%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO204+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 : 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 12:26:05 PM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO204+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n018.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 13:28:44 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.41 fof(f1,axiom,(
% 0.14/0.41 (! [X] : ~ distinct_points(X,X) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f4,axiom,(
% 0.14/0.41 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f7,axiom,(
% 0.14/0.41 (! [X,Y,Z] :( distinct_points(X,Y)=> ( apart_point_and_line(Z,line_connecting(X,Y))=> ( distinct_points(Z,X)& distinct_points(Z,Y) ) ) ) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f9,axiom,(
% 0.14/0.41 (! [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) ) ) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f13,conjecture,(
% 0.14/0.41 (! [X,Y,Z] :( ( distinct_points(X,Y)& ~ distinct_points(Y,Z) )=> ( distinct_points(X,Z)& ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z)) ) ) )),
% 0.14/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.41 fof(f14,negated_conjecture,(
% 0.14/0.41 ~((! [X,Y,Z] :( ( distinct_points(X,Y)& ~ distinct_points(Y,Z) )=> ( distinct_points(X,Z)& ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z)) ) ) ))),
% 0.14/0.41 inference(negated_conjecture,[status(cth)],[f13])).
% 0.14/0.41 fof(f15,plain,(
% 0.14/0.41 ![X0]: (~distinct_points(X0,X0))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.41 fof(f18,plain,(
% 0.14/0.41 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.14/0.41 fof(f19,plain,(
% 0.14/0.41 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.14/0.41 inference(miniscoping,[status(thm)],[f18])).
% 0.14/0.41 fof(f20,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f19])).
% 0.14/0.41 fof(f27,plain,(
% 0.14/0.41 ![X,Y,Z]: (~distinct_points(X,Y)|(~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.14/0.41 fof(f28,plain,(
% 0.14/0.41 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (~apart_point_and_line(Z,line_connecting(X,Y))|(distinct_points(Z,X)&distinct_points(Z,Y)))))),
% 0.14/0.41 inference(miniscoping,[status(thm)],[f27])).
% 0.14/0.41 fof(f29,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X0))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f28])).
% 0.14/0.41 fof(f30,plain,(
% 0.14/0.41 ![X0,X1,X2]: (~distinct_points(X0,X1)|~apart_point_and_line(X2,line_connecting(X0,X1))|distinct_points(X2,X1))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f28])).
% 0.14/0.41 fof(f35,plain,(
% 0.14/0.41 ![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)))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.14/0.41 fof(f36,plain,(
% 0.14/0.41 ![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))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f35])).
% 0.14/0.41 fof(f45,plain,(
% 0.14/0.41 (?[X,Y,Z]: ((distinct_points(X,Y)&~distinct_points(Y,Z))&(~distinct_points(X,Z)|distinct_lines(line_connecting(X,Y),line_connecting(X,Z)))))),
% 0.14/0.41 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.14/0.41 fof(f46,plain,(
% 0.14/0.41 ((distinct_points(sK0_skl,sK1_skl)&~distinct_points(sK1_skl,sK2_skl))&(~distinct_points(sK0_skl,sK2_skl)|distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))))),
% 0.14/0.41 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])).
% 0.14/0.41 fof(f47,plain,(
% 0.14/0.41 distinct_points(sK0_skl,sK1_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.41 fof(f48,plain,(
% 0.14/0.41 ~distinct_points(sK1_skl,sK2_skl)),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.41 fof(f49,plain,(
% 0.14/0.41 ~distinct_points(sK0_skl,sK2_skl)|distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))),
% 0.14/0.41 inference(cnf_transformation,[status(thm)],[f46])).
% 0.14/0.41 fof(f50,definition,(
% 0.14/0.41 sQ0_spl <=> (distinct_points(sK0_skl,sK2_skl))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f52,plain,(
% 0.14/0.41 ~distinct_points(sK0_skl,sK2_skl)|sQ0_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f50])).
% 0.14/0.41 fof(f53,definition,(
% 0.14/0.41 sQ1_spl <=> (distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f54,plain,(
% 0.14/0.41 distinct_lines(line_connecting(sK0_skl,sK1_skl),line_connecting(sK0_skl,sK2_skl))|~sQ1_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f53])).
% 0.14/0.41 fof(f56,plain,(
% 0.14/0.41 ~sQ0_spl|sQ1_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f49,f50,f53])).
% 0.14/0.41 fof(f57,plain,(
% 0.14/0.41 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.14/0.41 inference(resolution,[status(thm)],[f20,f47])).
% 0.14/0.41 fof(f58,plain,(
% 0.14/0.41 distinct_points(sK0_skl,sK2_skl)),
% 0.14/0.41 inference(resolution,[status(thm)],[f57,f48])).
% 0.14/0.41 fof(f59,plain,(
% 0.14/0.41 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.14/0.41 inference(resolution,[status(thm)],[f57,f20])).
% 0.14/0.41 fof(f61,plain,(
% 0.14/0.41 $false|sQ0_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f58,f52])).
% 0.14/0.41 fof(f62,plain,(
% 0.14/0.41 sQ0_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f61])).
% 0.14/0.41 fof(f76,plain,(
% 0.14/0.41 distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK2_skl)),
% 0.14/0.41 inference(resolution,[status(thm)],[f59,f48])).
% 0.14/0.41 fof(f86,definition,(
% 0.14/0.41 sQ4_spl <=> (distinct_points(sK0_skl,sK1_skl))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f93,definition,(
% 0.14/0.41 sQ6_spl <=> (distinct_points(sK1_skl,sK2_skl))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f94,plain,(
% 0.14/0.41 distinct_points(sK1_skl,sK2_skl)|~sQ6_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f93])).
% 0.14/0.41 fof(f96,plain,(
% 0.14/0.41 sQ4_spl|sQ6_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f76,f86,f93])).
% 0.14/0.41 fof(f143,plain,(
% 0.14/0.41 ![X0,X1]: (~distinct_points(X0,X1)|apart_point_and_line(X0,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X0,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(X1,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(X1,line_connecting(sK0_skl,sK2_skl))|~sQ1_spl)),
% 0.14/0.41 inference(resolution,[status(thm)],[f36,f54])).
% 0.14/0.41 fof(f203,definition,(
% 0.14/0.41 sQ11_spl <=> (distinct_points(sK1_skl,sK1_skl))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f204,plain,(
% 0.14/0.41 distinct_points(sK1_skl,sK1_skl)|~sQ11_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f203])).
% 0.14/0.41 fof(f207,plain,(
% 0.14/0.41 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))|~sQ1_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f143,f47])).
% 0.14/0.41 fof(f236,definition,(
% 0.14/0.41 sQ12_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f237,plain,(
% 0.14/0.41 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ12_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f236])).
% 0.14/0.41 fof(f239,definition,(
% 0.14/0.41 sQ13_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f240,plain,(
% 0.14/0.41 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK2_skl))|~sQ13_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f239])).
% 0.14/0.41 fof(f242,definition,(
% 0.14/0.41 sQ14_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f243,plain,(
% 0.14/0.41 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ14_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f242])).
% 0.14/0.41 fof(f245,definition,(
% 0.14/0.41 sQ15_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl)))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f246,plain,(
% 0.14/0.41 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK2_skl))|~sQ15_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f245])).
% 0.14/0.41 fof(f248,plain,(
% 0.14/0.41 sQ12_spl|sQ13_spl|sQ14_spl|sQ15_spl|~sQ1_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f207,f236,f239,f242,f245,f53])).
% 0.14/0.41 fof(f387,plain,(
% 0.14/0.41 ~distinct_points(sK0_skl,sK2_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ13_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f240,f29])).
% 0.14/0.41 fof(f393,definition,(
% 0.14/0.41 sQ36_spl <=> (distinct_points(sK0_skl,sK0_skl))),
% 0.14/0.41 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.14/0.41 fof(f394,plain,(
% 0.14/0.41 distinct_points(sK0_skl,sK0_skl)|~sQ36_spl),
% 0.14/0.41 inference(component_clause,[status(thm)],[f393])).
% 0.14/0.41 fof(f396,plain,(
% 0.14/0.41 ~sQ0_spl|sQ36_spl|~sQ13_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f387,f50,f393,f239])).
% 0.14/0.41 fof(f398,plain,(
% 0.14/0.41 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK0_skl,sK0_skl)|~sQ12_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f237,f29])).
% 0.14/0.41 fof(f404,plain,(
% 0.14/0.41 ~sQ4_spl|sQ36_spl|~sQ12_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f398,f86,f393,f236])).
% 0.14/0.41 fof(f405,plain,(
% 0.14/0.41 $false|~sQ6_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f94,f48])).
% 0.14/0.41 fof(f406,plain,(
% 0.14/0.41 ~sQ6_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f405])).
% 0.14/0.41 fof(f407,plain,(
% 0.14/0.41 $false|~sQ36_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f394,f15])).
% 0.14/0.41 fof(f408,plain,(
% 0.14/0.41 ~sQ36_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f407])).
% 0.14/0.41 fof(f534,plain,(
% 0.14/0.41 ~distinct_points(sK0_skl,sK2_skl)|distinct_points(sK1_skl,sK2_skl)|~sQ15_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f246,f30])).
% 0.14/0.41 fof(f540,plain,(
% 0.14/0.41 ~sQ0_spl|sQ6_spl|~sQ15_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f534,f50,f93,f245])).
% 0.14/0.41 fof(f552,plain,(
% 0.14/0.41 ~distinct_points(sK0_skl,sK1_skl)|distinct_points(sK1_skl,sK1_skl)|~sQ14_spl),
% 0.14/0.41 inference(resolution,[status(thm)],[f243,f30])).
% 0.14/0.41 fof(f558,plain,(
% 0.14/0.41 ~sQ4_spl|sQ11_spl|~sQ14_spl),
% 0.14/0.41 inference(split_clause,[status(thm)],[f552,f86,f203,f242])).
% 0.14/0.41 fof(f560,plain,(
% 0.14/0.41 $false|~sQ11_spl),
% 0.14/0.41 inference(forward_subsumption_resolution,[status(thm)],[f204,f15])).
% 0.14/0.41 fof(f561,plain,(
% 0.14/0.41 ~sQ11_spl),
% 0.14/0.41 inference(contradiction_clause,[status(thm)],[f560])).
% 0.14/0.41 fof(f562,plain,(
% 0.14/0.41 $false),
% 0.14/0.41 inference(sat_refutation,[status(thm)],[f56,f62,f96,f248,f396,f404,f406,f408,f540,f558,f561])).
% 0.14/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.44 % Elapsed time: 0.059645 seconds
% 0.14/0.44 % CPU time: 0.193457 seconds
% 0.14/0.44 % Total memory used: 18.466 MB
% 0.14/0.44 % Net memory used: 17.946 MB
%------------------------------------------------------------------------------