%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO543+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 : n006.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 0.99s 0.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO543+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
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 17:27:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.99/0.56 % Refutation found
% 0.99/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.99/0.56 % SZS output start CNFRefutation for theBenchmark
% 0.99/0.56 fof(f4,axiom,(
% 0.99/0.56 (! [A,B,C,D] :( para(A,B,C,D)=> para(A,B,D,C) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f5,axiom,(
% 0.99/0.56 (! [A,B,C,D] :( para(A,B,C,D)=> para(C,D,A,B) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f11,axiom,(
% 0.99/0.56 (! [A,B,M] :( midp(M,B,A)=> midp(M,A,B) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f14,axiom,(
% 0.99/0.56 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(A,B,D,C) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f15,axiom,(
% 0.99/0.56 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(A,C,B,D) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f16,axiom,(
% 0.99/0.56 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(B,A,C,D) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f17,axiom,(
% 0.99/0.56 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f19,axiom,(
% 0.99/0.56 (! [A,B,C,D,P,Q,U,V] :( eqangle(A,B,C,D,P,Q,U,V)=> eqangle(C,D,A,B,U,V,P,Q) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f39,axiom,(
% 0.99/0.56 (! [A,B,C,D,P,Q] :( eqangle(A,B,P,Q,C,D,P,Q)=> para(A,B,C,D) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f40,axiom,(
% 0.99/0.56 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f43,axiom,(
% 0.99/0.56 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f64,axiom,(
% 0.99/0.56 (! [A,B,C,D,M] :( ( midp(M,A,B)& midp(M,C,D) )=> para(A,C,B,D) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f67,axiom,(
% 0.99/0.56 (! [A,B,C] :( para(A,B,A,C)=> coll(A,B,C) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f95,conjecture,(
% 0.99/0.56 (! [A,B,C,D,E,F,H,A1,P,Q] :( ( perp(D,A,B,C)& coll(D,B,C)& perp(E,B,A,C)& coll(E,A,C)& perp(F,C,A,B)& coll(F,A,B)& coll(H,B,E)& coll(H,C,F)& midp(A1,C,B)& midp(P,E,B)& midp(Q,F,C) )=> cyclic(P,Q,H,D) ) )),
% 0.99/0.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.99/0.56 fof(f96,negated_conjecture,(
% 0.99/0.56 ~((! [A,B,C,D,E,F,H,A1,P,Q] :( ( perp(D,A,B,C)& coll(D,B,C)& perp(E,B,A,C)& coll(E,A,C)& perp(F,C,A,B)& coll(F,A,B)& coll(H,B,E)& coll(H,C,F)& midp(A1,C,B)& midp(P,E,B)& midp(Q,F,C) )=> cyclic(P,Q,H,D) ) ))),
% 0.99/0.56 inference(negated_conjecture,[status(cth)],[f95])).
% 0.99/0.56 fof(f104,plain,(
% 0.99/0.56 ![A,B,C,D]: (~para(A,B,C,D)|para(A,B,D,C))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.99/0.56 fof(f105,plain,(
% 0.99/0.56 ![X0,X1,X2,X3]: (~para(X0,X1,X2,X3)|para(X0,X1,X3,X2))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f104])).
% 0.99/0.56 fof(f106,plain,(
% 0.99/0.56 ![A,B,C,D]: (~para(A,B,C,D)|para(C,D,A,B))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.99/0.56 fof(f107,plain,(
% 0.99/0.56 ![X0,X1,X2,X3]: (~para(X0,X1,X2,X3)|para(X2,X3,X0,X1))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f106])).
% 0.99/0.56 fof(f121,plain,(
% 0.99/0.56 ![A,B,M]: (~midp(M,B,A)|midp(M,A,B))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.99/0.56 fof(f122,plain,(
% 0.99/0.56 ![X0,X1,X2]: (~midp(X0,X1,X2)|midp(X0,X2,X1))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f121])).
% 0.99/0.56 fof(f128,plain,(
% 0.99/0.56 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(A,B,D,C))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.99/0.56 fof(f129,plain,(
% 0.99/0.56 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X0,X1,X3,X2))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f128])).
% 0.99/0.56 fof(f130,plain,(
% 0.99/0.56 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(A,C,B,D))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.99/0.56 fof(f131,plain,(
% 0.99/0.56 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X0,X2,X1,X3))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f130])).
% 0.99/0.56 fof(f132,plain,(
% 0.99/0.56 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(B,A,C,D))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.99/0.56 fof(f133,plain,(
% 0.99/0.56 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X1,X0,X2,X3))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f132])).
% 0.99/0.56 fof(f134,plain,(
% 0.99/0.56 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.99/0.56 fof(f135,plain,(
% 0.99/0.56 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 0.99/0.56 inference(miniscoping,[status(thm)],[f134])).
% 0.99/0.56 fof(f136,plain,(
% 0.99/0.56 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f135])).
% 0.99/0.56 fof(f139,plain,(
% 0.99/0.56 ![A,B,C,D,P,Q,U,V]: (~eqangle(A,B,C,D,P,Q,U,V)|eqangle(C,D,A,B,U,V,P,Q))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.99/0.56 fof(f140,plain,(
% 0.99/0.56 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|eqangle(X2,X3,X0,X1,X6,X7,X4,X5))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f139])).
% 0.99/0.56 fof(f184,plain,(
% 0.99/0.56 ![A,B,C,D,P,Q]: (~eqangle(A,B,P,Q,C,D,P,Q)|para(A,B,C,D))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 0.99/0.56 fof(f185,plain,(
% 0.99/0.56 ![A,B,C,D]: ((![P,Q]: ~eqangle(A,B,P,Q,C,D,P,Q))|para(A,B,C,D))),
% 0.99/0.56 inference(miniscoping,[status(thm)],[f184])).
% 0.99/0.56 fof(f186,plain,(
% 0.99/0.56 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X2,X3,X4,X5,X2,X3)|para(X0,X1,X4,X5))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f185])).
% 0.99/0.56 fof(f187,plain,(
% 0.99/0.56 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 0.99/0.56 fof(f188,plain,(
% 0.99/0.56 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 0.99/0.56 inference(miniscoping,[status(thm)],[f187])).
% 0.99/0.56 fof(f189,plain,(
% 0.99/0.56 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f188])).
% 0.99/0.56 fof(f194,plain,(
% 0.99/0.56 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 0.99/0.56 fof(f195,plain,(
% 0.99/0.56 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f194])).
% 0.99/0.56 fof(f247,plain,(
% 0.99/0.56 ![A,B,C,D,M]: ((~midp(M,A,B)|~midp(M,C,D))|para(A,C,B,D))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f64])).
% 0.99/0.56 fof(f248,plain,(
% 0.99/0.56 ![A,B,C,D]: ((![M]: (~midp(M,A,B)|~midp(M,C,D)))|para(A,C,B,D))),
% 0.99/0.56 inference(miniscoping,[status(thm)],[f247])).
% 0.99/0.56 fof(f249,plain,(
% 0.99/0.56 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~midp(X0,X3,X4)|para(X1,X3,X2,X4))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f248])).
% 0.99/0.56 fof(f255,plain,(
% 0.99/0.56 ![A,B,C]: (~para(A,B,A,C)|coll(A,B,C))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f67])).
% 0.99/0.56 fof(f256,plain,(
% 0.99/0.56 ![X0,X1,X2]: (~para(X0,X1,X0,X2)|coll(X0,X1,X2))),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f255])).
% 0.99/0.56 fof(f369,plain,(
% 0.99/0.56 (?[A,B,C,D,E,F,H,A1,P,Q]: (((((((((((perp(D,A,B,C)&coll(D,B,C))&perp(E,B,A,C))&coll(E,A,C))&perp(F,C,A,B))&coll(F,A,B))&coll(H,B,E))&coll(H,C,F))&midp(A1,C,B))&midp(P,E,B))&midp(Q,F,C))&~cyclic(P,Q,H,D)))),
% 0.99/0.56 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 0.99/0.56 fof(f370,plain,(
% 0.99/0.56 ?[D,H,P,Q]: ((?[C,F]: ((?[B,E]: (((((?[A]: (((((perp(D,A,B,C)&coll(D,B,C))&perp(E,B,A,C))&coll(E,A,C))&perp(F,C,A,B))&coll(F,A,B)))&coll(H,B,E))&coll(H,C,F))&(?[A1]: midp(A1,C,B)))&midp(P,E,B)))&midp(Q,F,C)))&~cyclic(P,Q,H,D))),
% 0.99/0.56 inference(miniscoping,[status(thm)],[f369])).
% 0.99/0.56 fof(f371,plain,(
% 0.99/0.56 (((((((((((perp(sK20_skl,sK28_skl,sK26_skl,sK24_skl)&coll(sK20_skl,sK26_skl,sK24_skl))&perp(sK27_skl,sK26_skl,sK28_skl,sK24_skl))&coll(sK27_skl,sK28_skl,sK24_skl))&perp(sK25_skl,sK24_skl,sK28_skl,sK26_skl))&coll(sK25_skl,sK28_skl,sK26_skl))&coll(sK21_skl,sK26_skl,sK27_skl))&coll(sK21_skl,sK24_skl,sK25_skl))&midp(sK29_skl,sK24_skl,sK26_skl))&midp(sK22_skl,sK27_skl,sK26_skl))&midp(sK23_skl,sK25_skl,sK24_skl))&~cyclic(sK22_skl,sK23_skl,sK21_skl,sK20_skl))),
% 0.99/0.56 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]),skolemize(D,sK20_skl),skolemize(H,sK21_skl),skolemize(P,sK22_skl),skolemize(Q,sK23_skl),skolemize(C,sK24_skl),skolemize(F,sK25_skl),skolemize(B,sK26_skl),skolemize(E,sK27_skl),skolemize(A,sK28_skl),skolemize(A1,sK29_skl)],[f370])).
% 0.99/0.56 fof(f381,plain,(
% 0.99/0.56 midp(sK22_skl,sK27_skl,sK26_skl)),
% 0.99/0.56 inference(cnf_transformation,[status(thm)],[f371])).
% 0.99/0.57 fof(f383,plain,(
% 0.99/0.57 ~cyclic(sK22_skl,sK23_skl,sK21_skl,sK20_skl)),
% 0.99/0.57 inference(cnf_transformation,[status(thm)],[f371])).
% 0.99/0.57 fof(f524,plain,(
% 0.99/0.57 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X2,X3,X0,X1,X4,X5)|para(X2,X3,X4,X5))),
% 0.99/0.57 inference(resolution,[status(thm)],[f140,f186])).
% 0.99/0.57 fof(f594,plain,(
% 0.99/0.57 ![X0,X1]: (~midp(sK22_skl,X0,X1)|para(X0,sK27_skl,X1,sK26_skl))),
% 0.99/0.57 inference(resolution,[status(thm)],[f249,f381])).
% 0.99/0.57 fof(f608,plain,(
% 0.99/0.57 ![X0,X1]: (para(X0,sK27_skl,X1,sK26_skl)|~midp(sK22_skl,X1,X0))),
% 0.99/0.57 inference(resolution,[status(thm)],[f594,f122])).
% 0.99/0.57 fof(f642,plain,(
% 0.99/0.57 para(sK26_skl,sK27_skl,sK27_skl,sK26_skl)),
% 0.99/0.57 inference(resolution,[status(thm)],[f608,f381])).
% 0.99/0.57 fof(f655,plain,(
% 0.99/0.57 para(sK27_skl,sK26_skl,sK26_skl,sK27_skl)),
% 0.99/0.57 inference(resolution,[status(thm)],[f642,f107])).
% 0.99/0.57 fof(f665,plain,(
% 0.99/0.57 para(sK27_skl,sK26_skl,sK27_skl,sK26_skl)),
% 0.99/0.57 inference(resolution,[status(thm)],[f655,f105])).
% 0.99/0.57 fof(f671,plain,(
% 0.99/0.57 ![X0,X1]: (eqangle(sK27_skl,sK26_skl,X0,X1,sK27_skl,sK26_skl,X0,X1))),
% 0.99/0.57 inference(resolution,[status(thm)],[f665,f189])).
% 0.99/0.57 fof(f1088,plain,(
% 0.99/0.57 ![X0,X1]: (para(X0,X1,X0,X1))),
% 0.99/0.57 inference(resolution,[status(thm)],[f524,f671])).
% 0.99/0.57 fof(f1114,plain,(
% 0.99/0.57 ![X0,X1,X2,X3]: (eqangle(X0,X1,X2,X3,X0,X1,X2,X3))),
% 0.99/0.57 inference(resolution,[status(thm)],[f1088,f189])).
% 0.99/0.57 fof(f1118,plain,(
% 0.99/0.57 ![X0,X1]: (coll(X0,X1,X1))),
% 0.99/0.57 inference(resolution,[status(thm)],[f1088,f256])).
% 0.99/0.57 fof(f1133,plain,(
% 0.99/0.57 ![X0,X1,X2]: (~coll(X0,X0,X1)|cyclic(X2,X1,X0,X0))),
% 0.99/0.57 inference(resolution,[status(thm)],[f1114,f195])).
% 0.99/0.57 fof(f1144,plain,(
% 0.99/0.57 ![X0,X1]: (cyclic(X0,X1,X1,X1))),
% 0.99/0.57 inference(resolution,[status(thm)],[f1133,f1118])).
% 0.99/0.57 fof(f1158,plain,(
% 0.99/0.57 ![X0,X1]: (cyclic(X0,X1,X0,X0))),
% 0.99/0.57 inference(resolution,[status(thm)],[f1144,f133])).
% 0.99/0.57 fof(f1171,plain,(
% 0.99/0.57 ![X0,X1]: (cyclic(X0,X0,X1,X0))),
% 0.99/0.57 inference(resolution,[status(thm)],[f1158,f131])).
% 0.99/0.57 fof(f1184,plain,(
% 0.99/0.57 ![X0,X1]: (cyclic(X0,X0,X0,X1))),
% 0.99/0.57 inference(resolution,[status(thm)],[f1171,f129])).
% 0.99/0.57 fof(f1192,plain,(
% 0.99/0.57 ![X0,X1,X2]: (~cyclic(X0,X0,X0,X1)|cyclic(X0,X0,X1,X2))),
% 0.99/0.57 inference(resolution,[status(thm)],[f1184,f136])).
% 0.99/0.57 fof(f1200,plain,(
% 0.99/0.57 ![X0,X1,X2]: (cyclic(X0,X0,X1,X2))),
% 0.99/0.57 inference(forward_subsumption_resolution,[status(thm)],[f1192,f1184])).
% 0.99/0.57 fof(f1208,plain,(
% 0.99/0.57 ![X0,X1,X2,X3]: (~cyclic(X0,X0,X1,X2)|cyclic(X0,X1,X2,X3))),
% 0.99/0.57 inference(resolution,[status(thm)],[f1200,f136])).
% 0.99/0.57 fof(f1216,plain,(
% 0.99/0.57 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3))),
% 0.99/0.57 inference(forward_subsumption_resolution,[status(thm)],[f1208,f1200])).
% 0.99/0.57 fof(f1219,plain,(
% 0.99/0.57 $false),
% 0.99/0.57 inference(backward_subsumption_resolution,[status(thm)],[f383,f1216])).
% 0.99/0.57 % SZS output end CNFRefutation for theBenchmark.p
% 0.99/0.58 % Elapsed time: 0.196305 seconds
% 0.99/0.58 % CPU time: 1.266250 seconds
% 0.99/0.58 % Total memory used: 99.804 MB
% 0.99/0.58 % Net memory used: 98.654 MB
%------------------------------------------------------------------------------