%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO203+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 12:26:04 PM UTC 2026
% Result : Theorem 3.14s 0.92s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO203+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Sun Sep 20 13:26:13 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.37 % Drodi V4.1.1
% 3.14/0.92 % Refutation found
% 3.14/0.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.14/0.92 % SZS output start CNFRefutation for theBenchmark
% 3.14/0.92 fof(f2,axiom,(
% 3.14/0.92 (! [X] : ~ distinct_lines(X,X) )),
% 3.14/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.14/0.92 fof(f3,axiom,(
% 3.14/0.92 (! [X] : ~ convergent_lines(X,X) )),
% 3.14/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.14/0.92 fof(f5,axiom,(
% 3.14/0.92 (! [X,Y,Z] :( distinct_lines(X,Y)=> ( distinct_lines(X,Z)| distinct_lines(Y,Z) ) ) )),
% 3.14/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.14/0.92 fof(f6,axiom,(
% 3.14/0.92 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( convergent_lines(X,Z)| convergent_lines(Y,Z) ) ) )),
% 3.14/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.14/0.92 fof(f11,axiom,(
% 3.14/0.92 (! [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) ) ) )),
% 3.14/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.14/0.92 fof(f13,axiom,(
% 3.14/0.92 (! [X,Y,Z] :( apart_point_and_line(X,Y)=> ( distinct_lines(Y,Z)| apart_point_and_line(X,Z) ) ) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f14,axiom,(
% 3.93/0.92 (! [X,Y,Z] :( convergent_lines(X,Y)=> ( distinct_lines(Y,Z)| convergent_lines(X,Z) ) ) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f15,axiom,(
% 3.93/0.92 (! [X,Y] :( distinct_lines(X,Y)=> convergent_lines(X,Y) ) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f16,axiom,(
% 3.93/0.92 (! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f17,axiom,(
% 3.93/0.92 (! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f19,axiom,(
% 3.93/0.92 (! [L,M] :( convergent_lines(L,M)| unorthogonal_lines(L,M) ) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f21,axiom,(
% 3.93/0.92 (! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f32,axiom,(
% 3.93/0.92 (! [X,Y] :( equal_lines(X,Y)<=> ~ distinct_lines(X,Y) ) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f34,axiom,(
% 3.93/0.92 (! [X,Y] :( incident_point_and_line(X,Y)<=> ~ apart_point_and_line(X,Y) ) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f36,conjecture,(
% 3.93/0.92 (! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(X,Z)& distinct_points(intersection_point(X,Y),intersection_point(X,Z)) )=> equal_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ) )),
% 3.93/0.92 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.93/0.92 fof(f37,negated_conjecture,(
% 3.93/0.92 ~((! [X,Y,Z] :( ( convergent_lines(X,Y)& convergent_lines(X,Z)& distinct_points(intersection_point(X,Y),intersection_point(X,Z)) )=> equal_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ) ))),
% 3.93/0.92 inference(negated_conjecture,[status(cth)],[f36])).
% 3.93/0.92 fof(f39,plain,(
% 3.93/0.92 ![X0]: (~distinct_lines(X0,X0))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f2])).
% 3.93/0.92 fof(f40,plain,(
% 3.93/0.92 ![X0]: (~convergent_lines(X0,X0))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f3])).
% 3.93/0.92 fof(f44,plain,(
% 3.93/0.92 ![X,Y,Z]: (~distinct_lines(X,Y)|(distinct_lines(X,Z)|distinct_lines(Y,Z)))),
% 3.93/0.92 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 3.93/0.92 fof(f45,plain,(
% 3.93/0.92 ![X,Y]: (~distinct_lines(X,Y)|(![Z]: (distinct_lines(X,Z)|distinct_lines(Y,Z))))),
% 3.93/0.92 inference(miniscoping,[status(thm)],[f44])).
% 3.93/0.92 fof(f46,plain,(
% 3.93/0.92 ![X0,X1,X2]: (~distinct_lines(X0,X1)|distinct_lines(X0,X2)|distinct_lines(X1,X2))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f45])).
% 3.93/0.92 fof(f47,plain,(
% 3.93/0.92 ![X,Y,Z]: (~convergent_lines(X,Y)|(convergent_lines(X,Z)|convergent_lines(Y,Z)))),
% 3.93/0.92 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 3.93/0.92 fof(f48,plain,(
% 3.93/0.92 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (convergent_lines(X,Z)|convergent_lines(Y,Z))))),
% 3.93/0.92 inference(miniscoping,[status(thm)],[f47])).
% 3.93/0.92 fof(f49,plain,(
% 3.93/0.92 ![X0,X1,X2]: (~convergent_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f48])).
% 3.93/0.92 fof(f58,plain,(
% 3.93/0.92 ![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)))),
% 3.93/0.92 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 3.93/0.92 fof(f59,plain,(
% 3.93/0.92 ![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))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f58])).
% 3.93/0.92 fof(f63,plain,(
% 3.93/0.92 ![X,Y,Z]: (~apart_point_and_line(X,Y)|(distinct_lines(Y,Z)|apart_point_and_line(X,Z)))),
% 3.93/0.92 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 3.93/0.92 fof(f64,plain,(
% 3.93/0.92 ![X,Y]: (~apart_point_and_line(X,Y)|(![Z]: (distinct_lines(Y,Z)|apart_point_and_line(X,Z))))),
% 3.93/0.92 inference(miniscoping,[status(thm)],[f63])).
% 3.93/0.92 fof(f65,plain,(
% 3.93/0.92 ![X0,X1,X2]: (~apart_point_and_line(X0,X1)|distinct_lines(X1,X2)|apart_point_and_line(X0,X2))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f64])).
% 3.93/0.92 fof(f66,plain,(
% 3.93/0.92 ![X,Y,Z]: (~convergent_lines(X,Y)|(distinct_lines(Y,Z)|convergent_lines(X,Z)))),
% 3.93/0.92 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 3.93/0.92 fof(f67,plain,(
% 3.93/0.92 ![X,Y]: (~convergent_lines(X,Y)|(![Z]: (distinct_lines(Y,Z)|convergent_lines(X,Z))))),
% 3.93/0.92 inference(miniscoping,[status(thm)],[f66])).
% 3.93/0.92 fof(f68,plain,(
% 3.93/0.92 ![X0,X1,X2]: (~convergent_lines(X0,X1)|distinct_lines(X1,X2)|convergent_lines(X0,X2))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f67])).
% 3.93/0.92 fof(f69,plain,(
% 3.93/0.92 ![X,Y]: (~distinct_lines(X,Y)|convergent_lines(X,Y))),
% 3.93/0.92 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 3.93/0.92 fof(f70,plain,(
% 3.93/0.92 ![X0,X1]: (~distinct_lines(X0,X1)|convergent_lines(X0,X1))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f69])).
% 3.93/0.92 fof(f71,plain,(
% 3.93/0.92 ![X0,X1]: (~convergent_lines(parallel_through_point(X0,X1),X0))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f16])).
% 3.93/0.92 fof(f72,plain,(
% 3.93/0.92 ![X0,X1]: (~apart_point_and_line(X0,parallel_through_point(X1,X0)))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f17])).
% 3.93/0.92 fof(f76,plain,(
% 3.93/0.92 ![X0,X1]: (convergent_lines(X0,X1)|unorthogonal_lines(X0,X1))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f19])).
% 3.93/0.92 fof(f83,plain,(
% 3.93/0.92 ![X0,X1]: (~unorthogonal_lines(orthogonal_through_point(X0,X1),X0))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f21])).
% 3.93/0.92 fof(f111,plain,(
% 3.93/0.92 ![X,Y]: ((~equal_lines(X,Y)|~distinct_lines(X,Y))&(equal_lines(X,Y)|distinct_lines(X,Y)))),
% 3.93/0.92 inference(NNF_transformation,[status(thm)],[f32])).
% 3.93/0.92 fof(f112,plain,(
% 3.93/0.92 (![X,Y]: (~equal_lines(X,Y)|~distinct_lines(X,Y)))&(![X,Y]: (equal_lines(X,Y)|distinct_lines(X,Y)))),
% 3.93/0.92 inference(miniscoping,[status(thm)],[f111])).
% 3.93/0.92 fof(f113,plain,(
% 3.93/0.92 ![X0,X1]: (~equal_lines(X0,X1)|~distinct_lines(X0,X1))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f112])).
% 3.93/0.92 fof(f114,plain,(
% 3.93/0.92 ![X0,X1]: (equal_lines(X0,X1)|distinct_lines(X0,X1))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f112])).
% 3.93/0.92 fof(f119,plain,(
% 3.93/0.92 ![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)))),
% 3.93/0.92 inference(NNF_transformation,[status(thm)],[f34])).
% 3.93/0.92 fof(f120,plain,(
% 3.93/0.92 (![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)))),
% 3.93/0.92 inference(miniscoping,[status(thm)],[f119])).
% 3.93/0.92 fof(f121,plain,(
% 3.93/0.92 ![X0,X1]: (~incident_point_and_line(X0,X1)|~apart_point_and_line(X0,X1))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f120])).
% 3.93/0.92 fof(f122,plain,(
% 3.93/0.92 ![X0,X1]: (incident_point_and_line(X0,X1)|apart_point_and_line(X0,X1))),
% 3.93/0.92 inference(cnf_transformation,[status(thm)],[f120])).
% 3.93/0.92 fof(f127,plain,(
% 3.93/0.92 (?[X,Y,Z]: (((convergent_lines(X,Y)&convergent_lines(X,Z))&distinct_points(intersection_point(X,Y),intersection_point(X,Z)))&~equal_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X)))),
% 3.93/0.92 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 3.93/0.92 fof(f128,plain,(
% 3.93/0.92 (((convergent_lines(sK0_skl,sK1_skl)&convergent_lines(sK0_skl,sK2_skl))&distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)))&~equal_lines(line_connecting(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl)),sK0_skl))),
% 3.93/0.94 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)],[f127])).
% 3.93/0.94 fof(f131,plain,(
% 3.93/0.94 distinct_points(intersection_point(sK0_skl,sK1_skl),intersection_point(sK0_skl,sK2_skl))),
% 3.93/0.94 inference(cnf_transformation,[status(thm)],[f128])).
% 3.93/0.94 fof(f188,plain,(
% 3.93/0.94 ![X0,X1,X2]: (unorthogonal_lines(X0,X1)|convergent_lines(X0,X2)|convergent_lines(X1,X2))),
% 3.93/0.94 inference(resolution,[status(thm)],[f76,f49])).
% 3.93/0.94 fof(f201,plain,(
% 3.93/0.94 ![X0,X1,X2]: (distinct_lines(X0,X1)|distinct_lines(X2,X1)|equal_lines(X0,X2))),
% 3.93/0.94 inference(resolution,[status(thm)],[f46,f114])).
% 3.93/0.94 fof(f262,plain,(
% 3.93/0.94 ![X0,X1]: (unorthogonal_lines(X0,X1)|convergent_lines(X1,X0))),
% 3.93/0.94 inference(resolution,[status(thm)],[f188,f40])).
% 3.93/0.94 fof(f278,plain,(
% 3.93/0.94 ![X0,X1,X2]: (distinct_lines(X0,X1)|apart_point_and_line(X2,X1)|incident_point_and_line(X2,X0))),
% 3.93/0.94 inference(resolution,[status(thm)],[f65,f122])).
% 3.93/0.94 fof(f296,plain,(
% 3.93/0.94 ![X0,X1,X2]: (distinct_lines(X0,X1)|convergent_lines(X2,X1)|unorthogonal_lines(X0,X2))),
% 3.93/0.94 inference(resolution,[status(thm)],[f68,f262])).
% 3.93/0.94 fof(f303,plain,(
% 3.93/0.94 ![X0,X1]: (convergent_lines(X0,X1)|equal_lines(X0,X1))),
% 3.93/0.94 inference(resolution,[status(thm)],[f70,f114])).
% 3.93/0.94 fof(f364,plain,(
% 3.93/0.94 ![X0,X1]: (equal_lines(parallel_through_point(X0,X1),X0))),
% 3.93/0.94 inference(resolution,[status(thm)],[f303,f71])).
% 3.93/0.94 fof(f398,plain,(
% 3.93/0.94 ![X0,X1]: (~distinct_lines(parallel_through_point(X0,X1),X0))),
% 3.93/0.94 inference(resolution,[status(thm)],[f113,f364])).
% 3.93/0.94 fof(f580,plain,(
% 3.93/0.94 ![X0,X1]: (distinct_lines(X0,X1)|equal_lines(X1,X0))),
% 3.93/0.94 inference(resolution,[status(thm)],[f201,f39])).
% 3.93/0.94 fof(f590,plain,(
% 3.93/0.94 ![X0,X1]: (equal_lines(X0,parallel_through_point(X0,X1)))),
% 3.93/0.94 inference(resolution,[status(thm)],[f580,f398])).
% 3.93/0.94 fof(f596,plain,(
% 3.93/0.94 ![X0,X1]: (~distinct_lines(X0,parallel_through_point(X0,X1)))),
% 3.93/0.94 inference(resolution,[status(thm)],[f590,f113])).
% 3.93/0.94 fof(f776,plain,(
% 3.93/0.94 ![X0,X1,X2]: (apart_point_and_line(X0,parallel_through_point(X1,X2))|incident_point_and_line(X0,X1))),
% 3.93/0.94 inference(resolution,[status(thm)],[f278,f596])).
% 3.93/0.94 fof(f792,plain,(
% 3.93/0.94 ![X0,X1]: (incident_point_and_line(X0,X1))),
% 3.93/0.94 inference(resolution,[status(thm)],[f776,f72])).
% 3.93/0.94 fof(f795,plain,(
% 3.93/0.94 ![X0,X1]: (~apart_point_and_line(X0,X1))),
% 3.93/0.94 inference(backward_subsumption_resolution,[status(thm)],[f121,f792])).
% 3.93/0.94 fof(f798,plain,(
% 3.93/0.94 ![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))),
% 3.93/0.94 inference(backward_subsumption_resolution,[status(thm)],[f59,f795])).
% 3.93/0.94 fof(f856,plain,(
% 3.93/0.94 ![X0,X1,X2,X3]: (~distinct_points(X0,X1)|~distinct_lines(X2,X3)|apart_point_and_line(X0,X3)|apart_point_and_line(X1,X2))),
% 3.93/0.94 inference(forward_subsumption_resolution,[status(thm)],[f798,f795])).
% 3.93/0.94 fof(f1253,plain,(
% 3.93/0.94 ![X0,X1,X2]: (distinct_lines(X0,X1)|unorthogonal_lines(X0,parallel_through_point(X1,X2)))),
% 3.93/0.94 inference(resolution,[status(thm)],[f296,f71])).
% 3.93/0.94 fof(f1280,plain,(
% 3.93/0.94 ![X0,X1,X2]: (distinct_lines(orthogonal_through_point(parallel_through_point(X0,X1),X2),X0))),
% 3.93/0.94 inference(resolution,[status(thm)],[f1253,f83])).
% 3.93/0.94 fof(f1288,plain,(
% 3.93/0.94 ![X0,X1]: (~distinct_lines(X0,X1)|apart_point_and_line(intersection_point(sK0_skl,sK1_skl),X1)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0))),
% 3.93/0.94 inference(resolution,[status(thm)],[f856,f131])).
% 3.93/0.94 fof(f1305,plain,(
% 3.93/0.94 ![X0,X1]: (~distinct_lines(X0,X1)|apart_point_and_line(intersection_point(sK0_skl,sK2_skl),X0))),
% 3.93/0.94 inference(forward_subsumption_resolution,[status(thm)],[f1288,f795])).
% 3.93/0.94 fof(f1364,plain,(
% 3.93/0.94 ![X0,X1]: (~distinct_lines(X0,X1))),
% 3.93/0.94 inference(resolution,[status(thm)],[f1305,f795])).
% 3.93/0.94 fof(f1386,plain,(
% 3.93/0.94 $false),
% 3.93/0.94 inference(backward_subsumption_resolution,[status(thm)],[f1280,f1364])).
% 3.93/0.94 % SZS output end CNFRefutation for theBenchmark.p
% 3.93/0.95 % Elapsed time: 0.579476 seconds
% 3.93/0.95 % CPU time: 4.340521 seconds
% 3.93/0.95 % Total memory used: 56.290 MB
% 3.93/0.95 % Net memory used: 48.564 MB
%------------------------------------------------------------------------------