%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO631+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:26:45 PM UTC 2026
% Result : Theorem 2.47s 0.80s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO631+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 18:09:10 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.38 % Drodi V4.1.1
% 2.47/0.80 % Refutation found
% 2.47/0.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.47/0.80 % SZS output start CNFRefutation for theBenchmark
% 2.47/0.80 fof(f8,axiom,(
% 2.47/0.80 (! [A,B,C,D] :( perp(A,B,C,D)=> perp(C,D,A,B) ) )),
% 2.47/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.47/0.80 fof(f9,axiom,(
% 2.47/0.80 (! [A,B,C,D,E,F] :( ( perp(A,B,C,D)& perp(C,D,E,F) )=> para(A,B,E,F) ) )),
% 2.47/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.47/0.80 fof(f17,axiom,(
% 2.47/0.80 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 2.47/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.47/0.80 fof(f21,axiom,(
% 2.47/0.80 (! [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) ) )),
% 2.47/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.47/0.80 fof(f40,axiom,(
% 2.47/0.80 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 2.47/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.47/0.80 fof(f42,axiom,(
% 2.47/0.80 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& ~ coll(P,Q,A) )=> cyclic(A,B,P,Q) ) )),
% 2.47/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.47/0.80 fof(f43,axiom,(
% 2.47/0.80 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 2.47/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.47/0.80 fof(f95,conjecture,(
% 2.47/0.80 (! [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :( ( circle(O,A,B,C)& circle(O,A,D,NWPNT1)& circle(O,A,P,NWPNT2)& perp(F,P,A,D)& coll(F,A,D)& perp(G,P,A,B)& coll(G,A,B)& perp(H,P,B,C)& coll(H,B,C)& perp(E,P,C,D)& coll(E,C,D)& coll(I,F,G)& coll(I,H,E) )=> cyclic(P,G,I,H) ) )),
% 2.47/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.47/0.80 fof(f96,negated_conjecture,(
% 2.47/0.80 ~((! [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :( ( circle(O,A,B,C)& circle(O,A,D,NWPNT1)& circle(O,A,P,NWPNT2)& perp(F,P,A,D)& coll(F,A,D)& perp(G,P,A,B)& coll(G,A,B)& perp(H,P,B,C)& coll(H,B,C)& perp(E,P,C,D)& coll(E,C,D)& coll(I,F,G)& coll(I,H,E) )=> cyclic(P,G,I,H) ) ))),
% 2.47/0.80 inference(negated_conjecture,[status(cth)],[f95])).
% 2.47/0.80 fof(f113,plain,(
% 2.47/0.80 ![A,B,C,D]: (~perp(A,B,C,D)|perp(C,D,A,B))),
% 2.47/0.80 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 2.47/0.80 fof(f114,plain,(
% 2.47/0.80 ![X0,X1,X2,X3]: (~perp(X0,X1,X2,X3)|perp(X2,X3,X0,X1))),
% 2.47/0.80 inference(cnf_transformation,[status(thm)],[f113])).
% 2.47/0.80 fof(f115,plain,(
% 2.47/0.80 ![A,B,C,D,E,F]: ((~perp(A,B,C,D)|~perp(C,D,E,F))|para(A,B,E,F))),
% 2.47/0.80 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 2.47/0.80 fof(f116,plain,(
% 2.47/0.80 ![A,B,E,F]: ((![C,D]: (~perp(A,B,C,D)|~perp(C,D,E,F)))|para(A,B,E,F))),
% 2.47/0.80 inference(miniscoping,[status(thm)],[f115])).
% 2.47/0.80 fof(f117,plain,(
% 2.47/0.80 ![X0,X1,X2,X3,X4,X5]: (~perp(X0,X1,X2,X3)|~perp(X2,X3,X4,X5)|para(X0,X1,X4,X5))),
% 2.47/0.80 inference(cnf_transformation,[status(thm)],[f116])).
% 2.47/0.80 fof(f134,plain,(
% 2.47/0.80 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 2.47/0.80 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 2.47/0.80 fof(f135,plain,(
% 2.47/0.80 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 2.47/0.80 inference(miniscoping,[status(thm)],[f134])).
% 2.47/0.80 fof(f136,plain,(
% 2.47/0.80 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 2.47/0.80 inference(cnf_transformation,[status(thm)],[f135])).
% 2.47/0.80 fof(f143,plain,(
% 2.47/0.80 ![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))),
% 2.47/0.80 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 2.47/0.80 fof(f144,plain,(
% 2.47/0.80 ![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))),
% 2.47/0.80 inference(cnf_transformation,[status(thm)],[f143])).
% 2.47/0.80 fof(f187,plain,(
% 2.47/0.80 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 2.47/0.80 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 2.47/0.80 fof(f188,plain,(
% 2.47/0.80 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 2.47/0.80 inference(miniscoping,[status(thm)],[f187])).
% 2.47/0.80 fof(f189,plain,(
% 2.47/0.80 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 2.47/0.80 inference(cnf_transformation,[status(thm)],[f188])).
% 2.47/0.80 fof(f192,plain,(
% 2.47/0.80 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|coll(P,Q,A))|cyclic(A,B,P,Q))),
% 2.47/0.80 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 2.47/0.80 fof(f193,plain,(
% 2.47/0.80 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|coll(X0,X3,X1)|cyclic(X1,X2,X0,X3))),
% 2.47/0.80 inference(cnf_transformation,[status(thm)],[f192])).
% 2.47/0.80 fof(f194,plain,(
% 2.47/0.80 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 2.47/0.80 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 2.47/0.80 fof(f195,plain,(
% 2.47/0.80 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 2.47/0.80 inference(cnf_transformation,[status(thm)],[f194])).
% 2.47/0.80 fof(f369,plain,(
% 2.47/0.80 (?[A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2]: (((((((((((((circle(O,A,B,C)&circle(O,A,D,NWPNT1))&circle(O,A,P,NWPNT2))&perp(F,P,A,D))&coll(F,A,D))&perp(G,P,A,B))&coll(G,A,B))&perp(H,P,B,C))&coll(H,B,C))&perp(E,P,C,D))&coll(E,C,D))&coll(I,F,G))&coll(I,H,E))&~cyclic(P,G,I,H)))),
% 2.47/0.80 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 2.47/0.80 fof(f370,plain,(
% 2.47/0.80 ?[P,G,H,I]: ((?[E]: ((?[F]: ((?[C,D]: (((?[B]: (((?[A]: (((((?[O]: ((circle(O,A,B,C)&(?[NWPNT1]: circle(O,A,D,NWPNT1)))&(?[NWPNT2]: circle(O,A,P,NWPNT2))))&perp(F,P,A,D))&coll(F,A,D))&perp(G,P,A,B))&coll(G,A,B)))&perp(H,P,B,C))&coll(H,B,C)))&perp(E,P,C,D))&coll(E,C,D)))&coll(I,F,G)))&coll(I,H,E)))&~cyclic(P,G,I,H))),
% 2.47/0.80 inference(miniscoping,[status(thm)],[f369])).
% 2.47/0.80 fof(f371,plain,(
% 2.47/0.80 (((((((((((((circle(sK30_skl,sK29_skl,sK28_skl,sK26_skl)&circle(sK30_skl,sK29_skl,sK27_skl,sK31_skl))&circle(sK30_skl,sK29_skl,sK20_skl,sK32_skl))&perp(sK25_skl,sK20_skl,sK29_skl,sK27_skl))&coll(sK25_skl,sK29_skl,sK27_skl))&perp(sK21_skl,sK20_skl,sK29_skl,sK28_skl))&coll(sK21_skl,sK29_skl,sK28_skl))&perp(sK22_skl,sK20_skl,sK28_skl,sK26_skl))&coll(sK22_skl,sK28_skl,sK26_skl))&perp(sK24_skl,sK20_skl,sK26_skl,sK27_skl))&coll(sK24_skl,sK26_skl,sK27_skl))&coll(sK23_skl,sK25_skl,sK21_skl))&coll(sK23_skl,sK22_skl,sK24_skl))&~cyclic(sK20_skl,sK21_skl,sK23_skl,sK22_skl))),
% 2.47/0.80 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,sK31_skl,sK32_skl]),skolemize(P,sK20_skl),skolemize(G,sK21_skl),skolemize(H,sK22_skl),skolemize(I,sK23_skl),skolemize(E,sK24_skl),skolemize(F,sK25_skl),skolemize(C,sK26_skl),skolemize(D,sK27_skl),skolemize(B,sK28_skl),skolemize(A,sK29_skl),skolemize(O,sK30_skl),skolemize(NWPNT1,sK31_skl),skolemize(NWPNT2,sK32_skl)],[f370])).
% 2.47/0.80 fof(f381,plain,(
% 2.47/0.80 perp(sK24_skl,sK20_skl,sK26_skl,sK27_skl)),
% 2.47/0.80 inference(cnf_transformation,[status(thm)],[f371])).
% 2.47/0.80 fof(f385,plain,(
% 2.47/0.80 ~cyclic(sK20_skl,sK21_skl,sK23_skl,sK22_skl)),
% 2.47/0.80 inference(cnf_transformation,[status(thm)],[f371])).
% 2.47/0.80 fof(f392,plain,(
% 2.47/0.80 ![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))),
% 2.47/0.80 inference(resolution,[status(thm)],[f117,f189])).
% 2.47/0.80 fof(f694,plain,(
% 2.47/0.80 ![X0,X1,X2,X3]: (~perp(X0,X1,sK24_skl,sK20_skl)|eqangle(X0,X1,X2,X3,sK26_skl,sK27_skl,X2,X3))),
% 2.47/0.80 inference(resolution,[status(thm)],[f392,f381])).
% 2.47/0.80 fof(f707,plain,(
% 2.47/0.80 ![X0,X1,X2,X3]: (eqangle(X0,X1,X2,X3,sK26_skl,sK27_skl,X2,X3)|~perp(sK24_skl,sK20_skl,X0,X1))),
% 2.47/0.80 inference(resolution,[status(thm)],[f694,f114])).
% 2.47/0.80 fof(f727,plain,(
% 2.47/0.80 ![X0,X1]: (eqangle(sK26_skl,sK27_skl,X0,X1,sK26_skl,sK27_skl,X0,X1))),
% 2.47/0.80 inference(resolution,[status(thm)],[f707,f381])).
% 2.47/0.80 fof(f737,plain,(
% 2.47/0.80 ![X0,X1]: (eqangle(sK26_skl,sK27_skl,sK26_skl,sK27_skl,X0,X1,X0,X1))),
% 2.47/0.80 inference(resolution,[status(thm)],[f727,f144])).
% 2.47/0.80 fof(f772,plain,(
% 2.47/0.80 ![X0]: (~coll(sK26_skl,X0,sK27_skl)|cyclic(sK27_skl,sK27_skl,sK26_skl,X0))),
% 2.47/0.80 inference(resolution,[status(thm)],[f737,f195])).
% 2.47/0.80 fof(f773,plain,(
% 2.47/0.80 ![X0]: (coll(sK26_skl,X0,sK27_skl)|cyclic(sK27_skl,sK27_skl,sK26_skl,X0))),
% 2.47/0.80 inference(resolution,[status(thm)],[f737,f193])).
% 2.47/0.80 fof(f775,plain,(
% 2.47/0.80 ![X0]: (cyclic(sK27_skl,sK27_skl,sK26_skl,X0))),
% 2.47/0.80 inference(forward_subsumption_resolution,[status(thm)],[f773,f772])).
% 2.47/0.80 fof(f782,plain,(
% 2.47/0.80 ![X0,X1]: (~cyclic(sK27_skl,sK27_skl,sK26_skl,X0)|cyclic(sK27_skl,sK26_skl,X0,X1))),
% 2.47/0.80 inference(resolution,[status(thm)],[f775,f136])).
% 2.47/0.80 fof(f790,plain,(
% 2.47/0.80 ![X0,X1]: (cyclic(sK27_skl,sK26_skl,X0,X1))),
% 2.47/0.80 inference(forward_subsumption_resolution,[status(thm)],[f782,f775])).
% 2.47/0.80 fof(f797,plain,(
% 2.47/0.80 ![X0,X1,X2]: (~cyclic(sK27_skl,sK26_skl,X0,X1)|cyclic(sK26_skl,X0,X1,X2))),
% 2.47/0.80 inference(resolution,[status(thm)],[f790,f136])).
% 2.47/0.80 fof(f805,plain,(
% 2.47/0.80 ![X0,X1,X2]: (cyclic(sK26_skl,X0,X1,X2))),
% 2.47/0.81 inference(forward_subsumption_resolution,[status(thm)],[f797,f790])).
% 2.47/0.81 fof(f814,plain,(
% 2.47/0.81 ![X0,X1,X2,X3]: (~cyclic(sK26_skl,X0,X1,X2)|cyclic(X0,X1,X2,X3))),
% 2.47/0.81 inference(resolution,[status(thm)],[f805,f136])).
% 2.47/0.81 fof(f826,plain,(
% 2.47/0.81 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3))),
% 2.47/0.81 inference(forward_subsumption_resolution,[status(thm)],[f814,f805])).
% 2.47/0.81 fof(f827,plain,(
% 2.47/0.81 $false),
% 2.47/0.81 inference(backward_subsumption_resolution,[status(thm)],[f385,f826])).
% 2.47/0.81 % SZS output end CNFRefutation for theBenchmark.p
% 2.47/0.83 % Elapsed time: 0.448855 seconds
% 2.47/0.83 % CPU time: 3.243709 seconds
% 2.47/0.83 % Total memory used: 107.389 MB
% 2.47/0.83 % Net memory used: 104.486 MB
%------------------------------------------------------------------------------