%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO197+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 : n026.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 12:26:03 PM UTC 2026
% Result : Theorem 1.72s 0.77s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO197+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
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 13:19:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 1.72/0.77 % Refutation found
% 1.72/0.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.72/0.77 % SZS output start CNFRefutation for theBenchmark
% 1.72/0.77 fof(f3,axiom,(
% 1.72/0.77 (! [X] : ~ convergent_lines(X,X) )),
% 1.72/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.72/0.77 fof(f6,axiom,(
% 1.72/0.77 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 1.72/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.72/0.77 fof(f9,axiom,(
% 1.72/0.77 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),X) ) )),
% 1.72/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.72/0.77 fof(f10,axiom,(
% 1.72/0.77 (! [X,Y] :( convergent_lines(X,Y)=> ~ apart_point_and_line(intersection_point(X,Y),Y) ) )),
% 1.72/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.72/0.77 fof(f11,axiom,(
% 1.72/0.77 (! [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) ) ) )),
% 1.72/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.72/0.77 fof(f12,axiom,(
% 1.72/0.77 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_points(X,Z)| apart_point_and_line(Z,Y) ) ) )),
% 1.72/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.72/0.77 fof(f14,axiom,(
% 1.72/0.77 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 1.72/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.72/0.77 fof(f15,conjecture,(
% 1.72/0.77 (! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(Z,Y)& convergent_lines(X,Z)& ~ apart_point_and_line(intersection_point(X,Y),Z) )=> ~ apart_point_and_line(intersection_point(Z,Y),X) ) )),
% 1.72/0.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.72/0.77 fof(f16,negated_conjecture,(
% 1.72/0.77 ~((! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(Z,Y)& convergent_lines(X,Z)& ~ apart_point_and_line(intersection_point(X,Y),Z) )=> ~ apart_point_and_line(intersection_point(Z,Y),X) ) ))),
% 1.72/0.77 inference(negated_conjecture,[status(cth)],[f15])).
% 1.72/0.77 fof(f19,plain,(
% 1.72/0.77 ![X0]: (~convergent_lines(X0,X0))),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f3])).
% 1.72/0.77 fof(f26,plain,(
% 1.72/0.77 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 1.72/0.77 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 1.72/0.77 fof(f27,plain,(
% 1.72/0.77 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 1.72/0.77 inference(miniscoping,[status(thm)],[f26])).
% 1.72/0.77 fof(f28,plain,(
% 1.72/0.77 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f27])).
% 1.72/0.77 fof(f33,plain,(
% 1.72/0.77 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),X))),
% 1.72/0.77 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 1.72/0.77 fof(f34,plain,(
% 1.72/0.77 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X0))),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f33])).
% 1.72/0.77 fof(f35,plain,(
% 1.72/0.77 ![X,Y]: (~convergent_lines(X,Y)|~apart_point_and_line(intersection_point(X,Y),Y))),
% 1.72/0.77 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 1.72/0.77 fof(f36,plain,(
% 1.72/0.77 ![X0,X1]: (~convergent_lines(X0,X1)|~apart_point_and_line(intersection_point(X0,X1),X1))),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f35])).
% 1.72/0.77 fof(f37,plain,(
% 1.72/0.77 ![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)))),
% 1.72/0.77 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 1.72/0.77 fof(f38,plain,(
% 1.72/0.77 ![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))),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f37])).
% 1.72/0.77 fof(f39,plain,(
% 1.72/0.77 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_points(X,Z)|apart_point_and_line(Z,Y)))),
% 1.72/0.77 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 1.72/0.77 fof(f40,plain,(
% 1.72/0.77 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_points(X,Z)|apart_point_and_line(Z,Y))))),
% 1.72/0.77 inference(miniscoping,[status(thm)],[f39])).
% 1.72/0.77 fof(f41,plain,(
% 1.72/0.77 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_points(X0,X2)|apart_point_and_line(X2,X1))),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f40])).
% 1.72/0.77 fof(f45,plain,(
% 1.72/0.77 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 1.72/0.77 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 1.72/0.77 fof(f46,plain,(
% 1.72/0.77 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 1.72/0.77 inference(miniscoping,[status(thm)],[f45])).
% 1.72/0.77 fof(f47,plain,(
% 1.72/0.77 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f46])).
% 1.72/0.77 fof(f48,plain,(
% 1.72/0.77 (?[X,Y,Z]: ((((convergent_lines(X,Y)&convergent_lines(Z,Y))&convergent_lines(X,Z))&~apart_point_and_line(intersection_point(X,Y),Z))&apart_point_and_line(intersection_point(Z,Y),X)))),
% 1.72/0.77 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 1.72/0.77 fof(f49,plain,(
% 1.72/0.77 ((((convergent_lines(sK0_skl,sK1_skl)&convergent_lines(sK2_skl,sK1_skl))&convergent_lines(sK0_skl,sK2_skl))&~apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl))&apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK0_skl))),
% 1.72/0.77 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])).
% 1.72/0.77 fof(f50,plain,(
% 1.72/0.77 convergent_lines(sK0_skl,sK1_skl)),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f49])).
% 1.72/0.77 fof(f51,plain,(
% 1.72/0.77 convergent_lines(sK2_skl,sK1_skl)),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f49])).
% 1.72/0.77 fof(f53,plain,(
% 1.72/0.77 ~apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK2_skl)),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f49])).
% 1.72/0.77 fof(f54,plain,(
% 1.72/0.77 apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK0_skl)),
% 1.72/0.77 inference(cnf_transformation,[status(thm)],[f49])).
% 1.72/0.77 fof(f55,plain,(
% 1.72/0.77 ![X0]: (convergent_lines(sK2_skl,X0)|convergent_lines(sK1_skl,X0))),
% 1.72/0.77 inference(resolution,[status(thm)],[f28,f51])).
% 1.72/0.77 fof(f58,plain,(
% 1.72/0.77 ![X0,X1]: (convergent_lines(sK1_skl,X0)|convergent_lines(sK2_skl,X1)|convergent_lines(X0,X1))),
% 1.72/0.77 inference(resolution,[status(thm)],[f55,f28])).
% 1.72/0.77 fof(f72,plain,(
% 1.72/0.77 ![X0]: (convergent_lines(sK1_skl,X0)|convergent_lines(X0,sK2_skl))),
% 1.72/0.77 inference(resolution,[status(thm)],[f58,f19])).
% 1.72/0.77 fof(f171,plain,(
% 1.72/0.77 ![X0]: (distinct_points(intersection_point(sK2_skl,sK1_skl),X0)|apart_point_and_line(X0,sK0_skl))),
% 1.72/0.77 inference(resolution,[status(thm)],[f41,f54])).
% 1.72/0.77 fof(f191,plain,(
% 1.72/0.77 ![X0,X1]: (distinct_lines(sK2_skl,X0)|convergent_lines(X1,X0)|convergent_lines(sK1_skl,X1))),
% 1.72/0.77 inference(resolution,[status(thm)],[f47,f72])).
% 1.72/0.77 fof(f332,plain,(
% 1.72/0.77 ![X0,X1,X2]: (apart_point_and_line(X0,sK0_skl)|~distinct_lines(X1,X2)|apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X1)|apart_point_and_line(intersection_point(sK2_skl,sK1_skl),X2)|apart_point_and_line(X0,X1)|apart_point_and_line(X0,X2))),
% 1.72/0.77 inference(resolution,[status(thm)],[f171,f38])).
% 1.72/0.77 fof(f391,plain,(
% 1.72/0.77 distinct_lines(sK2_skl,sK1_skl)),
% 1.72/0.77 inference(resolution,[status(thm)],[f191,f19])).
% 1.72/0.77 fof(f543,plain,(
% 1.72/0.77 ![X0]: (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl)|apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK1_skl))),
% 1.72/0.77 inference(resolution,[status(thm)],[f332,f391])).
% 1.72/0.77 fof(f570,definition,(
% 1.72/0.77 sQ30_spl <=> (apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl))),
% 1.72/0.77 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 1.72/0.77 fof(f571,plain,(
% 1.72/0.77 apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK1_skl)|~sQ30_spl),
% 1.72/0.77 inference(component_clause,[status(thm)],[f570])).
% 1.72/0.77 fof(f602,definition,(
% 1.72/0.77 ![X0]: (sQ38_spl <=> (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK1_skl)))),
% 1.72/0.77 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 1.72/0.77 fof(f603,plain,(
% 1.72/0.77 ![X0]: (apart_point_and_line(X0,sK0_skl)|apart_point_and_line(X0,sK2_skl)|apart_point_and_line(X0,sK1_skl)|~sQ38_spl)),
% 1.72/0.77 inference(component_clause,[status(thm)],[f602])).
% 1.72/0.77 fof(f605,definition,(
% 1.72/0.77 sQ39_spl <=> (apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl))),
% 1.72/0.77 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 1.72/0.77 fof(f606,plain,(
% 1.72/0.77 apart_point_and_line(intersection_point(sK2_skl,sK1_skl),sK2_skl)|~sQ39_spl),
% 1.72/0.77 inference(component_clause,[status(thm)],[f605])).
% 1.72/0.77 fof(f608,plain,(
% 1.72/0.77 sQ38_spl|sQ39_spl|sQ30_spl),
% 1.72/0.77 inference(split_clause,[status(thm)],[f543,f602,f605,f570])).
% 1.72/0.77 fof(f688,plain,(
% 1.72/0.77 ~convergent_lines(sK2_skl,sK1_skl)|~sQ39_spl),
% 1.72/0.77 inference(resolution,[status(thm)],[f606,f34])).
% 1.72/0.77 fof(f691,plain,(
% 1.72/0.77 $false|~sQ39_spl),
% 1.72/0.77 inference(forward_subsumption_resolution,[status(thm)],[f688,f51])).
% 1.72/0.77 fof(f692,plain,(
% 1.72/0.77 ~sQ39_spl),
% 1.72/0.77 inference(contradiction_clause,[status(thm)],[f691])).
% 1.72/0.77 fof(f693,plain,(
% 1.72/0.77 ~convergent_lines(sK2_skl,sK1_skl)|~sQ30_spl),
% 1.72/0.77 inference(resolution,[status(thm)],[f571,f36])).
% 1.72/0.77 fof(f696,plain,(
% 1.72/0.77 $false|~sQ30_spl),
% 1.72/0.77 inference(forward_subsumption_resolution,[status(thm)],[f693,f51])).
% 1.72/0.77 fof(f697,plain,(
% 1.72/0.77 ~sQ30_spl),
% 1.72/0.77 inference(contradiction_clause,[status(thm)],[f696])).
% 1.72/0.77 fof(f1483,plain,(
% 1.72/0.77 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ38_spl),
% 1.72/0.77 inference(resolution,[status(thm)],[f603,f53])).
% 1.72/0.77 fof(f1488,definition,(
% 1.72/0.77 sQ86_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl))),
% 1.72/0.77 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 1.72/0.77 fof(f1489,plain,(
% 1.72/0.77 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK0_skl)|~sQ86_spl),
% 1.72/0.77 inference(component_clause,[status(thm)],[f1488])).
% 1.72/0.77 fof(f1491,definition,(
% 1.72/0.77 sQ87_spl <=> (apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl))),
% 1.72/0.77 introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition])).
% 1.72/0.77 fof(f1492,plain,(
% 1.72/0.77 apart_point_and_line(intersection_point(sK0_skl,sK1_skl),sK1_skl)|~sQ87_spl),
% 1.72/0.77 inference(component_clause,[status(thm)],[f1491])).
% 1.72/0.77 fof(f1494,plain,(
% 1.72/0.77 sQ86_spl|sQ87_spl|~sQ38_spl),
% 1.72/0.77 inference(split_clause,[status(thm)],[f1483,f1488,f1491,f602])).
% 1.72/0.77 fof(f1495,plain,(
% 1.72/0.77 ~convergent_lines(sK0_skl,sK1_skl)|~sQ86_spl),
% 1.72/0.77 inference(resolution,[status(thm)],[f1489,f34])).
% 1.72/0.77 fof(f1498,plain,(
% 1.72/0.77 $false|~sQ86_spl),
% 1.72/0.77 inference(forward_subsumption_resolution,[status(thm)],[f1495,f50])).
% 1.72/0.77 fof(f1499,plain,(
% 1.72/0.77 ~sQ86_spl),
% 1.72/0.77 inference(contradiction_clause,[status(thm)],[f1498])).
% 1.72/0.77 fof(f1500,plain,(
% 1.72/0.77 ~convergent_lines(sK0_skl,sK1_skl)|~sQ87_spl),
% 1.72/0.77 inference(resolution,[status(thm)],[f1492,f36])).
% 1.72/0.77 fof(f1503,plain,(
% 1.72/0.77 $false|~sQ87_spl),
% 1.72/0.77 inference(forward_subsumption_resolution,[status(thm)],[f1500,f50])).
% 1.72/0.77 fof(f1504,plain,(
% 1.72/0.77 ~sQ87_spl),
% 1.72/0.77 inference(contradiction_clause,[status(thm)],[f1503])).
% 1.72/0.77 fof(f1505,plain,(
% 1.72/0.77 $false),
% 1.72/0.77 inference(sat_refutation,[status(thm)],[f608,f692,f697,f1494,f1499,f1504])).
% 1.72/0.77 % SZS output end CNFRefutation for theBenchmark.p
% 1.98/0.79 % Elapsed time: 0.401696 seconds
% 1.98/0.79 % CPU time: 2.979285 seconds
% 1.98/0.79 % Total memory used: 42.525 MB
% 1.98/0.79 % Net memory used: 35.303 MB
%------------------------------------------------------------------------------