%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO624+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 : 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 12:26:44 PM UTC 2026
% Result : Theorem 0.13s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO624+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
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 18:00:40 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.52 % Refutation found
% 0.13/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.52 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.52 fof(f1,axiom,(
% 0.13/0.52 (! [A,B,C] :( coll(A,B,C)=> coll(A,C,B) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f2,axiom,(
% 0.13/0.52 (! [A,B,C] :( coll(A,B,C)=> coll(B,A,C) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f3,axiom,(
% 0.13/0.52 (! [A,B,C,D] :( ( coll(A,B,C)& coll(A,B,D) )=> coll(C,D,A) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f8,axiom,(
% 0.13/0.52 (! [A,B,C,D] :( perp(A,B,C,D)=> perp(C,D,A,B) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f9,axiom,(
% 0.13/0.52 (! [A,B,C,D,E,F] :( ( perp(A,B,C,D)& perp(C,D,E,F) )=> para(A,B,E,F) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f17,axiom,(
% 0.13/0.52 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f19,axiom,(
% 0.13/0.52 (! [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) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f21,axiom,(
% 0.13/0.52 (! [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) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f39,axiom,(
% 0.13/0.52 (! [A,B,C,D,P,Q] :( eqangle(A,B,P,Q,C,D,P,Q)=> para(A,B,C,D) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f40,axiom,(
% 0.13/0.52 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f43,axiom,(
% 0.13/0.52 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f67,axiom,(
% 0.13/0.52 (! [A,B,C] :( para(A,B,A,C)=> coll(A,B,C) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f95,conjecture,(
% 0.13/0.52 (! [O,X,L,A,Y,B,P,Q,Q1,P1] :( ( perp(A,L,O,X)& coll(A,O,X)& perp(B,L,O,Y)& coll(B,O,Y)& coll(L,A,P)& cong(L,A,L,P)& coll(L,B,Q)& cong(L,B,L,Q)& coll(Q1,L,A)& coll(Q1,O,Y)& coll(P1,O,X)& coll(P1,L,B) )=> cyclic(O,P,Q,P1) ) )),
% 0.13/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.52 fof(f96,negated_conjecture,(
% 0.13/0.52 ~((! [O,X,L,A,Y,B,P,Q,Q1,P1] :( ( perp(A,L,O,X)& coll(A,O,X)& perp(B,L,O,Y)& coll(B,O,Y)& coll(L,A,P)& cong(L,A,L,P)& coll(L,B,Q)& cong(L,B,L,Q)& coll(Q1,L,A)& coll(Q1,O,Y)& coll(P1,O,X)& coll(P1,L,B) )=> cyclic(O,P,Q,P1) ) ))),
% 0.13/0.52 inference(negated_conjecture,[status(cth)],[f95])).
% 0.13/0.52 fof(f97,plain,(
% 0.13/0.52 ![A,B,C]: (~coll(A,B,C)|coll(A,C,B))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.13/0.52 fof(f98,plain,(
% 0.13/0.52 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X0,X2,X1))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f97])).
% 0.13/0.52 fof(f99,plain,(
% 0.13/0.52 ![A,B,C]: (~coll(A,B,C)|coll(B,A,C))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.13/0.52 fof(f100,plain,(
% 0.13/0.52 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X1,X0,X2))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f99])).
% 0.13/0.52 fof(f101,plain,(
% 0.13/0.52 ![A,B,C,D]: ((~coll(A,B,C)|~coll(A,B,D))|coll(C,D,A))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.13/0.52 fof(f102,plain,(
% 0.13/0.52 ![A,C,D]: ((![B]: (~coll(A,B,C)|~coll(A,B,D)))|coll(C,D,A))),
% 0.13/0.52 inference(miniscoping,[status(thm)],[f101])).
% 0.13/0.52 fof(f103,plain,(
% 0.13/0.52 ![X0,X1,X2,X3]: (~coll(X0,X1,X2)|~coll(X0,X1,X3)|coll(X2,X3,X0))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f102])).
% 0.13/0.52 fof(f113,plain,(
% 0.13/0.52 ![A,B,C,D]: (~perp(A,B,C,D)|perp(C,D,A,B))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.13/0.52 fof(f114,plain,(
% 0.13/0.52 ![X0,X1,X2,X3]: (~perp(X0,X1,X2,X3)|perp(X2,X3,X0,X1))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f113])).
% 0.13/0.52 fof(f115,plain,(
% 0.13/0.52 ![A,B,C,D,E,F]: ((~perp(A,B,C,D)|~perp(C,D,E,F))|para(A,B,E,F))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.13/0.52 fof(f116,plain,(
% 0.13/0.52 ![A,B,E,F]: ((![C,D]: (~perp(A,B,C,D)|~perp(C,D,E,F)))|para(A,B,E,F))),
% 0.13/0.52 inference(miniscoping,[status(thm)],[f115])).
% 0.13/0.52 fof(f117,plain,(
% 0.13/0.52 ![X0,X1,X2,X3,X4,X5]: (~perp(X0,X1,X2,X3)|~perp(X2,X3,X4,X5)|para(X0,X1,X4,X5))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f116])).
% 0.13/0.52 fof(f134,plain,(
% 0.13/0.52 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.13/0.52 fof(f135,plain,(
% 0.13/0.52 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 0.13/0.52 inference(miniscoping,[status(thm)],[f134])).
% 0.13/0.52 fof(f136,plain,(
% 0.13/0.52 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f135])).
% 0.13/0.52 fof(f139,plain,(
% 0.13/0.52 ![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))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.13/0.52 fof(f140,plain,(
% 0.13/0.52 ![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))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f139])).
% 0.13/0.52 fof(f143,plain,(
% 0.13/0.52 ![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))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.13/0.52 fof(f144,plain,(
% 0.13/0.52 ![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))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f143])).
% 0.13/0.52 fof(f184,plain,(
% 0.13/0.52 ![A,B,C,D,P,Q]: (~eqangle(A,B,P,Q,C,D,P,Q)|para(A,B,C,D))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 0.13/0.52 fof(f185,plain,(
% 0.13/0.52 ![A,B,C,D]: ((![P,Q]: ~eqangle(A,B,P,Q,C,D,P,Q))|para(A,B,C,D))),
% 0.13/0.52 inference(miniscoping,[status(thm)],[f184])).
% 0.13/0.52 fof(f186,plain,(
% 0.13/0.52 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X2,X3,X4,X5,X2,X3)|para(X0,X1,X4,X5))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f185])).
% 0.13/0.52 fof(f187,plain,(
% 0.13/0.52 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 0.13/0.52 fof(f188,plain,(
% 0.13/0.52 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 0.13/0.52 inference(miniscoping,[status(thm)],[f187])).
% 0.13/0.52 fof(f189,plain,(
% 0.13/0.52 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f188])).
% 0.13/0.52 fof(f194,plain,(
% 0.13/0.52 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 0.13/0.52 fof(f195,plain,(
% 0.13/0.52 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f194])).
% 0.13/0.52 fof(f255,plain,(
% 0.13/0.52 ![A,B,C]: (~para(A,B,A,C)|coll(A,B,C))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f67])).
% 0.13/0.52 fof(f256,plain,(
% 0.13/0.52 ![X0,X1,X2]: (~para(X0,X1,X0,X2)|coll(X0,X1,X2))),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f255])).
% 0.13/0.52 fof(f369,plain,(
% 0.13/0.52 (?[O,X,L,A,Y,B,P,Q,Q1,P1]: ((((((((((((perp(A,L,O,X)&coll(A,O,X))&perp(B,L,O,Y))&coll(B,O,Y))&coll(L,A,P))&cong(L,A,L,P))&coll(L,B,Q))&cong(L,B,L,Q))&coll(Q1,L,A))&coll(Q1,O,Y))&coll(P1,O,X))&coll(P1,L,B))&~cyclic(O,P,Q,P1)))),
% 0.13/0.52 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 0.13/0.52 fof(f370,plain,(
% 0.13/0.52 ?[O,P,Q,P1]: ((?[L,B]: ((?[X]: ((?[Y,Q1]: ((?[A]: ((((((((perp(A,L,O,X)&coll(A,O,X))&perp(B,L,O,Y))&coll(B,O,Y))&coll(L,A,P))&cong(L,A,L,P))&coll(L,B,Q))&cong(L,B,L,Q))&coll(Q1,L,A)))&coll(Q1,O,Y)))&coll(P1,O,X)))&coll(P1,L,B)))&~cyclic(O,P,Q,P1))),
% 0.13/0.52 inference(miniscoping,[status(thm)],[f369])).
% 0.13/0.52 fof(f371,plain,(
% 0.13/0.52 ((((((((((((perp(sK29_skl,sK24_skl,sK20_skl,sK26_skl)&coll(sK29_skl,sK20_skl,sK26_skl))&perp(sK25_skl,sK24_skl,sK20_skl,sK27_skl))&coll(sK25_skl,sK20_skl,sK27_skl))&coll(sK24_skl,sK29_skl,sK21_skl))&cong(sK24_skl,sK29_skl,sK24_skl,sK21_skl))&coll(sK24_skl,sK25_skl,sK22_skl))&cong(sK24_skl,sK25_skl,sK24_skl,sK22_skl))&coll(sK28_skl,sK24_skl,sK29_skl))&coll(sK28_skl,sK20_skl,sK27_skl))&coll(sK23_skl,sK20_skl,sK26_skl))&coll(sK23_skl,sK24_skl,sK25_skl))&~cyclic(sK20_skl,sK21_skl,sK22_skl,sK23_skl))),
% 0.13/0.52 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(O,sK20_skl),skolemize(P,sK21_skl),skolemize(Q,sK22_skl),skolemize(P1,sK23_skl),skolemize(L,sK24_skl),skolemize(B,sK25_skl),skolemize(X,sK26_skl),skolemize(Y,sK27_skl),skolemize(Q1,sK28_skl),skolemize(A,sK29_skl)],[f370])).
% 0.13/0.52 fof(f374,plain,(
% 0.13/0.52 perp(sK25_skl,sK24_skl,sK20_skl,sK27_skl)),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f371])).
% 0.13/0.52 fof(f384,plain,(
% 0.13/0.52 ~cyclic(sK20_skl,sK21_skl,sK22_skl,sK23_skl)),
% 0.13/0.52 inference(cnf_transformation,[status(thm)],[f371])).
% 0.13/0.52 fof(f519,plain,(
% 0.13/0.52 perp(sK20_skl,sK27_skl,sK25_skl,sK24_skl)),
% 0.13/0.52 inference(resolution,[status(thm)],[f114,f374])).
% 0.13/0.52 fof(f533,plain,(
% 0.13/0.52 ![X0,X1]: (~perp(X0,X1,sK25_skl,sK24_skl)|para(X0,X1,sK20_skl,sK27_skl))),
% 0.13/0.52 inference(resolution,[status(thm)],[f117,f374])).
% 0.13/0.52 fof(f1090,plain,(
% 0.13/0.52 para(sK20_skl,sK27_skl,sK20_skl,sK27_skl)),
% 0.13/0.52 inference(resolution,[status(thm)],[f519,f533])).
% 0.13/0.52 fof(f1116,plain,(
% 0.13/0.52 ![X0,X1]: (eqangle(sK20_skl,sK27_skl,X0,X1,sK20_skl,sK27_skl,X0,X1))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1090,f189])).
% 0.13/0.52 fof(f1180,plain,(
% 0.13/0.52 ![X0,X1]: (eqangle(X0,X1,sK20_skl,sK27_skl,X0,X1,sK20_skl,sK27_skl))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1116,f140])).
% 0.13/0.52 fof(f1253,plain,(
% 0.13/0.52 ![X0,X1]: (para(X0,X1,X0,X1))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1180,f186])).
% 0.13/0.52 fof(f1261,plain,(
% 0.13/0.52 ![X0,X1,X2,X3]: (eqangle(X0,X1,X2,X3,X0,X1,X2,X3))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1253,f189])).
% 0.13/0.52 fof(f1262,plain,(
% 0.13/0.52 ![X0,X1]: (coll(X0,X1,X1))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1253,f256])).
% 0.13/0.52 fof(f1275,plain,(
% 0.13/0.52 ![X0,X1]: (coll(X0,X1,X0))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1262,f100])).
% 0.13/0.52 fof(f1300,plain,(
% 0.13/0.52 ![X0,X1]: (coll(X0,X0,X1))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1275,f98])).
% 0.13/0.52 fof(f1313,plain,(
% 0.13/0.52 ![X0,X1,X2]: (~coll(X0,X0,X1)|coll(X1,X2,X0))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1300,f103])).
% 0.13/0.52 fof(f1318,plain,(
% 0.13/0.52 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|cyclic(X1,X2,X0,X3))),
% 0.13/0.52 inference(backward_subsumption_resolution,[status(thm)],[f195,f1324])).
% 0.13/0.52 fof(f1324,plain,(
% 0.13/0.52 ![X0,X1,X2]: (coll(X0,X1,X2))),
% 0.13/0.52 inference(forward_subsumption_resolution,[status(thm)],[f1313,f1300])).
% 0.13/0.52 fof(f1333,plain,(
% 0.13/0.52 ![X0,X1,X2,X3]: (eqangle(X0,X1,X0,X1,X2,X3,X2,X3))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1261,f144])).
% 0.13/0.52 fof(f1407,plain,(
% 0.13/0.52 ![X0,X1,X2]: (cyclic(X0,X0,X1,X2))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1318,f1333])).
% 0.13/0.52 fof(f1414,plain,(
% 0.13/0.52 ![X0,X1,X2,X3]: (~cyclic(X0,X0,X1,X2)|cyclic(X0,X1,X2,X3))),
% 0.13/0.52 inference(resolution,[status(thm)],[f1407,f136])).
% 0.13/0.52 fof(f1423,plain,(
% 0.13/0.52 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3))),
% 0.13/0.52 inference(forward_subsumption_resolution,[status(thm)],[f1414,f1407])).
% 0.13/0.52 fof(f1424,plain,(
% 0.13/0.52 $false),
% 0.13/0.52 inference(backward_subsumption_resolution,[status(thm)],[f384,f1423])).
% 0.13/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.61/0.56 % Elapsed time: 0.181005 seconds
% 0.61/0.56 % CPU time: 1.073464 seconds
% 0.61/0.56 % Total memory used: 95.333 MB
% 0.61/0.56 % Net memory used: 94.388 MB
%------------------------------------------------------------------------------