%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO170+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 : n001.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 12:25:55 PM UTC 2026
% Result : Theorem 0.19s 0.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO170+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n001.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 13:00:27 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.49 % Drodi V4.1.1
% 0.19/0.50 % Refutation found
% 0.19/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.50 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.50 fof(f1,axiom,(
% 0.19/0.50 (! [X] : ~ distinct_points(X,X) )),
% 0.19/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.50 fof(f4,axiom,(
% 0.19/0.50 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.19/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.50 fof(f7,axiom,(
% 0.19/0.50 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 0.19/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.50 fof(f9,axiom,(
% 0.19/0.50 (! [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) ) ) )),
% 0.19/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.50 fof(f13,conjecture,(
% 0.19/0.50 (! [X,Y,Z] :( ( distinct_points(X,Y)& ~ apart_point_and_line(X,Z)& ~ apart_point_and_line(Y,Z) )=> ~ distinct_lines(Z,line_connecting(X,Y)) ) )),
% 0.19/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.50 fof(f14,negated_conjecture,(
% 0.19/0.50 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& ~ apart_point_and_line(X,Z)& ~ apart_point_and_line(Y,Z) )=> ~ distinct_lines(Z,line_connecting(X,Y)) ) ))),
% 0.19/0.50 inference(negated_conjecture,[status(cth)],[f13])).
% 0.19/0.50 fof(f15,plain,(
% 0.19/0.50 ![X0]: (~distinct_points(X0,X0))),
% 0.19/0.50 inference(cnf_transformation,[status(thm)],[f1])).
% 0.19/0.50 fof(f18,plain,(
% 0.19/0.50 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.19/0.50 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.19/0.50 fof(f19,plain,(
% 0.19/0.50 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.19/0.50 inference(miniscoping,[status(thm)],[f18])).
% 0.19/0.50 fof(f20,plain,(
% 0.19/0.50 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.19/0.50 inference(cnf_transformation,[status(thm)],[f19])).
% 0.19/0.50 fof(f27,plain,(
% 0.19/0.50 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 0.19/0.50 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.19/0.50 fof(f28,plain,(
% 0.19/0.50 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 0.19/0.50 inference(miniscoping,[status(thm)],[f27])).
% 0.19/0.50 fof(f29,plain,(
% 0.19/0.50 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 0.19/0.50 inference(cnf_transformation,[status(thm)],[f28])).
% 0.19/0.50 fof(f30,plain,(
% 0.19/0.50 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 0.19/0.50 inference(cnf_transformation,[status(thm)],[f28])).
% 0.19/0.50 fof(f35,plain,(
% 0.19/0.50 ![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)))),
% 0.19/0.50 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.19/0.50 fof(f36,plain,(
% 0.19/0.50 ![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))),
% 0.19/0.50 inference(cnf_transformation,[status(thm)],[f35])).
% 0.19/0.50 fof(f45,plain,(
% 0.19/0.50 (?[X,Y,Z]: (((distinct_points(X,Y)&~apart_point_and_line(X,Z))&~apart_point_and_line(Y,Z))&distinct_lines(Z,line_connecting(X,Y))))),
% 0.19/0.50 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.19/0.50 fof(f46,plain,(
% 0.19/0.50 (((distinct_points(sK0_skl,sK1_skl)&~apart_point_and_line(sK0_skl,sK2_skl))&~apart_point_and_line(sK1_skl,sK2_skl))&distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.19/0.50 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)],[f45])).
% 0.19/0.50 fof(f47,plain,(
% 0.19/0.50 distinct_points(sK0_skl,sK1_skl)),
% 0.19/0.50 inference(cnf_transformation,[status(thm)],[f46])).
% 0.19/0.50 fof(f48,plain,(
% 0.19/0.50 ~apart_point_and_line(sK0_skl,sK2_skl)),
% 0.19/0.50 inference(cnf_transformation,[status(thm)],[f46])).
% 0.19/0.50 fof(f49,plain,(
% 0.19/0.50 ~apart_point_and_line(sK1_skl,sK2_skl)),
% 0.19/0.50 inference(cnf_transformation,[status(thm)],[f46])).
% 0.19/0.50 fof(f50,plain,(
% 0.19/0.50 distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.19/0.50 inference(cnf_transformation,[status(thm)],[f46])).
% 0.19/0.50 fof(f51,plain,(
% 0.19/0.50 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.19/0.50 inference(resolution,[status(thm)],[f20,f47])).
% 0.19/0.50 fof(f52,plain,(
% 0.19/0.50 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.19/0.50 inference(resolution,[status(thm)],[f51,f20])).
% 0.19/0.50 fof(f57,plain,(
% 0.19/0.50 distinct_points(sK1_skl,sK0_skl)),
% 0.19/0.50 inference(resolution,[status(thm)],[f52,f15])).
% 0.19/0.50 fof(f72,definition,(
% 0.19/0.50 sQ2_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f74,plain,(
% 0.19/0.50 ~distinct_points(sK0_skl,sK1_skl)|sQ2_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f72])).
% 0.19/0.50 fof(f87,plain,(
% 0.19/0.50 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,sK2_skl)|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl)))),
% 0.19/0.50 inference(resolution,[status(thm)],[f36,f50])).
% 0.19/0.50 fof(f115,plain,(
% 0.19/0.50 apart_point_and_line(sK1_skl,sK2_skl)|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,sK2_skl)|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.19/0.50 inference(resolution,[status(thm)],[f87,f57])).
% 0.19/0.50 fof(f139,definition,(
% 0.19/0.50 sQ5_spl <=> (apart_point_and_line(sK1_skl,sK2_skl))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f140,plain,(
% 0.19/0.50 apart_point_and_line(sK1_skl,sK2_skl)|~sQ5_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f139])).
% 0.19/0.50 fof(f142,definition,(
% 0.19/0.50 sQ6_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f143,plain,(
% 0.19/0.50 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ6_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f142])).
% 0.19/0.50 fof(f145,definition,(
% 0.19/0.50 sQ7_spl <=> (apart_point_and_line(sK0_skl,sK2_skl))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f146,plain,(
% 0.19/0.50 apart_point_and_line(sK0_skl,sK2_skl)|~sQ7_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f145])).
% 0.19/0.50 fof(f148,definition,(
% 0.19/0.50 sQ8_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f149,plain,(
% 0.19/0.50 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ8_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f148])).
% 0.19/0.50 fof(f151,plain,(
% 0.19/0.50 sQ5_spl|sQ6_spl|sQ7_spl|sQ8_spl),
% 0.19/0.50 inference(split_clause,[status(thm)],[f115,f139,f142,f145,f148])).
% 0.19/0.50 fof(f205,plain,(
% 0.19/0.50 $false|~sQ5_spl),
% 0.19/0.50 inference(forward_subsumption_resolution,[status(thm)],[f140,f49])).
% 0.19/0.50 fof(f206,plain,(
% 0.19/0.50 ~sQ5_spl),
% 0.19/0.50 inference(contradiction_clause,[status(thm)],[f205])).
% 0.19/0.50 fof(f215,plain,(
% 0.19/0.50 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ6_spl),
% 0.19/0.50 inference(resolution,[status(thm)],[f143,f30])).
% 0.19/0.50 fof(f221,definition,(
% 0.19/0.50 sQ19_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f222,plain,(
% 0.19/0.50 distinct_points(sK1_skl,sK1_skl)|~sQ19_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f221])).
% 0.19/0.50 fof(f224,plain,(
% 0.19/0.50 ~sQ2_spl|sQ19_spl|~sQ6_spl),
% 0.19/0.50 inference(split_clause,[status(thm)],[f215,f72,f221,f142])).
% 0.19/0.50 fof(f226,plain,(
% 0.19/0.50 $false|sQ2_spl),
% 0.19/0.50 inference(forward_subsumption_resolution,[status(thm)],[f74,f47])).
% 0.19/0.50 fof(f227,plain,(
% 0.19/0.50 sQ2_spl),
% 0.19/0.50 inference(contradiction_clause,[status(thm)],[f226])).
% 0.19/0.50 fof(f228,plain,(
% 0.19/0.50 $false|~sQ19_spl),
% 0.19/0.50 inference(forward_subsumption_resolution,[status(thm)],[f222,f15])).
% 0.19/0.50 fof(f229,plain,(
% 0.19/0.50 ~sQ19_spl),
% 0.19/0.50 inference(contradiction_clause,[status(thm)],[f228])).
% 0.19/0.50 fof(f230,plain,(
% 0.19/0.50 $false|~sQ7_spl),
% 0.19/0.50 inference(forward_subsumption_resolution,[status(thm)],[f146,f48])).
% 0.19/0.50 fof(f231,plain,(
% 0.19/0.50 ~sQ7_spl),
% 0.19/0.50 inference(contradiction_clause,[status(thm)],[f230])).
% 0.19/0.50 fof(f233,plain,(
% 0.19/0.50 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ8_spl),
% 0.19/0.50 inference(resolution,[status(thm)],[f149,f29])).
% 0.19/0.50 fof(f239,definition,(
% 0.19/0.50 sQ20_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 0.19/0.50 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.19/0.50 fof(f240,plain,(
% 0.19/0.50 distinct_points(sK0_skl,sK0_skl)|~sQ20_spl),
% 0.19/0.50 inference(component_clause,[status(thm)],[f239])).
% 0.19/0.50 fof(f242,plain,(
% 0.19/0.50 ~sQ2_spl|sQ20_spl|~sQ8_spl),
% 0.19/0.50 inference(split_clause,[status(thm)],[f233,f72,f239,f148])).
% 0.19/0.50 fof(f243,plain,(
% 0.19/0.50 $false|~sQ20_spl),
% 0.19/0.50 inference(forward_subsumption_resolution,[status(thm)],[f240,f15])).
% 0.19/0.50 fof(f244,plain,(
% 0.19/0.50 ~sQ20_spl),
% 0.19/0.50 inference(contradiction_clause,[status(thm)],[f243])).
% 0.19/0.50 fof(f245,plain,(
% 0.19/0.50 $false),
% 0.19/0.50 inference(sat_refutation,[status(thm)],[f151,f206,f224,f227,f229,f231,f242,f244])).
% 0.19/0.50 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.56 % Elapsed time: 0.076311 seconds
% 0.19/0.56 % CPU time: 0.076316 seconds
% 0.19/0.56 % Total memory used: 1.791 MB
% 0.19/0.56 % Net memory used: 1.763 MB
%------------------------------------------------------------------------------