%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO184+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 : n014.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 12:25:59 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO184+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 13:13:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f1,axiom,(
% 0.10/0.40 (! [X] : ~ distinct_points(X,X) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f4,axiom,(
% 0.10/0.40 (! [X,Y,Z] :( distinct_points(X,Y)=> ( distinct_points(X,Z)| distinct_points(Y,Z) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f7,axiom,(
% 0.10/0.40 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f8,axiom,(
% 0.10/0.40 (! [X,Y] :( distinct_points(X,Y)=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f11,axiom,(
% 0.10/0.40 (! [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) ) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f32,axiom,(
% 0.10/0.40 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f34,axiom,(
% 0.10/0.40 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f36,conjecture,(
% 0.10/0.40 (! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& incident_point_and_line(X,U)& incident_point_and_line(Y,U) )=> equal_lines(U,line_connecting(X,Y)) ) )),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f37,negated_conjecture,(
% 0.10/0.40 ~((! [X,Y,U,V] :( ( distinct_points(X,Y)& convergent_lines(U,V)& incident_point_and_line(X,U)& incident_point_and_line(Y,U) )=> equal_lines(U,line_connecting(X,Y)) ) ))),
% 0.10/0.40 inference(negated_conjecture,[status(cth)],[f36])).
% 0.10/0.40 fof(f38,plain,(
% 0.10/0.40 ![X0]: (~distinct_points(X0,X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.40 fof(f41,plain,(
% 0.10/0.40 ![X,Y,Z]: (~distinct_points(X,Y)|(distinct_points(X,Z)|distinct_points(Y,Z)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.10/0.40 fof(f42,plain,(
% 0.10/0.40 ![X,Y]: (~distinct_points(X,Y)|(![Z]: (distinct_points(X,Z)|distinct_points(Y,Z))))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f41])).
% 0.10/0.40 fof(f43,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~distinct_points(X0,X1)|distinct_points(X0,X2)|distinct_points(X1,X2))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f42])).
% 0.10/0.40 fof(f50,plain,(
% 0.10/0.40 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(X,line_connecting(X,Y)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.10/0.40 fof(f51,plain,(
% 0.10/0.40 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X0,line_connecting(X0,X1)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f50])).
% 0.10/0.40 fof(f52,plain,(
% 0.10/0.40 ![X,Y]: (~distinct_points(X,Y)|~apart_point_and_line(Y,line_connecting(X,Y)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.10/0.40 fof(f53,plain,(
% 0.10/0.40 ![X0,X1]: (~distinct_points(X0,X1)|~apart_point_and_line(X1,line_connecting(X0,X1)))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f52])).
% 0.10/0.40 fof(f58,plain,(
% 0.10/0.40 ![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)))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.10/0.40 fof(f59,plain,(
% 0.10/0.40 ![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))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f58])).
% 0.10/0.40 fof(f111,plain,(
% 0.10/0.40 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f32])).
% 0.10/0.40 fof(f112,plain,(
% 0.10/0.40 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f111])).
% 0.10/0.40 fof(f114,plain,(
% 0.10/0.40 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f112])).
% 0.10/0.40 fof(f119,plain,(
% 0.10/0.40 ![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)))),
% 0.10/0.40 inference(NNF_transformation,[status(thm)],[f34])).
% 0.10/0.40 fof(f120,plain,(
% 0.10/0.40 (![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)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f119])).
% 0.10/0.40 fof(f121,plain,(
% 0.10/0.40 ![X0,X1]: (~incident_point_and_line(X0,X1)|~apart_point_and_line(X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f120])).
% 0.10/0.40 fof(f127,plain,(
% 0.10/0.40 (?[X,Y,U,V]: ((((distinct_points(X,Y)&convergent_lines(U,V))&incident_point_and_line(X,U))&incident_point_and_line(Y,U))&~equal_lines(U,line_connecting(X,Y))))),
% 0.10/0.40 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.10/0.40 fof(f128,plain,(
% 0.10/0.40 ?[X,Y,U]: ((((distinct_points(X,Y)&(?[V]: convergent_lines(U,V)))&incident_point_and_line(X,U))&incident_point_and_line(Y,U))&~equal_lines(U,line_connecting(X,Y)))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f127])).
% 0.10/0.40 fof(f129,plain,(
% 0.10/0.40 ((((distinct_points(sK0_skl,sK1_skl)&convergent_lines(sK2_skl,sK3_skl))&incident_point_and_line(sK0_skl,sK2_skl))&incident_point_and_line(sK1_skl,sK2_skl))&~equal_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.10/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(U,sK2_skl),skolemize(V,sK3_skl)],[f128])).
% 0.10/0.40 fof(f130,plain,(
% 0.10/0.40 distinct_points(sK0_skl,sK1_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f129])).
% 0.10/0.40 fof(f132,plain,(
% 0.10/0.40 incident_point_and_line(sK0_skl,sK2_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f129])).
% 0.10/0.40 fof(f133,plain,(
% 0.10/0.40 incident_point_and_line(sK1_skl,sK2_skl)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f129])).
% 0.10/0.40 fof(f134,plain,(
% 0.10/0.40 ~equal_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f129])).
% 0.10/0.40 fof(f146,plain,(
% 0.10/0.40 ![X0]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f43,f130])).
% 0.10/0.40 fof(f150,plain,(
% 0.10/0.40 distinct_lines(sK2_skl,line_connecting(sK0_skl,sK1_skl))),
% 0.10/0.40 inference(resolution,[status(thm)],[f134,f114])).
% 0.10/0.40 fof(f151,plain,(
% 0.10/0.40 ![X0,X1]: (distinct_points(sK0_skl,X0)|distinct_points(sK1_skl,X1)|distinct_points(X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f146,f43])).
% 0.10/0.40 fof(f163,plain,(
% 0.10/0.40 distinct_points(sK1_skl,sK0_skl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f151,f38])).
% 0.10/0.40 fof(f186,plain,(
% 0.10/0.40 ![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)))),
% 0.10/0.40 inference(resolution,[status(thm)],[f59,f150])).
% 0.10/0.40 fof(f236,plain,(
% 0.10/0.40 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))),
% 0.10/0.40 inference(resolution,[status(thm)],[f186,f163])).
% 0.10/0.40 fof(f247,definition,(
% 0.10/0.40 sQ8_spl <=> (apart_point_and_line(sK1_skl,sK2_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f248,plain,(
% 0.10/0.40 apart_point_and_line(sK1_skl,sK2_skl)|~sQ8_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f247])).
% 0.10/0.40 fof(f250,definition,(
% 0.10/0.40 sQ9_spl <=> (apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f251,plain,(
% 0.10/0.40 apart_point_and_line(sK1_skl,line_connecting(sK0_skl,sK1_skl))|~sQ9_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f250])).
% 0.10/0.40 fof(f253,definition,(
% 0.10/0.40 sQ10_spl <=> (apart_point_and_line(sK0_skl,sK2_skl))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f254,plain,(
% 0.10/0.40 apart_point_and_line(sK0_skl,sK2_skl)|~sQ10_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f253])).
% 0.10/0.40 fof(f256,definition,(
% 0.10/0.40 sQ11_spl <=> (apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f257,plain,(
% 0.10/0.40 apart_point_and_line(sK0_skl,line_connecting(sK0_skl,sK1_skl))|~sQ11_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f256])).
% 0.10/0.40 fof(f259,plain,(
% 0.10/0.40 sQ8_spl|sQ9_spl|sQ10_spl|sQ11_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f236,f247,f250,f253,f256])).
% 0.10/0.40 fof(f303,plain,(
% 0.10/0.40 ~incident_point_and_line(sK0_skl,sK2_skl)|~sQ10_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f254,f121])).
% 0.10/0.40 fof(f304,plain,(
% 0.10/0.40 $false|~sQ10_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f303,f132])).
% 0.10/0.40 fof(f305,plain,(
% 0.10/0.40 ~sQ10_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f304])).
% 0.10/0.40 fof(f306,plain,(
% 0.10/0.40 ~distinct_points(sK0_skl,sK1_skl)|~sQ11_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f257,f51])).
% 0.10/0.40 fof(f310,plain,(
% 0.10/0.40 $false|~sQ11_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f306,f130])).
% 0.10/0.40 fof(f311,plain,(
% 0.10/0.40 ~sQ11_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f310])).
% 0.10/0.40 fof(f314,plain,(
% 0.10/0.40 ~incident_point_and_line(sK1_skl,sK2_skl)|~sQ8_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f248,f121])).
% 0.10/0.40 fof(f315,plain,(
% 0.10/0.40 $false|~sQ8_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f314,f133])).
% 0.10/0.40 fof(f316,plain,(
% 0.10/0.40 ~sQ8_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f315])).
% 0.10/0.40 fof(f317,plain,(
% 0.10/0.40 ~distinct_points(sK0_skl,sK1_skl)|~sQ9_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f251,f53])).
% 0.10/0.40 fof(f321,plain,(
% 0.10/0.40 $false|~sQ9_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f317,f130])).
% 0.10/0.40 fof(f322,plain,(
% 0.10/0.40 ~sQ9_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f321])).
% 0.10/0.40 fof(f323,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(sat_refutation,[status(thm)],[f259,f305,f311,f316,f322])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.42 % Elapsed time: 0.044194 seconds
% 0.10/0.42 % CPU time: 0.138819 seconds
% 0.10/0.42 % Total memory used: 18.758 MB
% 0.10/0.42 % Net memory used: 18.611 MB
%------------------------------------------------------------------------------