%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO639+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 : n010.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 9.56s 1.71s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO639+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
% 0.10/0.36 % Computer : n010.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 18:19:54 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 9.56/1.71 % Refutation found
% 9.56/1.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.56/1.71 % SZS output start CNFRefutation for theBenchmark
% 9.56/1.71 fof(f4,axiom,(
% 9.56/1.71 (! [A,B,C,D] :( para(A,B,C,D)=> para(A,B,D,C) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f5,axiom,(
% 9.56/1.71 (! [A,B,C,D] :( para(A,B,C,D)=> para(C,D,A,B) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f6,axiom,(
% 9.56/1.71 (! [A,B,C,D,E,F] :( ( para(A,B,C,D)& para(C,D,E,F) )=> para(A,B,E,F) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f11,axiom,(
% 9.56/1.71 (! [A,B,M] :( midp(M,B,A)=> midp(M,A,B) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f18,axiom,(
% 9.56/1.71 (! [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) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f19,axiom,(
% 9.56/1.71 (! [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) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f20,axiom,(
% 9.56/1.71 (! [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) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f21,axiom,(
% 9.56/1.71 (! [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) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f22,axiom,(
% 9.56/1.71 (! [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) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f23,axiom,(
% 9.56/1.71 (! [A,B,C,D] :( cong(A,B,C,D)=> cong(A,B,D,C) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f24,axiom,(
% 9.56/1.71 (! [A,B,C,D] :( cong(A,B,C,D)=> cong(C,D,A,B) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f39,axiom,(
% 9.56/1.71 (! [A,B,C,D,P,Q] :( eqangle(A,B,P,Q,C,D,P,Q)=> para(A,B,C,D) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f40,axiom,(
% 9.56/1.71 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f42,axiom,(
% 9.56/1.71 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& ~ coll(P,Q,A) )=> cyclic(A,B,P,Q) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f43,axiom,(
% 9.56/1.71 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f44,axiom,(
% 9.56/1.71 (! [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) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f45,axiom,(
% 9.56/1.71 (! [A,B,C,E,F] :( ( midp(E,A,B)& midp(F,A,C) )=> para(E,F,B,C) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f64,axiom,(
% 9.56/1.71 (! [A,B,C,D,M] :( ( midp(M,A,B)& midp(M,C,D) )=> para(A,C,B,D) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f65,axiom,(
% 9.56/1.71 (! [A,B,C,D,M] :( ( midp(M,A,B)& para(A,C,B,D)& para(A,D,B,C) )=> midp(M,C,D) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f67,axiom,(
% 9.56/1.71 (! [A,B,C] :( para(A,B,A,C)=> coll(A,B,C) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f68,axiom,(
% 9.56/1.71 (! [A,B,C] :( ( cong(A,B,A,C)& coll(A,B,C) )=> midp(A,B,C) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f95,conjecture,(
% 9.56/1.71 (! [P,Q,A,N,D,O,B,C,E,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7] :( ( ( cong(A,P,P,Q)| cong(A,P,A,Q) )& perp(P,A,P,N)& perp(Q,A,Q,N)& circle(N,P,NWPNT1,NWPNT2)& coll(D,A,N)& circle(N,P,D,NWPNT3)& midp(O,D,A)& circle(O,D,NWPNT4,NWPNT5)& coll(B,P,A)& circle(O,D,B,NWPNT6)& coll(C,Q,A)& circle(O,D,C,NWPNT7)& coll(E,P,Q)& coll(E,A,N) )=> eqangle(A,B,B,E,E,B,B,C) ) )),
% 9.56/1.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 9.56/1.71 fof(f96,negated_conjecture,(
% 9.56/1.71 ~((! [P,Q,A,N,D,O,B,C,E,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7] :( ( ( cong(A,P,P,Q)| cong(A,P,A,Q) )& perp(P,A,P,N)& perp(Q,A,Q,N)& circle(N,P,NWPNT1,NWPNT2)& coll(D,A,N)& circle(N,P,D,NWPNT3)& midp(O,D,A)& circle(O,D,NWPNT4,NWPNT5)& coll(B,P,A)& circle(O,D,B,NWPNT6)& coll(C,Q,A)& circle(O,D,C,NWPNT7)& coll(E,P,Q)& coll(E,A,N) )=> eqangle(A,B,B,E,E,B,B,C) ) ))),
% 9.56/1.71 inference(negated_conjecture,[status(cth)],[f95])).
% 9.56/1.71 fof(f104,plain,(
% 9.56/1.71 ![A,B,C,D]: (~para(A,B,C,D)|para(A,B,D,C))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 9.56/1.71 fof(f105,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (~para(X0,X1,X2,X3)|para(X0,X1,X3,X2))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f104])).
% 9.56/1.71 fof(f106,plain,(
% 9.56/1.71 ![A,B,C,D]: (~para(A,B,C,D)|para(C,D,A,B))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 9.56/1.71 fof(f107,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (~para(X0,X1,X2,X3)|para(X2,X3,X0,X1))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f106])).
% 9.56/1.71 fof(f108,plain,(
% 9.56/1.71 ![A,B,C,D,E,F]: ((~para(A,B,C,D)|~para(C,D,E,F))|para(A,B,E,F))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 9.56/1.71 fof(f109,plain,(
% 9.56/1.71 ![A,B,E,F]: ((![C,D]: (~para(A,B,C,D)|~para(C,D,E,F)))|para(A,B,E,F))),
% 9.56/1.71 inference(miniscoping,[status(thm)],[f108])).
% 9.56/1.71 fof(f110,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|~para(X2,X3,X4,X5)|para(X0,X1,X4,X5))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f109])).
% 9.56/1.71 fof(f121,plain,(
% 9.56/1.71 ![A,B,M]: (~midp(M,B,A)|midp(M,A,B))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 9.56/1.71 fof(f122,plain,(
% 9.56/1.71 ![X0,X1,X2]: (~midp(X0,X1,X2)|midp(X0,X2,X1))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f121])).
% 9.56/1.71 fof(f137,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 9.56/1.71 fof(f138,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f137])).
% 9.56/1.71 fof(f139,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 9.56/1.71 fof(f140,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f139])).
% 9.56/1.71 fof(f141,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 9.56/1.71 fof(f142,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f141])).
% 9.56/1.71 fof(f143,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 9.56/1.71 fof(f144,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f143])).
% 9.56/1.71 fof(f145,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 9.56/1.71 fof(f146,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(miniscoping,[status(thm)],[f145])).
% 9.56/1.71 fof(f147,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f146])).
% 9.56/1.71 fof(f148,plain,(
% 9.56/1.71 ![A,B,C,D]: (~cong(A,B,C,D)|cong(A,B,D,C))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 9.56/1.71 fof(f149,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X3)|cong(X0,X1,X3,X2))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f148])).
% 9.56/1.71 fof(f150,plain,(
% 9.56/1.71 ![A,B,C,D]: (~cong(A,B,C,D)|cong(C,D,A,B))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 9.56/1.71 fof(f151,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X3)|cong(X2,X3,X0,X1))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f150])).
% 9.56/1.71 fof(f184,plain,(
% 9.56/1.71 ![A,B,C,D,P,Q]: (~eqangle(A,B,P,Q,C,D,P,Q)|para(A,B,C,D))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 9.56/1.71 fof(f185,plain,(
% 9.56/1.71 ![A,B,C,D]: ((![P,Q]: ~eqangle(A,B,P,Q,C,D,P,Q))|para(A,B,C,D))),
% 9.56/1.71 inference(miniscoping,[status(thm)],[f184])).
% 9.56/1.71 fof(f186,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X2,X3,X4,X5,X2,X3)|para(X0,X1,X4,X5))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f185])).
% 9.56/1.71 fof(f187,plain,(
% 9.56/1.71 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 9.56/1.71 fof(f188,plain,(
% 9.56/1.71 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 9.56/1.71 inference(miniscoping,[status(thm)],[f187])).
% 9.56/1.71 fof(f189,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f188])).
% 9.56/1.71 fof(f192,plain,(
% 9.56/1.71 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|coll(P,Q,A))|cyclic(A,B,P,Q))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 9.56/1.71 fof(f193,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|coll(X0,X3,X1)|cyclic(X1,X2,X0,X3))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f192])).
% 9.56/1.71 fof(f194,plain,(
% 9.56/1.71 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 9.56/1.71 fof(f195,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f194])).
% 9.56/1.71 fof(f196,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 9.56/1.71 fof(f197,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(miniscoping,[status(thm)],[f196])).
% 9.56/1.71 fof(f198,plain,(
% 9.56/1.71 ![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))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f197])).
% 9.56/1.71 fof(f199,plain,(
% 9.56/1.71 ![A,B,C,E,F]: ((~midp(E,A,B)|~midp(F,A,C))|para(E,F,B,C))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 9.56/1.71 fof(f200,plain,(
% 9.56/1.71 ![B,C,E,F]: ((![A]: (~midp(E,A,B)|~midp(F,A,C)))|para(E,F,B,C))),
% 9.56/1.71 inference(miniscoping,[status(thm)],[f199])).
% 9.56/1.71 fof(f201,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~midp(X3,X1,X4)|para(X0,X3,X2,X4))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f200])).
% 9.56/1.71 fof(f247,plain,(
% 9.56/1.71 ![A,B,C,D,M]: ((~midp(M,A,B)|~midp(M,C,D))|para(A,C,B,D))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f64])).
% 9.56/1.71 fof(f248,plain,(
% 9.56/1.71 ![A,B,C,D]: ((![M]: (~midp(M,A,B)|~midp(M,C,D)))|para(A,C,B,D))),
% 9.56/1.71 inference(miniscoping,[status(thm)],[f247])).
% 9.56/1.71 fof(f249,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~midp(X0,X3,X4)|para(X1,X3,X2,X4))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f248])).
% 9.56/1.71 fof(f250,plain,(
% 9.56/1.71 ![A,B,C,D,M]: (((~midp(M,A,B)|~para(A,C,B,D))|~para(A,D,B,C))|midp(M,C,D))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f65])).
% 9.56/1.71 fof(f251,plain,(
% 9.56/1.71 ![C,D,M]: ((![A,B]: ((~midp(M,A,B)|~para(A,C,B,D))|~para(A,D,B,C)))|midp(M,C,D))),
% 9.56/1.71 inference(miniscoping,[status(thm)],[f250])).
% 9.56/1.71 fof(f252,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~para(X1,X3,X2,X4)|~para(X1,X4,X2,X3)|midp(X0,X3,X4))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f251])).
% 9.56/1.71 fof(f255,plain,(
% 9.56/1.71 ![A,B,C]: (~para(A,B,A,C)|coll(A,B,C))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f67])).
% 9.56/1.71 fof(f256,plain,(
% 9.56/1.71 ![X0,X1,X2]: (~para(X0,X1,X0,X2)|coll(X0,X1,X2))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f255])).
% 9.56/1.71 fof(f257,plain,(
% 9.56/1.71 ![A,B,C]: ((~cong(A,B,A,C)|~coll(A,B,C))|midp(A,B,C))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f68])).
% 9.56/1.71 fof(f258,plain,(
% 9.56/1.71 ![X0,X1,X2]: (~cong(X0,X1,X0,X2)|~coll(X0,X1,X2)|midp(X0,X1,X2))),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f257])).
% 9.56/1.71 fof(f369,plain,(
% 9.56/1.71 (?[P,Q,A,N,D,O,B,C,E,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7]: (((((((((((((((cong(A,P,P,Q)|cong(A,P,A,Q))&perp(P,A,P,N))&perp(Q,A,Q,N))&circle(N,P,NWPNT1,NWPNT2))&coll(D,A,N))&circle(N,P,D,NWPNT3))&midp(O,D,A))&circle(O,D,NWPNT4,NWPNT5))&coll(B,P,A))&circle(O,D,B,NWPNT6))&coll(C,Q,A))&circle(O,D,C,NWPNT7))&coll(E,P,Q))&coll(E,A,N))&~eqangle(A,B,B,E,E,B,B,C)))),
% 9.56/1.71 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 9.56/1.71 fof(f370,plain,(
% 9.56/1.71 ?[A,B,C,E]: ((?[N]: ((?[P,Q]: ((?[D,O]: ((((((((((((cong(A,P,P,Q)|cong(A,P,A,Q))&perp(P,A,P,N))&perp(Q,A,Q,N))&(?[NWPNT1,NWPNT2]: circle(N,P,NWPNT1,NWPNT2)))&coll(D,A,N))&(?[NWPNT3]: circle(N,P,D,NWPNT3)))&midp(O,D,A))&(?[NWPNT4,NWPNT5]: circle(O,D,NWPNT4,NWPNT5)))&coll(B,P,A))&(?[NWPNT6]: circle(O,D,B,NWPNT6)))&coll(C,Q,A))&(?[NWPNT7]: circle(O,D,C,NWPNT7))))&coll(E,P,Q)))&coll(E,A,N)))&~eqangle(A,B,B,E,E,B,B,C))),
% 9.56/1.71 inference(miniscoping,[status(thm)],[f369])).
% 9.56/1.71 fof(f371,plain,(
% 9.56/1.71 (((((((((((((((cong(sK20_skl,sK25_skl,sK25_skl,sK26_skl)|cong(sK20_skl,sK25_skl,sK20_skl,sK26_skl))&perp(sK25_skl,sK20_skl,sK25_skl,sK24_skl))&perp(sK26_skl,sK20_skl,sK26_skl,sK24_skl))&circle(sK24_skl,sK25_skl,sK29_skl,sK30_skl))&coll(sK27_skl,sK20_skl,sK24_skl))&circle(sK24_skl,sK25_skl,sK27_skl,sK31_skl))&midp(sK28_skl,sK27_skl,sK20_skl))&circle(sK28_skl,sK27_skl,sK32_skl,sK33_skl))&coll(sK21_skl,sK25_skl,sK20_skl))&circle(sK28_skl,sK27_skl,sK21_skl,sK34_skl))&coll(sK22_skl,sK26_skl,sK20_skl))&circle(sK28_skl,sK27_skl,sK22_skl,sK35_skl))&coll(sK23_skl,sK25_skl,sK26_skl))&coll(sK23_skl,sK20_skl,sK24_skl))&~eqangle(sK20_skl,sK21_skl,sK21_skl,sK23_skl,sK23_skl,sK21_skl,sK21_skl,sK22_skl))),
% 9.56/1.71 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,sK33_skl,sK34_skl,sK35_skl]),skolemize(A,sK20_skl),skolemize(B,sK21_skl),skolemize(C,sK22_skl),skolemize(E,sK23_skl),skolemize(N,sK24_skl),skolemize(P,sK25_skl),skolemize(Q,sK26_skl),skolemize(D,sK27_skl),skolemize(O,sK28_skl),skolemize(NWPNT1,sK29_skl),skolemize(NWPNT2,sK30_skl),skolemize(NWPNT3,sK31_skl),skolemize(NWPNT4,sK32_skl),skolemize(NWPNT5,sK33_skl),skolemize(NWPNT6,sK34_skl),skolemize(NWPNT7,sK35_skl)],[f370])).
% 9.56/1.71 fof(f378,plain,(
% 9.56/1.71 midp(sK28_skl,sK27_skl,sK20_skl)),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f371])).
% 9.56/1.71 fof(f386,plain,(
% 9.56/1.71 ~eqangle(sK20_skl,sK21_skl,sK21_skl,sK23_skl,sK23_skl,sK21_skl,sK21_skl,sK22_skl)),
% 9.56/1.71 inference(cnf_transformation,[status(thm)],[f371])).
% 9.56/1.71 fof(f393,plain,(
% 9.56/1.71 ![X0,X1,X2]: (coll(X0,X1,X2)|~para(X0,X2,X0,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f256,f107])).
% 9.56/1.71 fof(f396,plain,(
% 9.56/1.71 ~eqangle(sK21_skl,sK20_skl,sK21_skl,sK23_skl,sK23_skl,sK21_skl,sK21_skl,sK22_skl)),
% 9.56/1.71 inference(resolution,[status(thm)],[f386,f138])).
% 9.56/1.71 fof(f400,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5,X6,X7]: (eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|~eqangle(X3,X2,X0,X1,X6,X7,X4,X5))),
% 9.56/1.71 inference(resolution,[status(thm)],[f140,f138])).
% 9.56/1.71 fof(f401,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5,X6,X7]: (eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|~eqangle(X5,X4,X6,X7,X0,X1,X2,X3))),
% 9.56/1.71 inference(resolution,[status(thm)],[f142,f138])).
% 9.56/1.71 fof(f405,plain,(
% 9.56/1.71 ![X0,X1,X2]: (coll(X0,X1,X2)|~para(X0,X2,X1,X0))),
% 9.56/1.71 inference(resolution,[status(thm)],[f393,f105])).
% 9.56/1.71 fof(f412,plain,(
% 9.56/1.71 ![X0,X1,X2]: (coll(X0,X1,X2)|~para(X1,X0,X0,X2))),
% 9.56/1.71 inference(resolution,[status(thm)],[f405,f107])).
% 9.56/1.71 fof(f414,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5,X6,X7]: (eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|~eqangle(X1,X0,X4,X5,X2,X3,X6,X7))),
% 9.56/1.71 inference(resolution,[status(thm)],[f144,f138])).
% 9.56/1.71 fof(f418,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11]: (~eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|eqangle(X0,X1,X2,X3,X8,X9,X10,X11)|~eqangle(X5,X4,X6,X7,X8,X9,X10,X11))),
% 9.56/1.71 inference(resolution,[status(thm)],[f147,f138])).
% 9.56/1.71 fof(f433,plain,(
% 9.56/1.71 ![X0,X1,X2]: (coll(X0,X1,X2)|~para(X1,X0,X2,X0))),
% 9.56/1.71 inference(resolution,[status(thm)],[f412,f105])).
% 9.56/1.71 fof(f449,plain,(
% 9.56/1.71 ![X0,X1,X2]: (~coll(X0,X1,X2)|midp(X0,X1,X2)|~cong(X0,X2,X0,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f258,f151])).
% 9.56/1.71 fof(f477,plain,(
% 9.56/1.71 ![X0,X1,X2]: (~coll(X0,X1,X2)|midp(X0,X1,X2)|~cong(X0,X2,X1,X0))),
% 9.56/1.71 inference(resolution,[status(thm)],[f449,f149])).
% 9.56/1.71 fof(f499,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5,X6,X7]: (eqangle(X0,X1,X2,X3,X4,X5,X2,X3)|~para(X0,X1,X6,X7)|~para(X6,X7,X4,X5))),
% 9.56/1.71 inference(resolution,[status(thm)],[f189,f110])).
% 9.56/1.71 fof(f609,plain,(
% 9.56/1.71 ![X0,X1]: (~midp(sK28_skl,X0,X1)|para(X0,sK27_skl,X1,sK20_skl))),
% 9.56/1.71 inference(resolution,[status(thm)],[f249,f378])).
% 9.56/1.71 fof(f610,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|para(X1,X3,X2,X4)|~midp(X0,X4,X3))),
% 9.56/1.71 inference(resolution,[status(thm)],[f249,f122])).
% 9.56/1.71 fof(f612,plain,(
% 9.56/1.71 ![X0,X1]: (para(X0,sK27_skl,X1,sK20_skl)|~midp(sK28_skl,X1,X0))),
% 9.56/1.71 inference(resolution,[status(thm)],[f609,f122])).
% 9.56/1.71 fof(f629,plain,(
% 9.56/1.71 para(sK20_skl,sK27_skl,sK27_skl,sK20_skl)),
% 9.56/1.71 inference(resolution,[status(thm)],[f612,f378])).
% 9.56/1.71 fof(f631,plain,(
% 9.56/1.71 ![X0,X1]: (eqangle(sK20_skl,sK27_skl,X0,X1,sK27_skl,sK20_skl,X0,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f629,f189])).
% 9.56/1.71 fof(f673,plain,(
% 9.56/1.71 ![X0,X1]: (eqangle(X0,X1,sK27_skl,sK20_skl,X0,X1,sK27_skl,sK20_skl))),
% 9.56/1.71 inference(resolution,[status(thm)],[f631,f400])).
% 9.56/1.71 fof(f913,plain,(
% 9.56/1.71 ![X0,X1]: (para(X0,X1,X0,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f673,f186])).
% 9.56/1.71 fof(f921,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (eqangle(X0,X1,X2,X3,X0,X1,X2,X3))),
% 9.56/1.71 inference(resolution,[status(thm)],[f913,f189])).
% 9.56/1.71 fof(f922,plain,(
% 9.56/1.71 ![X0,X1]: (coll(X0,X1,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f913,f433])).
% 9.56/1.71 fof(f942,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (eqangle(X0,X1,X1,X0,X2,X3,X2,X3))),
% 9.56/1.71 inference(resolution,[status(thm)],[f921,f414])).
% 9.56/1.71 fof(f973,plain,(
% 9.56/1.71 ![X0,X1,X2]: (~cyclic(X0,X0,X0,X1)|~cyclic(X0,X0,X0,X1)|~cyclic(X0,X0,X0,X2)|cong(X0,X0,X1,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f942,f198])).
% 9.56/1.71 fof(f974,plain,(
% 9.56/1.71 ![X0,X1]: (~coll(X0,X1,X0)|cyclic(X0,X0,X0,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f942,f195])).
% 9.56/1.71 fof(f975,plain,(
% 9.56/1.71 ![X0,X1]: (coll(X0,X1,X0)|cyclic(X0,X0,X0,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f942,f193])).
% 9.56/1.71 fof(f983,plain,(
% 9.56/1.71 ![X0,X1,X2]: (~cyclic(X0,X0,X0,X1)|~cyclic(X0,X0,X0,X2)|cong(X0,X0,X1,X1))),
% 9.56/1.71 inference(duplicate_literals_removal,[status(thm)],[f973])).
% 9.56/1.71 fof(f984,plain,(
% 9.56/1.71 ![X0,X1]: (~cyclic(X0,X0,X0,X1)|cong(X0,X0,X1,X1))),
% 9.56/1.71 inference(backward_subsumption_resolution,[status(thm)],[f983,f985])).
% 9.56/1.71 fof(f985,plain,(
% 9.56/1.71 ![X0,X1]: (cyclic(X0,X0,X0,X1))),
% 9.56/1.71 inference(forward_subsumption_resolution,[status(thm)],[f975,f974])).
% 9.56/1.71 fof(f989,plain,(
% 9.56/1.71 ![X0,X1]: (cong(X0,X0,X1,X1))),
% 9.56/1.71 inference(forward_subsumption_resolution,[status(thm)],[f984,f985])).
% 9.56/1.71 fof(f1025,plain,(
% 9.56/1.71 ![X0]: (~coll(X0,X0,X0)|midp(X0,X0,X0))),
% 9.56/1.71 inference(resolution,[status(thm)],[f989,f477])).
% 9.56/1.71 fof(f1035,plain,(
% 9.56/1.71 ![X0]: (midp(X0,X0,X0))),
% 9.56/1.71 inference(forward_subsumption_resolution,[status(thm)],[f1025,f922])).
% 9.56/1.71 fof(f1040,plain,(
% 9.56/1.71 ![X0,X1,X2]: (~para(X0,X1,X0,X2)|~para(X0,X2,X0,X1)|midp(X0,X1,X2))),
% 9.56/1.71 inference(resolution,[status(thm)],[f1035,f252])).
% 9.56/1.71 fof(f1051,plain,(
% 9.56/1.71 ![X0,X1,X2]: (~para(X0,X1,X0,X2)|midp(X0,X2,X1))),
% 9.56/1.71 inference(forward_subsumption_resolution,[status(thm)],[f1040,f107])).
% 9.56/1.71 fof(f1289,plain,(
% 9.56/1.71 ![X0,X1]: (midp(X0,X1,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f1051,f913])).
% 9.56/1.71 fof(f1318,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (~para(X0,X1,X0,X2)|~para(X0,X2,X0,X1)|midp(X3,X1,X2))),
% 9.56/1.71 inference(resolution,[status(thm)],[f1289,f252])).
% 9.56/1.71 fof(f1321,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (~midp(X0,X1,X2)|para(X0,X3,X2,X1))),
% 9.56/1.71 inference(resolution,[status(thm)],[f1289,f201])).
% 9.56/1.71 fof(f1329,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (~para(X0,X1,X0,X2)|midp(X3,X2,X1))),
% 9.56/1.71 inference(forward_subsumption_resolution,[status(thm)],[f1318,f107])).
% 9.56/1.71 fof(f2177,plain,(
% 9.56/1.71 ![X0,X1,X2]: (para(X0,X1,X2,X2))),
% 9.56/1.71 inference(resolution,[status(thm)],[f1321,f1289])).
% 9.56/1.71 fof(f2191,plain,(
% 9.56/1.71 ![X0,X1,X2]: (midp(X0,X1,X2))),
% 9.56/1.71 inference(resolution,[status(thm)],[f2177,f1329])).
% 9.56/1.71 fof(f2203,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4]: (para(X0,X1,X2,X3)|~midp(X4,X3,X1))),
% 9.56/1.71 inference(backward_subsumption_resolution,[status(thm)],[f610,f2191])).
% 9.56/1.71 fof(f2284,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5,X6,X7]: (eqangle(X0,X1,X2,X3,X4,X5,X2,X3)|~para(X6,X7,X4,X5))),
% 9.56/1.71 inference(backward_subsumption_resolution,[status(thm)],[f499,f2342])).
% 9.56/1.71 fof(f2342,plain,(
% 9.56/1.71 ![X0,X1,X2,X3]: (para(X0,X1,X2,X3))),
% 9.56/1.71 inference(forward_subsumption_resolution,[status(thm)],[f2203,f2191])).
% 9.56/1.71 fof(f2423,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5]: (eqangle(X0,X1,X2,X3,X4,X5,X2,X3))),
% 9.56/1.71 inference(forward_subsumption_resolution,[status(thm)],[f2284,f2342])).
% 9.56/1.71 fof(f2529,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9]: (~eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|eqangle(X0,X1,X2,X3,X8,X9,X6,X7))),
% 9.56/1.71 inference(resolution,[status(thm)],[f2423,f418])).
% 9.56/1.71 fof(f2532,plain,(
% 9.56/1.71 ![X0,X1,X2,X3,X4,X5]: (eqangle(X0,X1,X2,X3,X0,X1,X4,X5))),
% 9.56/1.71 inference(resolution,[status(thm)],[f2423,f400])).
% 5.63/1.72 fof(f2646,plain,(
% 5.63/1.72 ![X0,X1,X2,X3,X4,X5]: (eqangle(X0,X1,X2,X3,X1,X0,X4,X5))),
% 5.63/1.72 inference(resolution,[status(thm)],[f2532,f401])).
% 5.63/1.72 fof(f2728,plain,(
% 5.63/1.72 ![X0,X1]: (~eqangle(sK21_skl,sK20_skl,sK21_skl,sK23_skl,X0,X1,sK21_skl,sK22_skl))),
% 5.63/1.72 inference(resolution,[status(thm)],[f2529,f396])).
% 5.63/1.72 fof(f2905,plain,(
% 5.63/1.72 $false),
% 5.63/1.72 inference(resolution,[status(thm)],[f2728,f2646])).
% 5.63/1.72 % SZS output end CNFRefutation for theBenchmark.p
% 5.63/1.73 % Elapsed time: 1.351341 seconds
% 5.63/1.73 % CPU time: 10.481418 seconds
% 5.63/1.73 % Total memory used: 162.599 MB
% 5.63/1.73 % Net memory used: 152.943 MB
%------------------------------------------------------------------------------