%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO576+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 : n013.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 12:26:40 PM UTC 2026
% Result : Theorem 3.10s 0.83s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO576+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
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 17:36:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 3.10/0.83 % Refutation found
% 3.10/0.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.10/0.83 % SZS output start CNFRefutation for theBenchmark
% 3.10/0.83 fof(f1,axiom,(
% 3.10/0.83 (! [A,B,C] :( coll(A,B,C)=> coll(A,C,B) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f2,axiom,(
% 3.10/0.83 (! [A,B,C] :( coll(A,B,C)=> coll(B,A,C) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f3,axiom,(
% 3.10/0.83 (! [A,B,C,D] :( ( coll(A,B,C)& coll(A,B,D) )=> coll(C,D,A) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f4,axiom,(
% 3.10/0.83 (! [A,B,C,D] :( para(A,B,C,D)=> para(A,B,D,C) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f8,axiom,(
% 3.10/0.83 (! [A,B,C,D] :( perp(A,B,C,D)=> perp(C,D,A,B) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f9,axiom,(
% 3.10/0.83 (! [A,B,C,D,E,F] :( ( perp(A,B,C,D)& perp(C,D,E,F) )=> para(A,B,E,F) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f14,axiom,(
% 3.10/0.83 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(A,B,D,C) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f15,axiom,(
% 3.10/0.83 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(A,C,B,D) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f16,axiom,(
% 3.10/0.83 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(B,A,C,D) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f17,axiom,(
% 3.10/0.83 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f18,axiom,(
% 3.10/0.83 (! [A,B,C,D,P,Q,U,V] :( eqangle(A,B,C,D,P,Q,U,V)=> eqangle(B,A,C,D,P,Q,U,V) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f19,axiom,(
% 3.10/0.83 (! [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) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f20,axiom,(
% 3.10/0.83 (! [A,B,C,D,P,Q,U,V] :( eqangle(A,B,C,D,P,Q,U,V)=> eqangle(P,Q,U,V,A,B,C,D) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f21,axiom,(
% 3.10/0.83 (! [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) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f22,axiom,(
% 3.10/0.83 (! [A,B,C,D,P,Q,U,V,E,F,G,H] :( ( eqangle(A,B,C,D,P,Q,U,V)& eqangle(P,Q,U,V,E,F,G,H) )=> eqangle(A,B,C,D,E,F,G,H) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f39,axiom,(
% 3.10/0.83 (! [A,B,C,D,P,Q] :( eqangle(A,B,P,Q,C,D,P,Q)=> para(A,B,C,D) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f40,axiom,(
% 3.10/0.83 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f41,axiom,(
% 3.10/0.83 (! [A,B,P,Q] :( cyclic(A,B,P,Q)=> eqangle(P,A,P,B,Q,A,Q,B) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f43,axiom,(
% 3.10/0.83 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f44,axiom,(
% 3.10/0.83 (! [A,B,C,P,Q,R] :( ( cyclic(A,B,C,P)& cyclic(A,B,C,Q)& cyclic(A,B,C,R)& eqangle(C,A,C,B,R,P,R,Q) )=> cong(A,B,P,Q) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f46,axiom,(
% 3.10/0.83 (! [A,B,C,E,F] :( ( midp(E,A,B)& para(E,F,B,C)& coll(F,A,C) )=> midp(F,A,C) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f56,axiom,(
% 3.10/0.83 (! [A,B,M,O] :( ( midp(M,A,B)& perp(O,M,A,B) )=> cong(O,A,O,B) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f58,axiom,(
% 3.10/0.83 (! [A,B,P,Q] :( ( cong(A,P,B,P)& cong(A,Q,B,Q)& cyclic(A,B,P,Q) )=> perp(P,A,A,Q) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f64,axiom,(
% 3.10/0.83 (! [A,B,C,D,M] :( ( midp(M,A,B)& midp(M,C,D) )=> para(A,C,B,D) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f67,axiom,(
% 3.10/0.83 (! [A,B,C] :( para(A,B,A,C)=> coll(A,B,C) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f68,axiom,(
% 3.10/0.83 (! [A,B,C] :( ( cong(A,B,A,C)& coll(A,B,C) )=> midp(A,B,C) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f95,conjecture,(
% 3.10/0.83 (! [A,B,C,D,O,D1,P,NWPNT1] :( ( perp(D,A,B,C)& coll(D,B,C)& circle(O,A,B,C)& circle(O,A,D1,NWPNT1)& coll(D1,A,D)& perp(A,C,D1,P)& coll(P,B,C) )=> eqangle(O,A,A,D,C,A,A,P) ) )),
% 3.10/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.10/0.83 fof(f96,negated_conjecture,(
% 3.10/0.83 ~((! [A,B,C,D,O,D1,P,NWPNT1] :( ( perp(D,A,B,C)& coll(D,B,C)& circle(O,A,B,C)& circle(O,A,D1,NWPNT1)& coll(D1,A,D)& perp(A,C,D1,P)& coll(P,B,C) )=> eqangle(O,A,A,D,C,A,A,P) ) ))),
% 3.10/0.83 inference(negated_conjecture,[status(cth)],[f95])).
% 3.10/0.83 fof(f97,plain,(
% 3.10/0.83 ![A,B,C]: (~coll(A,B,C)|coll(A,C,B))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 3.10/0.83 fof(f98,plain,(
% 3.10/0.83 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X0,X2,X1))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f97])).
% 3.10/0.83 fof(f99,plain,(
% 3.10/0.83 ![A,B,C]: (~coll(A,B,C)|coll(B,A,C))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 3.10/0.83 fof(f100,plain,(
% 3.10/0.83 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X1,X0,X2))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f99])).
% 3.10/0.83 fof(f101,plain,(
% 3.10/0.83 ![A,B,C,D]: ((~coll(A,B,C)|~coll(A,B,D))|coll(C,D,A))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 3.10/0.83 fof(f102,plain,(
% 3.10/0.83 ![A,C,D]: ((![B]: (~coll(A,B,C)|~coll(A,B,D)))|coll(C,D,A))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f101])).
% 3.10/0.83 fof(f103,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~coll(X0,X1,X2)|~coll(X0,X1,X3)|coll(X2,X3,X0))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f102])).
% 3.10/0.83 fof(f104,plain,(
% 3.10/0.83 ![A,B,C,D]: (~para(A,B,C,D)|para(A,B,D,C))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 3.10/0.83 fof(f105,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~para(X0,X1,X2,X3)|para(X0,X1,X3,X2))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f104])).
% 3.10/0.83 fof(f113,plain,(
% 3.10/0.83 ![A,B,C,D]: (~perp(A,B,C,D)|perp(C,D,A,B))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 3.10/0.83 fof(f114,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~perp(X0,X1,X2,X3)|perp(X2,X3,X0,X1))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f113])).
% 3.10/0.83 fof(f115,plain,(
% 3.10/0.83 ![A,B,C,D,E,F]: ((~perp(A,B,C,D)|~perp(C,D,E,F))|para(A,B,E,F))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 3.10/0.83 fof(f116,plain,(
% 3.10/0.83 ![A,B,E,F]: ((![C,D]: (~perp(A,B,C,D)|~perp(C,D,E,F)))|para(A,B,E,F))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f115])).
% 3.10/0.83 fof(f117,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5]: (~perp(X0,X1,X2,X3)|~perp(X2,X3,X4,X5)|para(X0,X1,X4,X5))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f116])).
% 3.10/0.83 fof(f128,plain,(
% 3.10/0.83 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(A,B,D,C))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 3.10/0.83 fof(f129,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X0,X1,X3,X2))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f128])).
% 3.10/0.83 fof(f130,plain,(
% 3.10/0.83 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(A,C,B,D))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 3.10/0.83 fof(f131,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X0,X2,X1,X3))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f130])).
% 3.10/0.83 fof(f132,plain,(
% 3.10/0.83 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(B,A,C,D))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 3.10/0.83 fof(f133,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X1,X0,X2,X3))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f132])).
% 3.10/0.83 fof(f134,plain,(
% 3.10/0.83 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 3.10/0.83 fof(f135,plain,(
% 3.10/0.83 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f134])).
% 3.10/0.83 fof(f136,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f135])).
% 3.10/0.83 fof(f137,plain,(
% 3.10/0.83 ![A,B,C,D,P,Q,U,V]: (~eqangle(A,B,C,D,P,Q,U,V)|eqangle(B,A,C,D,P,Q,U,V))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 3.10/0.83 fof(f138,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|eqangle(X1,X0,X2,X3,X4,X5,X6,X7))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f137])).
% 3.10/0.83 fof(f139,plain,(
% 3.10/0.83 ![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))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 3.10/0.83 fof(f140,plain,(
% 3.10/0.83 ![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))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f139])).
% 3.10/0.83 fof(f141,plain,(
% 3.10/0.83 ![A,B,C,D,P,Q,U,V]: (~eqangle(A,B,C,D,P,Q,U,V)|eqangle(P,Q,U,V,A,B,C,D))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 3.10/0.83 fof(f142,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|eqangle(X4,X5,X6,X7,X0,X1,X2,X3))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f141])).
% 3.10/0.83 fof(f143,plain,(
% 3.10/0.83 ![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))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 3.10/0.83 fof(f144,plain,(
% 3.10/0.83 ![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))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f143])).
% 3.10/0.83 fof(f145,plain,(
% 3.10/0.83 ![A,B,C,D,P,Q,U,V,E,F,G,H]: ((~eqangle(A,B,C,D,P,Q,U,V)|~eqangle(P,Q,U,V,E,F,G,H))|eqangle(A,B,C,D,E,F,G,H))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 3.10/0.83 fof(f146,plain,(
% 3.10/0.83 ![A,B,C,D,E,F,G,H]: ((![P,Q,U,V]: (~eqangle(A,B,C,D,P,Q,U,V)|~eqangle(P,Q,U,V,E,F,G,H)))|eqangle(A,B,C,D,E,F,G,H))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f145])).
% 3.10/0.83 fof(f147,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11]: (~eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|~eqangle(X4,X5,X6,X7,X8,X9,X10,X11)|eqangle(X0,X1,X2,X3,X8,X9,X10,X11))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f146])).
% 3.10/0.83 fof(f184,plain,(
% 3.10/0.83 ![A,B,C,D,P,Q]: (~eqangle(A,B,P,Q,C,D,P,Q)|para(A,B,C,D))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 3.10/0.83 fof(f185,plain,(
% 3.10/0.83 ![A,B,C,D]: ((![P,Q]: ~eqangle(A,B,P,Q,C,D,P,Q))|para(A,B,C,D))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f184])).
% 3.10/0.83 fof(f186,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X2,X3,X4,X5,X2,X3)|para(X0,X1,X4,X5))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f185])).
% 3.10/0.83 fof(f187,plain,(
% 3.10/0.83 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 3.10/0.83 fof(f188,plain,(
% 3.10/0.83 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f187])).
% 3.10/0.83 fof(f189,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f188])).
% 3.10/0.83 fof(f190,plain,(
% 3.10/0.83 ![A,B,P,Q]: (~cyclic(A,B,P,Q)|eqangle(P,A,P,B,Q,A,Q,B))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 3.10/0.83 fof(f191,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|eqangle(X2,X0,X2,X1,X3,X0,X3,X1))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f190])).
% 3.10/0.83 fof(f194,plain,(
% 3.10/0.83 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 3.10/0.83 fof(f195,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f194])).
% 3.10/0.83 fof(f196,plain,(
% 3.10/0.83 ![A,B,C,P,Q,R]: ((((~cyclic(A,B,C,P)|~cyclic(A,B,C,Q))|~cyclic(A,B,C,R))|~eqangle(C,A,C,B,R,P,R,Q))|cong(A,B,P,Q))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 3.10/0.83 fof(f197,plain,(
% 3.10/0.83 ![A,B,P,Q]: ((![C,R]: (((~cyclic(A,B,C,P)|~cyclic(A,B,C,Q))|~cyclic(A,B,C,R))|~eqangle(C,A,C,B,R,P,R,Q)))|cong(A,B,P,Q))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f196])).
% 3.10/0.83 fof(f198,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|~cyclic(X0,X1,X2,X5)|~eqangle(X2,X0,X2,X1,X5,X3,X5,X4)|cong(X0,X1,X3,X4))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f197])).
% 3.10/0.83 fof(f202,plain,(
% 3.10/0.83 ![A,B,C,E,F]: (((~midp(E,A,B)|~para(E,F,B,C))|~coll(F,A,C))|midp(F,A,C))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 3.10/0.83 fof(f203,plain,(
% 3.10/0.83 ![A,C,F]: (((![B,E]: (~midp(E,A,B)|~para(E,F,B,C)))|~coll(F,A,C))|midp(F,A,C))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f202])).
% 3.10/0.83 fof(f204,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~para(X0,X3,X2,X4)|~coll(X3,X1,X4)|midp(X3,X1,X4))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f203])).
% 3.10/0.83 fof(f228,plain,(
% 3.10/0.83 ![A,B,M,O]: ((~midp(M,A,B)|~perp(O,M,A,B))|cong(O,A,O,B))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f56])).
% 3.10/0.83 fof(f229,plain,(
% 3.10/0.83 ![A,B,O]: ((![M]: (~midp(M,A,B)|~perp(O,M,A,B)))|cong(O,A,O,B))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f228])).
% 3.10/0.83 fof(f230,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~midp(X0,X1,X2)|~perp(X3,X0,X1,X2)|cong(X3,X1,X3,X2))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f229])).
% 3.10/0.83 fof(f233,plain,(
% 3.10/0.83 ![A,B,P,Q]: (((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q))|perp(P,A,A,Q))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 3.10/0.83 fof(f234,plain,(
% 3.10/0.83 ![A,P,Q]: ((![B]: ((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q)))|perp(P,A,A,Q))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f233])).
% 3.10/0.83 fof(f235,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|~cyclic(X0,X2,X1,X3)|perp(X1,X0,X0,X3))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f234])).
% 3.10/0.83 fof(f247,plain,(
% 3.10/0.83 ![A,B,C,D,M]: ((~midp(M,A,B)|~midp(M,C,D))|para(A,C,B,D))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f64])).
% 3.10/0.83 fof(f248,plain,(
% 3.10/0.83 ![A,B,C,D]: ((![M]: (~midp(M,A,B)|~midp(M,C,D)))|para(A,C,B,D))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f247])).
% 3.10/0.83 fof(f249,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~midp(X0,X3,X4)|para(X1,X3,X2,X4))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f248])).
% 3.10/0.83 fof(f255,plain,(
% 3.10/0.83 ![A,B,C]: (~para(A,B,A,C)|coll(A,B,C))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f67])).
% 3.10/0.83 fof(f256,plain,(
% 3.10/0.83 ![X0,X1,X2]: (~para(X0,X1,X0,X2)|coll(X0,X1,X2))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f255])).
% 3.10/0.83 fof(f257,plain,(
% 3.10/0.83 ![A,B,C]: ((~cong(A,B,A,C)|~coll(A,B,C))|midp(A,B,C))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f68])).
% 3.10/0.83 fof(f258,plain,(
% 3.10/0.83 ![X0,X1,X2]: (~cong(X0,X1,X0,X2)|~coll(X0,X1,X2)|midp(X0,X1,X2))),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f257])).
% 3.10/0.83 fof(f369,plain,(
% 3.10/0.83 (?[A,B,C,D,O,D1,P,NWPNT1]: (((((((perp(D,A,B,C)&coll(D,B,C))&circle(O,A,B,C))&circle(O,A,D1,NWPNT1))&coll(D1,A,D))&perp(A,C,D1,P))&coll(P,B,C))&~eqangle(O,A,A,D,C,A,A,P)))),
% 3.10/0.83 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 3.10/0.83 fof(f370,plain,(
% 3.10/0.83 ?[A,C,D,O,P]: ((?[B]: ((?[D1]: (((((perp(D,A,B,C)&coll(D,B,C))&circle(O,A,B,C))&(?[NWPNT1]: circle(O,A,D1,NWPNT1)))&coll(D1,A,D))&perp(A,C,D1,P)))&coll(P,B,C)))&~eqangle(O,A,A,D,C,A,A,P))),
% 3.10/0.83 inference(miniscoping,[status(thm)],[f369])).
% 3.10/0.83 fof(f371,plain,(
% 3.10/0.83 (((((((perp(sK22_skl,sK20_skl,sK25_skl,sK21_skl)&coll(sK22_skl,sK25_skl,sK21_skl))&circle(sK23_skl,sK20_skl,sK25_skl,sK21_skl))&circle(sK23_skl,sK20_skl,sK26_skl,sK27_skl))&coll(sK26_skl,sK20_skl,sK22_skl))&perp(sK20_skl,sK21_skl,sK26_skl,sK24_skl))&coll(sK24_skl,sK25_skl,sK21_skl))&~eqangle(sK23_skl,sK20_skl,sK20_skl,sK22_skl,sK21_skl,sK20_skl,sK20_skl,sK24_skl))),
% 3.10/0.83 inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl]),skolemize(A,sK20_skl),skolemize(C,sK21_skl),skolemize(D,sK22_skl),skolemize(O,sK23_skl),skolemize(P,sK24_skl),skolemize(B,sK25_skl),skolemize(D1,sK26_skl),skolemize(NWPNT1,sK27_skl)],[f370])).
% 3.10/0.83 fof(f372,plain,(
% 3.10/0.83 perp(sK22_skl,sK20_skl,sK25_skl,sK21_skl)),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f371])).
% 3.10/0.83 fof(f373,plain,(
% 3.10/0.83 coll(sK22_skl,sK25_skl,sK21_skl)),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f371])).
% 3.10/0.83 fof(f379,plain,(
% 3.10/0.83 ~eqangle(sK23_skl,sK20_skl,sK20_skl,sK22_skl,sK21_skl,sK20_skl,sK20_skl,sK24_skl)),
% 3.10/0.83 inference(cnf_transformation,[status(thm)],[f371])).
% 3.10/0.83 fof(f382,plain,(
% 3.10/0.83 coll(sK22_skl,sK21_skl,sK25_skl)),
% 3.10/0.83 inference(resolution,[status(thm)],[f98,f373])).
% 3.10/0.83 fof(f390,plain,(
% 3.10/0.83 coll(sK21_skl,sK22_skl,sK25_skl)),
% 3.10/0.83 inference(resolution,[status(thm)],[f100,f382])).
% 3.10/0.83 fof(f404,plain,(
% 3.10/0.83 ![X0]: (~coll(sK21_skl,sK22_skl,X0)|coll(X0,sK25_skl,sK21_skl))),
% 3.10/0.83 inference(resolution,[status(thm)],[f103,f390])).
% 3.10/0.83 fof(f461,plain,(
% 3.10/0.83 perp(sK25_skl,sK21_skl,sK22_skl,sK20_skl)),
% 3.10/0.83 inference(resolution,[status(thm)],[f114,f372])).
% 3.10/0.83 fof(f501,plain,(
% 3.10/0.83 ![X0,X1]: (~perp(X0,X1,sK22_skl,sK20_skl)|para(X0,X1,sK25_skl,sK21_skl))),
% 3.10/0.83 inference(resolution,[status(thm)],[f117,f372])).
% 3.10/0.83 fof(f503,plain,(
% 3.10/0.83 coll(sK25_skl,sK25_skl,sK21_skl)),
% 3.10/0.83 inference(resolution,[status(thm)],[f404,f390])).
% 3.10/0.83 fof(f699,plain,(
% 3.10/0.83 para(sK25_skl,sK21_skl,sK25_skl,sK21_skl)),
% 3.10/0.83 inference(resolution,[status(thm)],[f501,f461])).
% 3.10/0.83 fof(f1184,plain,(
% 3.10/0.83 ![X0,X1]: (eqangle(sK25_skl,sK21_skl,X0,X1,sK25_skl,sK21_skl,X0,X1))),
% 3.10/0.83 inference(resolution,[status(thm)],[f189,f699])).
% 3.10/0.83 fof(f1415,plain,(
% 3.10/0.83 ![X0,X1]: (eqangle(X0,X1,sK25_skl,sK21_skl,X0,X1,sK25_skl,sK21_skl))),
% 3.10/0.83 inference(resolution,[status(thm)],[f1184,f140])).
% 3.10/0.83 fof(f2657,plain,(
% 3.10/0.83 ![X0]: (~coll(sK25_skl,sK25_skl,sK21_skl)|cyclic(X0,sK21_skl,sK25_skl,sK25_skl))),
% 3.10/0.83 inference(resolution,[status(thm)],[f1415,f195])).
% 3.10/0.83 fof(f2659,plain,(
% 3.10/0.83 ![X0,X1]: (para(X0,X1,X0,X1))),
% 3.10/0.83 inference(resolution,[status(thm)],[f1415,f186])).
% 3.10/0.83 fof(f2669,plain,(
% 3.10/0.83 ![X0]: (cyclic(X0,sK21_skl,sK25_skl,sK25_skl))),
% 3.10/0.83 inference(forward_subsumption_resolution,[status(thm)],[f2657,f503])).
% 3.10/0.83 fof(f2676,plain,(
% 3.10/0.83 ![X0,X1]: (coll(X0,X1,X1))),
% 3.10/0.83 inference(resolution,[status(thm)],[f2659,f256])).
% 3.10/0.83 fof(f2679,plain,(
% 3.10/0.83 ![X0,X1]: (para(X0,X1,X1,X0))),
% 3.10/0.83 inference(resolution,[status(thm)],[f2659,f105])).
% 3.10/0.83 fof(f2846,plain,(
% 3.10/0.83 ![X0,X1]: (coll(X0,X1,X0))),
% 3.10/0.83 inference(resolution,[status(thm)],[f2676,f100])).
% 3.10/0.83 fof(f3014,plain,(
% 3.10/0.83 ![X0,X1]: (coll(X0,X0,X1))),
% 3.10/0.83 inference(resolution,[status(thm)],[f2846,f98])).
% 3.10/0.83 fof(f3041,plain,(
% 3.10/0.83 ![X0,X1,X2]: (~coll(X0,X0,X1)|coll(X1,X2,X0))),
% 3.10/0.83 inference(resolution,[status(thm)],[f3014,f103])).
% 3.10/0.83 fof(f3044,plain,(
% 3.10/0.83 ![X0,X1,X2]: (coll(X0,X1,X2))),
% 3.10/0.83 inference(forward_subsumption_resolution,[status(thm)],[f3041,f3014])).
% 3.10/0.83 fof(f3045,plain,(
% 3.10/0.83 ![X0,X1,X2]: (~cong(X0,X1,X0,X2)|midp(X0,X1,X2))),
% 3.10/0.83 inference(backward_subsumption_resolution,[status(thm)],[f258,f3044])).
% 3.10/0.83 fof(f3047,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~para(X0,X3,X2,X4)|midp(X3,X1,X4))),
% 3.10/0.83 inference(backward_subsumption_resolution,[status(thm)],[f204,f3044])).
% 3.10/0.83 fof(f3063,plain,(
% 3.10/0.83 ![X0,X1,X2]: (~midp(X0,X1,X2)|midp(X2,X1,X0))),
% 3.10/0.83 inference(resolution,[status(thm)],[f3047,f2679])).
% 3.10/0.83 fof(f3067,plain,(
% 3.10/0.83 ![X0]: (cyclic(sK21_skl,X0,sK25_skl,sK25_skl))),
% 3.10/0.83 inference(resolution,[status(thm)],[f2669,f133])).
% 3.10/0.83 fof(f3073,plain,(
% 3.10/0.83 ![X0]: (cyclic(sK21_skl,sK25_skl,X0,sK25_skl))),
% 3.10/0.83 inference(resolution,[status(thm)],[f3067,f131])).
% 3.10/0.83 fof(f3084,plain,(
% 3.10/0.83 ![X0]: (cyclic(sK21_skl,sK25_skl,sK25_skl,X0))),
% 3.10/0.83 inference(resolution,[status(thm)],[f3073,f129])).
% 3.10/0.83 fof(f3101,plain,(
% 3.10/0.83 ![X0,X1]: (~cyclic(sK21_skl,sK25_skl,sK25_skl,X0)|cyclic(sK25_skl,sK25_skl,X0,X1))),
% 3.10/0.83 inference(resolution,[status(thm)],[f3084,f136])).
% 3.10/0.83 fof(f3105,plain,(
% 3.10/0.83 ![X0,X1]: (cyclic(sK25_skl,sK25_skl,X0,X1))),
% 3.10/0.83 inference(forward_subsumption_resolution,[status(thm)],[f3101,f3084])).
% 3.10/0.83 fof(f3107,plain,(
% 3.10/0.83 ![X0,X1,X2]: (~cyclic(sK25_skl,sK25_skl,X0,X1)|cyclic(sK25_skl,X0,X1,X2))),
% 3.10/0.83 inference(resolution,[status(thm)],[f3105,f136])).
% 3.10/0.83 fof(f3111,plain,(
% 3.10/0.83 ![X0,X1,X2]: (cyclic(sK25_skl,X0,X1,X2))),
% 3.10/0.83 inference(forward_subsumption_resolution,[status(thm)],[f3107,f3105])).
% 3.10/0.83 fof(f3113,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~cyclic(sK25_skl,X0,X1,X2)|cyclic(X0,X1,X2,X3))),
% 3.10/0.83 inference(resolution,[status(thm)],[f3111,f136])).
% 3.10/0.83 fof(f3117,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3))),
% 3.10/0.83 inference(forward_subsumption_resolution,[status(thm)],[f3113,f3111])).
% 3.10/0.83 fof(f3118,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|perp(X1,X0,X0,X3))),
% 3.10/0.83 inference(backward_subsumption_resolution,[status(thm)],[f235,f3117])).
% 3.10/0.83 fof(f3120,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|~eqangle(X2,X0,X2,X1,X5,X3,X5,X4)|cong(X0,X1,X3,X4))),
% 3.10/0.83 inference(backward_subsumption_resolution,[status(thm)],[f198,f3117])).
% 3.10/0.83 fof(f3121,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (eqangle(X0,X1,X0,X2,X3,X1,X3,X2))),
% 3.10/0.83 inference(backward_subsumption_resolution,[status(thm)],[f191,f3117])).
% 3.10/0.83 fof(f3122,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5]: (~cyclic(X0,X1,X2,X3)|~eqangle(X2,X0,X2,X1,X4,X5,X4,X3)|cong(X0,X1,X5,X3))),
% 3.10/0.83 inference(forward_subsumption_resolution,[status(thm)],[f3120,f3117])).
% 3.10/0.83 fof(f3184,plain,(
% 3.10/0.83 ![X0,X1,X2,X3]: (eqangle(X0,X1,X1,X2,X3,X0,X3,X2))),
% 3.10/0.83 inference(resolution,[status(thm)],[f3121,f138])).
% 3.10/0.83 fof(f3332,plain,(
% 3.10/0.83 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X0,X2,X3,X4,X3,X5)|cong(X1,X2,X4,X5))),
% 3.10/0.83 inference(forward_subsumption_resolution,[status(thm)],[f3122,f3117])).
% 3.10/0.83 fof(f3333,plain,(
% 3.10/0.83 ![X0,X1]: (cong(X0,X1,X0,X1))),
% 3.10/0.83 inference(resolution,[status(thm)],[f3332,f3184])).
% 3.10/0.83 fof(f3341,plain,(
% 3.10/0.83 ![X0,X1,X2]: (~cong(X0,X1,X0,X1)|perp(X1,X0,X0,X2))),
% 3.10/0.84 inference(resolution,[status(thm)],[f3333,f3118])).
% 3.10/0.84 fof(f3342,plain,(
% 3.10/0.84 ![X0,X1]: (midp(X0,X1,X1))),
% 3.10/0.84 inference(resolution,[status(thm)],[f3333,f3045])).
% 3.10/0.84 fof(f3349,plain,(
% 3.10/0.84 ![X0,X1,X2]: (perp(X0,X1,X1,X2))),
% 3.10/0.84 inference(forward_subsumption_resolution,[status(thm)],[f3341,f3333])).
% 3.10/0.84 fof(f3352,plain,(
% 3.10/0.84 ![X0,X1]: (midp(X0,X0,X1))),
% 3.10/0.84 inference(resolution,[status(thm)],[f3342,f3063])).
% 3.10/0.84 fof(f3396,plain,(
% 3.10/0.84 ![X0,X1,X2]: (~midp(X0,X0,X1)|cong(X2,X0,X2,X1))),
% 3.10/0.84 inference(resolution,[status(thm)],[f3349,f230])).
% 3.10/0.84 fof(f3400,plain,(
% 3.10/0.84 ![X0,X1,X2]: (cong(X0,X1,X0,X2))),
% 3.10/0.84 inference(forward_subsumption_resolution,[status(thm)],[f3396,f3352])).
% 3.10/0.84 fof(f3444,plain,(
% 3.10/0.84 ![X0,X1,X2]: (midp(X0,X1,X2))),
% 3.10/0.84 inference(backward_subsumption_resolution,[status(thm)],[f3045,f3400])).
% 3.10/0.84 fof(f3456,plain,(
% 3.10/0.84 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|para(X3,X1,X4,X2))),
% 3.10/0.84 inference(backward_subsumption_resolution,[status(thm)],[f249,f3444])).
% 3.10/0.84 fof(f3464,plain,(
% 3.10/0.84 ![X0,X1,X2,X3]: (para(X0,X1,X2,X3))),
% 3.10/0.84 inference(forward_subsumption_resolution,[status(thm)],[f3456,f3444])).
% 3.10/0.84 fof(f3531,plain,(
% 3.10/0.84 ![X0,X1,X2,X3,X4,X5]: (eqangle(X0,X1,X2,X3,X4,X5,X2,X3))),
% 3.10/0.84 inference(backward_subsumption_resolution,[status(thm)],[f189,f3464])).
% 3.10/0.84 fof(f3565,plain,(
% 3.10/0.84 ![X0,X1,X2,X3,X4,X5]: (eqangle(X0,X1,X2,X3,X4,X5,X4,X5))),
% 3.10/0.84 inference(resolution,[status(thm)],[f3531,f144])).
% 3.10/0.84 fof(f3732,plain,(
% 3.10/0.84 ![X0,X1,X2,X3,X4,X5]: (eqangle(X0,X1,X0,X1,X2,X3,X4,X5))),
% 3.10/0.84 inference(resolution,[status(thm)],[f3565,f142])).
% 3.10/0.84 fof(f3972,plain,(
% 3.10/0.84 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9]: (~eqangle(X0,X1,X2,X3,X4,X5,X4,X5)|eqangle(X0,X1,X2,X3,X6,X7,X8,X9))),
% 3.10/0.84 inference(resolution,[status(thm)],[f3732,f147])).
% 3.10/0.84 fof(f3977,plain,(
% 3.10/0.84 ![X0,X1,X2,X3,X4,X5,X6,X7]: (eqangle(X0,X1,X2,X3,X4,X5,X6,X7))),
% 3.10/0.84 inference(forward_subsumption_resolution,[status(thm)],[f3972,f3565])).
% 3.10/0.84 fof(f4627,plain,(
% 3.10/0.84 $false),
% 3.10/0.84 inference(backward_subsumption_resolution,[status(thm)],[f379,f3977])).
% 3.10/0.84 % SZS output end CNFRefutation for theBenchmark.p
% 0.26/0.85 % Elapsed time: 0.462992 seconds
% 0.26/0.85 % CPU time: 3.356600 seconds
% 0.26/0.85 % Total memory used: 115.248 MB
% 0.26/0.85 % Net memory used: 111.460 MB
%------------------------------------------------------------------------------