%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO612+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:26:43 PM UTC 2026
% Result : Theorem 1.35s 0.67s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO612+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 17:53:47 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 1.35/0.67 % Refutation found
% 1.35/0.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.35/0.67 % SZS output start CNFRefutation for theBenchmark
% 1.35/0.67 fof(f8,axiom,(
% 1.35/0.67 (! [A,B,C,D] :( perp(A,B,C,D)=> perp(C,D,A,B) ) )),
% 1.35/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.35/0.67 fof(f9,axiom,(
% 1.35/0.67 (! [A,B,C,D,E,F] :( ( perp(A,B,C,D)& perp(C,D,E,F) )=> para(A,B,E,F) ) )),
% 1.35/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.35/0.67 fof(f17,axiom,(
% 1.35/0.67 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 1.35/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.35/0.67 fof(f21,axiom,(
% 1.35/0.67 (! [A,B,C,D,P,Q,U,V] :( eqangle(A,B,C,D,P,Q,U,V)=> eqangle(A,B,P,Q,C,D,U,V) ) )),
% 1.35/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.35/0.67 fof(f40,axiom,(
% 1.35/0.67 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 1.35/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.35/0.67 fof(f42,axiom,(
% 1.35/0.67 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& ~ coll(P,Q,A) )=> cyclic(A,B,P,Q) ) )),
% 1.35/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.35/0.67 fof(f43,axiom,(
% 1.35/0.67 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 1.35/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.35/0.67 fof(f95,conjecture,(
% 1.35/0.67 (! [A,B,C,O,G,D,E,F,NWPNT1] :( ( circle(O,A,B,C)& perp(G,C,A,B)& coll(G,A,B)& circle(O,C,D,NWPNT1)& coll(D,C,G)& perp(E,D,A,C)& coll(E,A,C)& perp(F,D,B,C)& coll(F,B,C) )=> cyclic(A,E,F,B) ) )),
% 1.35/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.35/0.67 fof(f96,negated_conjecture,(
% 1.35/0.67 ~((! [A,B,C,O,G,D,E,F,NWPNT1] :( ( circle(O,A,B,C)& perp(G,C,A,B)& coll(G,A,B)& circle(O,C,D,NWPNT1)& coll(D,C,G)& perp(E,D,A,C)& coll(E,A,C)& perp(F,D,B,C)& coll(F,B,C) )=> cyclic(A,E,F,B) ) ))),
% 1.35/0.67 inference(negated_conjecture,[status(cth)],[f95])).
% 1.35/0.67 fof(f113,plain,(
% 1.35/0.67 ![A,B,C,D]: (~perp(A,B,C,D)|perp(C,D,A,B))),
% 1.35/0.67 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 1.35/0.67 fof(f114,plain,(
% 1.35/0.67 ![X0,X1,X2,X3]: (~perp(X0,X1,X2,X3)|perp(X2,X3,X0,X1))),
% 1.35/0.67 inference(cnf_transformation,[status(thm)],[f113])).
% 1.35/0.67 fof(f115,plain,(
% 1.35/0.67 ![A,B,C,D,E,F]: ((~perp(A,B,C,D)|~perp(C,D,E,F))|para(A,B,E,F))),
% 1.35/0.67 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 1.35/0.67 fof(f116,plain,(
% 1.35/0.67 ![A,B,E,F]: ((![C,D]: (~perp(A,B,C,D)|~perp(C,D,E,F)))|para(A,B,E,F))),
% 1.35/0.67 inference(miniscoping,[status(thm)],[f115])).
% 1.35/0.67 fof(f117,plain,(
% 1.35/0.67 ![X0,X1,X2,X3,X4,X5]: (~perp(X0,X1,X2,X3)|~perp(X2,X3,X4,X5)|para(X0,X1,X4,X5))),
% 1.35/0.67 inference(cnf_transformation,[status(thm)],[f116])).
% 1.35/0.67 fof(f134,plain,(
% 1.35/0.67 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 1.35/0.67 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 1.35/0.67 fof(f135,plain,(
% 1.35/0.67 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 1.35/0.67 inference(miniscoping,[status(thm)],[f134])).
% 1.35/0.67 fof(f136,plain,(
% 1.35/0.67 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 1.35/0.67 inference(cnf_transformation,[status(thm)],[f135])).
% 1.35/0.67 fof(f143,plain,(
% 1.35/0.67 ![A,B,C,D,P,Q,U,V]: (~eqangle(A,B,C,D,P,Q,U,V)|eqangle(A,B,P,Q,C,D,U,V))),
% 1.35/0.67 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 1.35/0.67 fof(f144,plain,(
% 1.35/0.67 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|eqangle(X0,X1,X4,X5,X2,X3,X6,X7))),
% 1.35/0.67 inference(cnf_transformation,[status(thm)],[f143])).
% 1.35/0.67 fof(f187,plain,(
% 1.35/0.67 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 1.35/0.67 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 1.35/0.67 fof(f188,plain,(
% 1.35/0.67 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 1.35/0.67 inference(miniscoping,[status(thm)],[f187])).
% 1.35/0.67 fof(f189,plain,(
% 1.35/0.67 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 1.35/0.67 inference(cnf_transformation,[status(thm)],[f188])).
% 1.35/0.67 fof(f192,plain,(
% 1.35/0.67 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|coll(P,Q,A))|cyclic(A,B,P,Q))),
% 1.35/0.67 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 1.35/0.67 fof(f193,plain,(
% 1.35/0.67 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|coll(X0,X3,X1)|cyclic(X1,X2,X0,X3))),
% 1.35/0.67 inference(cnf_transformation,[status(thm)],[f192])).
% 1.35/0.67 fof(f194,plain,(
% 1.35/0.67 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 1.35/0.67 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 1.35/0.68 fof(f195,plain,(
% 1.35/0.68 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 1.35/0.68 inference(cnf_transformation,[status(thm)],[f194])).
% 1.35/0.68 fof(f369,plain,(
% 1.35/0.68 (?[A,B,C,O,G,D,E,F,NWPNT1]: (((((((((circle(O,A,B,C)&perp(G,C,A,B))&coll(G,A,B))&circle(O,C,D,NWPNT1))&coll(D,C,G))&perp(E,D,A,C))&coll(E,A,C))&perp(F,D,B,C))&coll(F,B,C))&~cyclic(A,E,F,B)))),
% 1.35/0.68 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 1.35/0.68 fof(f370,plain,(
% 1.35/0.68 ?[A,B,E,F]: ((?[C]: ((?[D]: ((((?[G]: ((?[O]: (((circle(O,A,B,C)&perp(G,C,A,B))&coll(G,A,B))&(?[NWPNT1]: circle(O,C,D,NWPNT1))))&coll(D,C,G)))&perp(E,D,A,C))&coll(E,A,C))&perp(F,D,B,C)))&coll(F,B,C)))&~cyclic(A,E,F,B))),
% 1.35/0.68 inference(miniscoping,[status(thm)],[f369])).
% 1.35/0.68 fof(f371,plain,(
% 1.35/0.68 (((((((((circle(sK27_skl,sK20_skl,sK21_skl,sK24_skl)&perp(sK26_skl,sK24_skl,sK20_skl,sK21_skl))&coll(sK26_skl,sK20_skl,sK21_skl))&circle(sK27_skl,sK24_skl,sK25_skl,sK28_skl))&coll(sK25_skl,sK24_skl,sK26_skl))&perp(sK22_skl,sK25_skl,sK20_skl,sK24_skl))&coll(sK22_skl,sK20_skl,sK24_skl))&perp(sK23_skl,sK25_skl,sK21_skl,sK24_skl))&coll(sK23_skl,sK21_skl,sK24_skl))&~cyclic(sK20_skl,sK22_skl,sK23_skl,sK21_skl))),
% 1.35/0.68 inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl]),skolemize(A,sK20_skl),skolemize(B,sK21_skl),skolemize(E,sK22_skl),skolemize(F,sK23_skl),skolemize(C,sK24_skl),skolemize(D,sK25_skl),skolemize(G,sK26_skl),skolemize(O,sK27_skl),skolemize(NWPNT1,sK28_skl)],[f370])).
% 1.35/0.68 fof(f379,plain,(
% 1.35/0.68 perp(sK23_skl,sK25_skl,sK21_skl,sK24_skl)),
% 1.35/0.68 inference(cnf_transformation,[status(thm)],[f371])).
% 1.35/0.68 fof(f381,plain,(
% 1.35/0.68 ~cyclic(sK20_skl,sK22_skl,sK23_skl,sK21_skl)),
% 1.35/0.68 inference(cnf_transformation,[status(thm)],[f371])).
% 1.35/0.68 fof(f387,plain,(
% 1.35/0.68 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~perp(X0,X1,X2,X3)|~perp(X2,X3,X4,X5)|eqangle(X0,X1,X6,X7,X4,X5,X6,X7))),
% 1.35/0.68 inference(resolution,[status(thm)],[f117,f189])).
% 1.35/0.68 fof(f638,plain,(
% 1.35/0.68 ![X0,X1,X2,X3]: (~perp(X0,X1,sK23_skl,sK25_skl)|eqangle(X0,X1,X2,X3,sK21_skl,sK24_skl,X2,X3))),
% 1.35/0.68 inference(resolution,[status(thm)],[f387,f379])).
% 1.35/0.68 fof(f650,plain,(
% 1.35/0.68 ![X0,X1,X2,X3]: (eqangle(X0,X1,X2,X3,sK21_skl,sK24_skl,X2,X3)|~perp(sK23_skl,sK25_skl,X0,X1))),
% 1.35/0.68 inference(resolution,[status(thm)],[f638,f114])).
% 1.35/0.68 fof(f664,plain,(
% 1.35/0.68 ![X0,X1]: (eqangle(sK21_skl,sK24_skl,X0,X1,sK21_skl,sK24_skl,X0,X1))),
% 1.35/0.68 inference(resolution,[status(thm)],[f650,f379])).
% 1.35/0.68 fof(f674,plain,(
% 1.35/0.68 ![X0,X1]: (eqangle(sK21_skl,sK24_skl,sK21_skl,sK24_skl,X0,X1,X0,X1))),
% 1.35/0.68 inference(resolution,[status(thm)],[f664,f144])).
% 1.35/0.68 fof(f716,plain,(
% 1.35/0.68 ![X0]: (~coll(sK21_skl,X0,sK24_skl)|cyclic(sK24_skl,sK24_skl,sK21_skl,X0))),
% 1.35/0.68 inference(resolution,[status(thm)],[f674,f195])).
% 1.35/0.68 fof(f717,plain,(
% 1.35/0.68 ![X0]: (coll(sK21_skl,X0,sK24_skl)|cyclic(sK24_skl,sK24_skl,sK21_skl,X0))),
% 1.35/0.68 inference(resolution,[status(thm)],[f674,f193])).
% 1.35/0.68 fof(f719,plain,(
% 1.35/0.68 ![X0]: (cyclic(sK24_skl,sK24_skl,sK21_skl,X0))),
% 1.35/0.68 inference(forward_subsumption_resolution,[status(thm)],[f717,f716])).
% 1.35/0.68 fof(f725,plain,(
% 1.35/0.68 ![X0,X1]: (~cyclic(sK24_skl,sK24_skl,sK21_skl,X0)|cyclic(sK24_skl,sK21_skl,X0,X1))),
% 1.35/0.68 inference(resolution,[status(thm)],[f719,f136])).
% 1.35/0.68 fof(f733,plain,(
% 1.35/0.68 ![X0,X1]: (cyclic(sK24_skl,sK21_skl,X0,X1))),
% 1.35/0.68 inference(forward_subsumption_resolution,[status(thm)],[f725,f719])).
% 1.35/0.68 fof(f739,plain,(
% 1.35/0.68 ![X0,X1,X2]: (~cyclic(sK24_skl,sK21_skl,X0,X1)|cyclic(sK21_skl,X0,X1,X2))),
% 1.35/0.68 inference(resolution,[status(thm)],[f733,f136])).
% 1.35/0.68 fof(f747,plain,(
% 1.35/0.68 ![X0,X1,X2]: (cyclic(sK21_skl,X0,X1,X2))),
% 1.35/0.68 inference(forward_subsumption_resolution,[status(thm)],[f739,f733])).
% 1.35/0.68 fof(f755,plain,(
% 1.35/0.68 ![X0,X1,X2,X3]: (~cyclic(sK21_skl,X0,X1,X2)|cyclic(X0,X1,X2,X3))),
% 1.35/0.68 inference(resolution,[status(thm)],[f747,f136])).
% 1.35/0.68 fof(f766,plain,(
% 1.35/0.68 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3))),
% 1.35/0.68 inference(forward_subsumption_resolution,[status(thm)],[f755,f747])).
% 1.35/0.68 fof(f767,plain,(
% 1.35/0.68 $false),
% 1.35/0.68 inference(backward_subsumption_resolution,[status(thm)],[f381,f766])).
% 1.35/0.68 % SZS output end CNFRefutation for theBenchmark.p
% 1.35/0.69 % Elapsed time: 0.335477 seconds
% 1.35/0.69 % CPU time: 2.395603 seconds
% 1.35/0.69 % Total memory used: 107.639 MB
% 1.35/0.69 % Net memory used: 104.937 MB
%------------------------------------------------------------------------------