%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO550+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 : n016.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 12:26:37 PM UTC 2026
% Result : Theorem 0.10s 0.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO550+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 17:26:23 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.53 % Refutation found
% 0.10/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.53 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.53 fof(f8,axiom,(
% 0.10/0.53 (! [A,B,C,D] :( perp(A,B,C,D)=> perp(C,D,A,B) ) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f9,axiom,(
% 0.10/0.53 (! [A,B,C,D,E,F] :( ( perp(A,B,C,D)& perp(C,D,E,F) )=> para(A,B,E,F) ) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f17,axiom,(
% 0.10/0.53 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f21,axiom,(
% 0.10/0.53 (! [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) ) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f40,axiom,(
% 0.10/0.53 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f42,axiom,(
% 0.10/0.53 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& ~ coll(P,Q,A) )=> cyclic(A,B,P,Q) ) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f43,axiom,(
% 0.10/0.53 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f87,axiom,(
% 0.10/0.53 (! [A,B,C,O] :(? [P] :( circle(O,A,B,C)=> perp(P,A,A,O) ) ))),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f95,conjecture,(
% 0.10/0.53 (! [A,B,C,D,P,E,O1,O,Q,NWPNT1,NWPNT2] :( ( coll(P,C,D)& coll(P,A,B)& coll(E,B,C)& coll(E,A,D)& circle(O1,C,D,E)& circle(O,E,B,A)& circle(O1,C,Q,NWPNT1)& circle(O,A,Q,NWPNT2) )=> cyclic(P,D,Q,A) ) )),
% 0.10/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f96,negated_conjecture,(
% 0.10/0.53 ~((! [A,B,C,D,P,E,O1,O,Q,NWPNT1,NWPNT2] :( ( coll(P,C,D)& coll(P,A,B)& coll(E,B,C)& coll(E,A,D)& circle(O1,C,D,E)& circle(O,E,B,A)& circle(O1,C,Q,NWPNT1)& circle(O,A,Q,NWPNT2) )=> cyclic(P,D,Q,A) ) ))),
% 0.10/0.53 inference(negated_conjecture,[status(cth)],[f95])).
% 0.10/0.53 fof(f113,plain,(
% 0.10/0.53 ![A,B,C,D]: (~perp(A,B,C,D)|perp(C,D,A,B))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.10/0.53 fof(f114,plain,(
% 0.10/0.53 ![X0,X1,X2,X3]: (~perp(X0,X1,X2,X3)|perp(X2,X3,X0,X1))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f113])).
% 0.10/0.53 fof(f115,plain,(
% 0.10/0.53 ![A,B,C,D,E,F]: ((~perp(A,B,C,D)|~perp(C,D,E,F))|para(A,B,E,F))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.10/0.53 fof(f116,plain,(
% 0.10/0.53 ![A,B,E,F]: ((![C,D]: (~perp(A,B,C,D)|~perp(C,D,E,F)))|para(A,B,E,F))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f115])).
% 0.10/0.53 fof(f117,plain,(
% 0.10/0.53 ![X0,X1,X2,X3,X4,X5]: (~perp(X0,X1,X2,X3)|~perp(X2,X3,X4,X5)|para(X0,X1,X4,X5))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f116])).
% 0.10/0.53 fof(f134,plain,(
% 0.10/0.53 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.10/0.53 fof(f135,plain,(
% 0.10/0.53 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f134])).
% 0.10/0.53 fof(f136,plain,(
% 0.10/0.53 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f135])).
% 0.10/0.53 fof(f143,plain,(
% 0.10/0.53 ![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))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.10/0.53 fof(f144,plain,(
% 0.10/0.53 ![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))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f143])).
% 0.10/0.53 fof(f187,plain,(
% 0.10/0.53 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 0.10/0.53 fof(f188,plain,(
% 0.10/0.53 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f187])).
% 0.10/0.53 fof(f189,plain,(
% 0.10/0.53 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f188])).
% 0.10/0.53 fof(f192,plain,(
% 0.10/0.53 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|coll(P,Q,A))|cyclic(A,B,P,Q))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 0.10/0.53 fof(f193,plain,(
% 0.10/0.53 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|coll(X0,X3,X1)|cyclic(X1,X2,X0,X3))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f192])).
% 0.10/0.53 fof(f194,plain,(
% 0.10/0.53 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 0.10/0.53 fof(f195,plain,(
% 0.10/0.53 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f194])).
% 0.10/0.53 fof(f331,plain,(
% 0.10/0.53 ![A,B,C,O]: (?[P]: (~circle(O,A,B,C)|perp(P,A,A,O)))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f87])).
% 0.10/0.53 fof(f332,plain,(
% 0.10/0.53 ![A,O]: ((![B,C]: ~circle(O,A,B,C))|(?[P]: perp(P,A,A,O)))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f331])).
% 0.10/0.53 fof(f333,plain,(
% 0.10/0.53 ![A,O]: ((![B,C]: ~circle(O,A,B,C))|perp(sK11_skl(O,A),A,A,O))),
% 0.10/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(P,sK11_skl(O,A))],[f332])).
% 0.10/0.53 fof(f334,plain,(
% 0.10/0.53 ![X0,X1,X2,X3]: (~circle(X0,X1,X2,X3)|perp(sK11_skl(X0,X1),X1,X1,X0))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f333])).
% 0.10/0.53 fof(f369,plain,(
% 0.10/0.53 (?[A,B,C,D,P,E,O1,O,Q,NWPNT1,NWPNT2]: ((((((((coll(P,C,D)&coll(P,A,B))&coll(E,B,C))&coll(E,A,D))&circle(O1,C,D,E))&circle(O,E,B,A))&circle(O1,C,Q,NWPNT1))&circle(O,A,Q,NWPNT2))&~cyclic(P,D,Q,A)))),
% 0.10/0.54 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 0.10/0.54 fof(f370,plain,(
% 0.10/0.54 ?[A,D,P,Q]: ((?[O]: ((?[C,O1]: ((?[B,E]: (((((coll(P,C,D)&coll(P,A,B))&coll(E,B,C))&coll(E,A,D))&circle(O1,C,D,E))&circle(O,E,B,A)))&(?[NWPNT1]: circle(O1,C,Q,NWPNT1))))&(?[NWPNT2]: circle(O,A,Q,NWPNT2))))&~cyclic(P,D,Q,A))),
% 0.10/0.54 inference(miniscoping,[status(thm)],[f369])).
% 0.10/0.54 fof(f371,plain,(
% 0.10/0.54 ((((((((coll(sK22_skl,sK25_skl,sK21_skl)&coll(sK22_skl,sK20_skl,sK27_skl))&coll(sK28_skl,sK27_skl,sK25_skl))&coll(sK28_skl,sK20_skl,sK21_skl))&circle(sK26_skl,sK25_skl,sK21_skl,sK28_skl))&circle(sK24_skl,sK28_skl,sK27_skl,sK20_skl))&circle(sK26_skl,sK25_skl,sK23_skl,sK29_skl))&circle(sK24_skl,sK20_skl,sK23_skl,sK30_skl))&~cyclic(sK22_skl,sK21_skl,sK23_skl,sK20_skl))),
% 0.10/0.54 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,sK29_skl,sK30_skl]),skolemize(A,sK20_skl),skolemize(D,sK21_skl),skolemize(P,sK22_skl),skolemize(Q,sK23_skl),skolemize(O,sK24_skl),skolemize(C,sK25_skl),skolemize(O1,sK26_skl),skolemize(B,sK27_skl),skolemize(E,sK28_skl),skolemize(NWPNT1,sK29_skl),skolemize(NWPNT2,sK30_skl)],[f370])).
% 0.10/0.54 fof(f379,plain,(
% 0.10/0.54 circle(sK24_skl,sK20_skl,sK23_skl,sK30_skl)),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f371])).
% 0.10/0.54 fof(f380,plain,(
% 0.10/0.54 ~cyclic(sK22_skl,sK21_skl,sK23_skl,sK20_skl)),
% 0.10/0.54 inference(cnf_transformation,[status(thm)],[f371])).
% 0.10/0.54 fof(f402,plain,(
% 0.10/0.54 ![X0,X1,X2,X3,X4,X5]: (~circle(X0,X1,X2,X3)|~perp(X4,X5,sK11_skl(X0,X1),X1)|para(X4,X5,X1,X0))),
% 0.10/0.54 inference(resolution,[status(thm)],[f334,f117])).
% 0.10/0.54 fof(f684,plain,(
% 0.10/0.54 ![X0,X1]: (~perp(X0,X1,sK11_skl(sK24_skl,sK20_skl),sK20_skl)|para(X0,X1,sK20_skl,sK24_skl))),
% 0.10/0.54 inference(resolution,[status(thm)],[f402,f379])).
% 0.10/0.54 fof(f691,plain,(
% 0.10/0.54 ![X0,X1]: (para(X0,X1,sK20_skl,sK24_skl)|~perp(sK11_skl(sK24_skl,sK20_skl),sK20_skl,X0,X1))),
% 0.10/0.54 inference(resolution,[status(thm)],[f684,f114])).
% 0.10/0.54 fof(f703,plain,(
% 0.10/0.54 ![X0,X1]: (para(sK20_skl,sK24_skl,sK20_skl,sK24_skl)|~circle(sK24_skl,sK20_skl,X0,X1))),
% 0.10/0.54 inference(resolution,[status(thm)],[f691,f334])).
% 0.10/0.54 fof(f708,plain,(
% 0.10/0.54 para(sK20_skl,sK24_skl,sK20_skl,sK24_skl)),
% 0.10/0.54 inference(resolution,[status(thm)],[f703,f379])).
% 0.10/0.54 fof(f710,plain,(
% 0.10/0.54 ![X0,X1]: (eqangle(sK20_skl,sK24_skl,X0,X1,sK20_skl,sK24_skl,X0,X1))),
% 0.10/0.54 inference(resolution,[status(thm)],[f708,f189])).
% 0.10/0.54 fof(f744,plain,(
% 0.10/0.54 ![X0,X1]: (eqangle(sK20_skl,sK24_skl,sK20_skl,sK24_skl,X0,X1,X0,X1))),
% 0.10/0.54 inference(resolution,[status(thm)],[f710,f144])).
% 0.10/0.54 fof(f790,plain,(
% 0.10/0.54 ![X0]: (~coll(sK20_skl,X0,sK24_skl)|cyclic(sK24_skl,sK24_skl,sK20_skl,X0))),
% 0.10/0.54 inference(resolution,[status(thm)],[f744,f195])).
% 0.10/0.54 fof(f791,plain,(
% 0.10/0.54 ![X0]: (coll(sK20_skl,X0,sK24_skl)|cyclic(sK24_skl,sK24_skl,sK20_skl,X0))),
% 0.10/0.54 inference(resolution,[status(thm)],[f744,f193])).
% 0.10/0.54 fof(f792,plain,(
% 0.10/0.54 ![X0]: (cyclic(sK24_skl,sK24_skl,sK20_skl,X0))),
% 0.10/0.54 inference(forward_subsumption_resolution,[status(thm)],[f791,f790])).
% 0.10/0.54 fof(f797,plain,(
% 0.10/0.54 ![X0,X1]: (~cyclic(sK24_skl,sK24_skl,sK20_skl,X0)|cyclic(sK24_skl,sK20_skl,X0,X1))),
% 0.10/0.54 inference(resolution,[status(thm)],[f792,f136])).
% 0.10/0.54 fof(f806,plain,(
% 0.10/0.54 ![X0,X1]: (cyclic(sK24_skl,sK20_skl,X0,X1))),
% 0.10/0.54 inference(forward_subsumption_resolution,[status(thm)],[f797,f792])).
% 0.10/0.54 fof(f811,plain,(
% 0.10/0.54 ![X0,X1,X2]: (~cyclic(sK24_skl,sK20_skl,X0,X1)|cyclic(sK20_skl,X0,X1,X2))),
% 0.10/0.54 inference(resolution,[status(thm)],[f806,f136])).
% 0.10/0.54 fof(f820,plain,(
% 0.10/0.54 ![X0,X1,X2]: (cyclic(sK20_skl,X0,X1,X2))),
% 0.10/0.54 inference(forward_subsumption_resolution,[status(thm)],[f811,f806])).
% 0.10/0.54 fof(f827,plain,(
% 0.10/0.54 ![X0,X1,X2,X3]: (~cyclic(sK20_skl,X0,X1,X2)|cyclic(X0,X1,X2,X3))),
% 0.10/0.54 inference(resolution,[status(thm)],[f820,f136])).
% 0.10/0.54 fof(f839,plain,(
% 0.10/0.54 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3))),
% 0.10/0.54 inference(forward_subsumption_resolution,[status(thm)],[f827,f820])).
% 0.10/0.54 fof(f840,plain,(
% 0.10/0.54 $false),
% 0.10/0.54 inference(backward_subsumption_resolution,[status(thm)],[f380,f839])).
% 0.10/0.54 % SZS output end CNFRefutation for theBenchmark.p
% 0.65/0.56 % Elapsed time: 0.183208 seconds
% 0.65/0.56 % CPU time: 1.188245 seconds
% 0.65/0.56 % Total memory used: 97.694 MB
% 0.65/0.56 % Net memory used: 96.946 MB
%------------------------------------------------------------------------------