%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO188+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 : n018.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 0.14s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n018.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 20 13:11:12 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.40 fof(f1,axiom,(
% 0.14/0.40 (! [X] : ~ distinct_points(X,X) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f4,axiom,(
% 0.14/0.40 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f7,axiom,(
% 0.14/0.40 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f8,axiom,(
% 0.14/0.40 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f11,axiom,(
% 0.14/0.40 (! [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) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f13,axiom,(
% 0.14/0.40 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f15,conjecture,(
% 0.14/0.40 (! [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(X,line_connecting(Z,Y)) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f16,negated_conjecture,(
% 0.14/0.40 ~((! [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(X,line_connecting(Z,Y)) ) ))),
% 0.14/0.40 inference(negated_conjecture,[status(cth)],[f15])).
% 0.14/0.40 fof(f17,plain,(
% 0.14/0.40 ![X0]: (~distinct_points(X0,X0))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.40 fof(f20,plain,(
% 0.14/0.40 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.14/0.40 fof(f21,plain,(
% 0.14/0.40 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f20])).
% 0.14/0.40 fof(f22,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f21])).
% 0.14/0.40 fof(f29,plain,(
% 0.14/0.40 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.14/0.40 fof(f30,plain,(
% 0.14/0.40 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f29])).
% 0.14/0.40 fof(f31,plain,(
% 0.14/0.40 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.14/0.40 fof(f32,plain,(
% 0.14/0.40 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f31])).
% 0.14/0.40 fof(f37,plain,(
% 0.14/0.40 ![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)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.14/0.40 fof(f38,plain,(
% 0.14/0.40 ![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))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f37])).
% 0.14/0.40 fof(f42,plain,(
% 0.14/0.40 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.14/0.40 fof(f43,plain,(
% 0.14/0.40 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f42])).
% 0.14/0.40 fof(f44,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/0.40 fof(f48,plain,(
% 0.14/0.40 (?[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(X,line_connecting(Z,Y))))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.14/0.40 fof(f49,plain,(
% 0.14/0.40 ((((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(sK0_skl,line_connecting(sK2_skl,sK1_skl)))),
% 0.14/0.40 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])).
% 0.14/0.40 fof(f50,plain,(
% 0.14/0.40 distinct_points(sK0_skl,sK1_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.14/0.40 fof(f52,plain,(
% 0.14/0.40 distinct_points(sK1_skl,sK2_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.14/0.40 fof(f53,plain,(
% 0.14/0.40 ~apart_point_and_line(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.14/0.40 fof(f54,plain,(
% 0.14/0.40 apart_point_and_line(sK0_skl,line_connecting(sK2_skl,sK1_skl))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.14/0.40 fof(f55,plain,(
% 0.14/0.40 ![X0]: (distinct_points(sK1_skl,X0)|distinct_points(sK2_skl,X0))),
% 0.14/0.40 inference(resolution,[status(thm)],[f22,f52])).
% 0.14/0.40 fof(f58,plain,(
% 0.14/0.40 ![X0,X1]: (distinct_points(sK1_skl,X0)|distinct_points(sK2_skl,X1)|distinct_points(X0,X1))),
% 0.14/0.40 inference(resolution,[status(thm)],[f55,f22])).
% 0.14/0.40 fof(f67,plain,(
% 0.14/0.40 distinct_points(sK2_skl,sK1_skl)),
% 0.14/0.40 inference(resolution,[status(thm)],[f58,f17])).
% 0.14/0.40 fof(f139,plain,(
% 0.14/0.40 ![X0]: (distinct_lines(line_connecting(sK2_skl,sK1_skl),X0)|apart_point_and_line(sK0_skl,X0))),
% 0.14/0.40 inference(resolution,[status(thm)],[f44,f54])).
% 0.14/0.40 fof(f203,plain,(
% 0.14/0.40 ![X0,X1,X2]: (apart_point_and_line(sK0_skl,X0)|~distinct_points(X1,X2)|apart_point_and_line(X1,line_connecting(sK2_skl,sK1_skl))|apart_point_and_line(X1,X0)|apart_point_and_line(X2,line_connecting(sK2_skl,sK1_skl))|apart_point_and_line(X2,X0))),
% 0.14/0.40 inference(resolution,[status(thm)],[f139,f38])).
% 0.14/0.40 fof(f402,plain,(
% 0.14/0.40 ![X0]: (apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl))|apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl))|apart_point_and_line(sK1_skl,X0))),
% 0.14/0.40 inference(resolution,[status(thm)],[f203,f67])).
% 0.14/0.40 fof(f486,definition,(
% 0.14/0.40 sQ17_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl)))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f487,plain,(
% 0.14/0.40 apart_point_and_line(sK1_skl,line_connecting(sK2_skl,sK1_skl))|~sQ17_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f486])).
% 0.14/0.40 fof(f493,definition,(
% 0.14/0.40 sQ19_spl <=> (apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl)))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f494,plain,(
% 0.14/0.40 apart_point_and_line(sK2_skl,line_connecting(sK2_skl,sK1_skl))|~sQ19_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f493])).
% 0.14/0.40 fof(f547,definition,(
% 0.14/0.40 ![X0]: (sQ31_spl <=> (apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f548,plain,(
% 0.14/0.40 ![X0]: (apart_point_and_line(sK0_skl,X0)|apart_point_and_line(sK2_skl,X0)|apart_point_and_line(sK1_skl,X0)|~sQ31_spl)),
% 0.14/0.40 inference(component_clause,[status(thm)],[f547])).
% 0.14/0.40 fof(f550,plain,(
% 0.14/0.40 sQ31_spl|sQ19_spl|sQ17_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f402,f547,f493,f486])).
% 0.14/0.40 fof(f699,plain,(
% 0.14/0.40 ~distinct_points(sK2_skl,sK1_skl)|~sQ17_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f487,f32])).
% 0.14/0.40 fof(f702,plain,(
% 0.14/0.40 $false|~sQ17_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f699,f67])).
% 0.14/0.40 fof(f703,plain,(
% 0.14/0.40 ~sQ17_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f702])).
% 0.14/0.40 fof(f705,plain,(
% 0.14/0.40 ~distinct_points(sK2_skl,sK1_skl)|~sQ19_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f494,f30])).
% 0.14/0.40 fof(f708,plain,(
% 0.14/0.40 $false|~sQ19_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f705,f67])).
% 0.14/0.40 fof(f709,plain,(
% 0.14/0.40 ~sQ19_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f708])).
% 0.14/0.40 fof(f711,plain,(
% 0.14/0.40 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ31_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f548,f53])).
% 0.14/0.40 fof(f716,definition,(
% 0.14/0.40 sQ58_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f717,plain,(
% 0.14/0.40 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ58_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f716])).
% 0.14/0.40 fof(f719,definition,(
% 0.14/0.40 sQ59_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f720,plain,(
% 0.14/0.40 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ59_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f719])).
% 0.14/0.40 fof(f722,plain,(
% 0.14/0.40 sQ58_spl|sQ59_spl|~sQ31_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f711,f716,f719,f547])).
% 0.14/0.40 fof(f723,plain,(
% 0.14/0.40 ~distinct_points(sK0_skl,sK1_skl)|~sQ58_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f717,f30])).
% 0.14/0.40 fof(f726,plain,(
% 0.14/0.40 $false|~sQ58_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f723,f50])).
% 0.14/0.40 fof(f727,plain,(
% 0.14/0.40 ~sQ58_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f726])).
% 0.14/0.40 fof(f728,plain,(
% 0.14/0.40 ~distinct_points(sK0_skl,sK1_skl)|~sQ59_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f720,f32])).
% 0.14/0.40 fof(f731,plain,(
% 0.14/0.40 $false|~sQ59_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f728,f50])).
% 0.14/0.40 fof(f732,plain,(
% 0.14/0.40 ~sQ59_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f731])).
% 0.14/0.40 fof(f733,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(sat_refutation,[status(thm)],[f550,f703,f709,f722,f727,f732])).
% 0.14/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.42 % Elapsed time: 0.055337 seconds
% 0.14/0.42 % CPU time: 0.229396 seconds
% 0.14/0.42 % Total memory used: 19.134 MB
% 0.14/0.42 % Net memory used: 18.438 MB
%------------------------------------------------------------------------------