/0.63 inference(forward_subsumption_resolution,[status(thm)],[f847,f50])).
% 0.19/0.63 fof(f851,plain,(
% 0.19/0.63 ~sQ62_spl),
% 0.19/0.63 inference(contradiction_clause,[status(thm)],[f850])).
% 0.19/0.63 fof(f852,plain,(
% 0.19/0.63 ~distinct_points(sK0_skl,sK1_skl)|~sQ63_spl),
% 0.19/0.63 inference(resolution,[status(thm)],[f844,f30])).
% 0.19/0.63 fof(f855,plain,(
% 0.19/0.63 $false|~sQ63_spl),
% 0.19/0.63 inference(forward_subsumption_resolution,[status(thm)],[f852,f50])).
% 0.19/0.63 fof(f856,plain,(
% 0.19/0.63 ~sQ63_spl),
% 0.19/0.63 inference(contradiction_clause,[status(thm)],[f855])).
% 0.19/0.63 fof(f857,plain,(
% 0.19/0.63 $false),
% 0.19/0.63 inference(sat_refutation,[status(thm)],[f84,f251,f349,f353,f846,f851,f856])).
% 0.19/0.63 % SZS output end CNFRefutation for theBenchmark.p
% 0.23/0.64 % Elapsed time: 0.143205 seconds
% 0.23/0.64 % CPU time: 0.815699 seconds
% 0.23/0.64 % Total memory used: 24.179 MB
% 0.23/0.64 % Net memory used: 22.629 MB
%------------------------------------------------------------------------------