%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO584+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 : n017.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 5.54s 1.28s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO584+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
% 0.09/0.36 % Computer : n017.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 17:33:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 5.54/1.28 % Refutation found
% 5.54/1.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.54/1.28 % SZS output start CNFRefutation for theBenchmark
% 5.54/1.28 fof(f1,axiom,(
% 5.54/1.28 (! [A,B,C] :( coll(A,B,C)=> coll(A,C,B) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f2,axiom,(
% 5.54/1.28 (! [A,B,C] :( coll(A,B,C)=> coll(B,A,C) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f3,axiom,(
% 5.54/1.28 (! [A,B,C,D] :( ( coll(A,B,C)& coll(A,B,D) )=> coll(C,D,A) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f8,axiom,(
% 5.54/1.28 (! [A,B,C,D] :( perp(A,B,C,D)=> perp(C,D,A,B) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f9,axiom,(
% 5.54/1.28 (! [A,B,C,D,E,F] :( ( perp(A,B,C,D)& perp(C,D,E,F) )=> para(A,B,E,F) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f17,axiom,(
% 5.54/1.28 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f19,axiom,(
% 5.54/1.28 (! [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) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f21,axiom,(
% 5.54/1.28 (! [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) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f22,axiom,(
% 5.54/1.28 (! [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) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f39,axiom,(
% 5.54/1.28 (! [A,B,C,D,P,Q] :( eqangle(A,B,P,Q,C,D,P,Q)=> para(A,B,C,D) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f40,axiom,(
% 5.54/1.28 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f41,axiom,(
% 5.54/1.28 (! [A,B,P,Q] :( cyclic(A,B,P,Q)=> eqangle(P,A,P,B,Q,A,Q,B) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f43,axiom,(
% 5.54/1.28 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f44,axiom,(
% 5.54/1.28 (! [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) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f53,axiom,(
% 5.54/1.28 (! [A,B,C,M] :( ( perp(A,B,B,C)& midp(M,A,C) )=> cong(A,M,B,M) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f57,axiom,(
% 5.54/1.28 (! [A,B,P,Q] :( ( cong(A,P,B,P)& cong(A,Q,B,Q) )=> perp(A,B,P,Q) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f58,axiom,(
% 5.54/1.28 (! [A,B,P,Q] :( ( cong(A,P,B,P)& cong(A,Q,B,Q)& cyclic(A,B,P,Q) )=> perp(P,A,A,Q) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f67,axiom,(
% 5.54/1.28 (! [A,B,C] :( para(A,B,A,C)=> coll(A,B,C) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f68,axiom,(
% 5.54/1.28 (! [A,B,C] :( ( cong(A,B,A,C)& coll(A,B,C) )=> midp(A,B,C) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f95,conjecture,(
% 5.54/1.28 (! [A,B,C,O,D,E,Q,P,S,R,NWPNT1,NWPNT2] :( ( circle(O,A,B,C)& circle(O,A,D,NWPNT1)& circle(O,A,E,NWPNT2)& perp(Q,E,B,C)& coll(Q,B,C)& perp(P,E,A,B)& coll(P,A,B)& perp(S,E,A,D)& coll(S,A,D)& perp(R,E,C,D)& coll(R,C,D) )=> eqangle(E,P,P,S,E,Q,Q,R) ) )),
% 5.54/1.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.54/1.28 fof(f96,negated_conjecture,(
% 5.54/1.28 ~((! [A,B,C,O,D,E,Q,P,S,R,NWPNT1,NWPNT2] :( ( circle(O,A,B,C)& circle(O,A,D,NWPNT1)& circle(O,A,E,NWPNT2)& perp(Q,E,B,C)& coll(Q,B,C)& perp(P,E,A,B)& coll(P,A,B)& perp(S,E,A,D)& coll(S,A,D)& perp(R,E,C,D)& coll(R,C,D) )=> eqangle(E,P,P,S,E,Q,Q,R) ) ))),
% 5.54/1.28 inference(negated_conjecture,[status(cth)],[f95])).
% 5.54/1.28 fof(f97,plain,(
% 5.54/1.28 ![A,B,C]: (~coll(A,B,C)|coll(A,C,B))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 5.54/1.28 fof(f98,plain,(
% 5.54/1.28 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X0,X2,X1))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f97])).
% 5.54/1.28 fof(f99,plain,(
% 5.54/1.28 ![A,B,C]: (~coll(A,B,C)|coll(B,A,C))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 5.54/1.28 fof(f100,plain,(
% 5.54/1.28 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X1,X0,X2))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f99])).
% 5.54/1.28 fof(f101,plain,(
% 5.54/1.28 ![A,B,C,D]: ((~coll(A,B,C)|~coll(A,B,D))|coll(C,D,A))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 5.54/1.28 fof(f102,plain,(
% 5.54/1.28 ![A,C,D]: ((![B]: (~coll(A,B,C)|~coll(A,B,D)))|coll(C,D,A))),
% 5.54/1.28 inference(miniscoping,[status(thm)],[f101])).
% 5.54/1.28 fof(f103,plain,(
% 5.54/1.28 ![X0,X1,X2,X3]: (~coll(X0,X1,X2)|~coll(X0,X1,X3)|coll(X2,X3,X0))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f102])).
% 5.54/1.28 fof(f113,plain,(
% 5.54/1.28 ![A,B,C,D]: (~perp(A,B,C,D)|perp(C,D,A,B))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 5.54/1.28 fof(f114,plain,(
% 5.54/1.28 ![X0,X1,X2,X3]: (~perp(X0,X1,X2,X3)|perp(X2,X3,X0,X1))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f113])).
% 5.54/1.28 fof(f115,plain,(
% 5.54/1.28 ![A,B,C,D,E,F]: ((~perp(A,B,C,D)|~perp(C,D,E,F))|para(A,B,E,F))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 5.54/1.28 fof(f116,plain,(
% 5.54/1.28 ![A,B,E,F]: ((![C,D]: (~perp(A,B,C,D)|~perp(C,D,E,F)))|para(A,B,E,F))),
% 5.54/1.28 inference(miniscoping,[status(thm)],[f115])).
% 5.54/1.28 fof(f117,plain,(
% 5.54/1.28 ![X0,X1,X2,X3,X4,X5]: (~perp(X0,X1,X2,X3)|~perp(X2,X3,X4,X5)|para(X0,X1,X4,X5))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f116])).
% 5.54/1.28 fof(f134,plain,(
% 5.54/1.28 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 5.54/1.28 fof(f135,plain,(
% 5.54/1.28 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 5.54/1.28 inference(miniscoping,[status(thm)],[f134])).
% 5.54/1.28 fof(f136,plain,(
% 5.54/1.28 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f135])).
% 5.54/1.28 fof(f139,plain,(
% 5.54/1.28 ![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))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 5.54/1.28 fof(f140,plain,(
% 5.54/1.28 ![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))),
% 5.54/1.28 inference(cnf_transformation,[status(thm)],[f139])).
% 5.54/1.28 fof(f143,plain,(
% 5.54/1.28 ![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))),
% 5.54/1.28 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 5.54/1.29 fof(f144,plain,(
% 5.54/1.29 ![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))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f143])).
% 5.54/1.29 fof(f145,plain,(
% 5.54/1.29 ![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))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 5.54/1.29 fof(f146,plain,(
% 5.54/1.29 ![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))),
% 5.54/1.29 inference(miniscoping,[status(thm)],[f145])).
% 5.54/1.29 fof(f147,plain,(
% 5.54/1.29 ![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))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f146])).
% 5.54/1.29 fof(f184,plain,(
% 5.54/1.29 ![A,B,C,D,P,Q]: (~eqangle(A,B,P,Q,C,D,P,Q)|para(A,B,C,D))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f39])).
% 5.54/1.29 fof(f185,plain,(
% 5.54/1.29 ![A,B,C,D]: ((![P,Q]: ~eqangle(A,B,P,Q,C,D,P,Q))|para(A,B,C,D))),
% 5.54/1.29 inference(miniscoping,[status(thm)],[f184])).
% 5.54/1.29 fof(f186,plain,(
% 5.54/1.29 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X2,X3,X4,X5,X2,X3)|para(X0,X1,X4,X5))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f185])).
% 5.54/1.29 fof(f187,plain,(
% 5.54/1.29 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 5.54/1.29 fof(f188,plain,(
% 5.54/1.29 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 5.54/1.29 inference(miniscoping,[status(thm)],[f187])).
% 5.54/1.29 fof(f189,plain,(
% 5.54/1.29 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f188])).
% 5.54/1.29 fof(f190,plain,(
% 5.54/1.29 ![A,B,P,Q]: (~cyclic(A,B,P,Q)|eqangle(P,A,P,B,Q,A,Q,B))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 5.54/1.29 fof(f191,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|eqangle(X2,X0,X2,X1,X3,X0,X3,X1))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f190])).
% 5.54/1.29 fof(f194,plain,(
% 5.54/1.29 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 5.54/1.29 fof(f195,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f194])).
% 5.54/1.29 fof(f196,plain,(
% 5.54/1.29 ![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))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 5.54/1.29 fof(f197,plain,(
% 5.54/1.29 ![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))),
% 5.54/1.29 inference(miniscoping,[status(thm)],[f196])).
% 5.54/1.29 fof(f198,plain,(
% 5.54/1.29 ![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))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f197])).
% 5.54/1.29 fof(f220,plain,(
% 5.54/1.29 ![A,B,C,M]: ((~perp(A,B,B,C)|~midp(M,A,C))|cong(A,M,B,M))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f53])).
% 5.54/1.29 fof(f221,plain,(
% 5.54/1.29 ![A,B,M]: ((![C]: (~perp(A,B,B,C)|~midp(M,A,C)))|cong(A,M,B,M))),
% 5.54/1.29 inference(miniscoping,[status(thm)],[f220])).
% 5.54/1.29 fof(f222,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (~perp(X0,X1,X1,X2)|~midp(X3,X0,X2)|cong(X0,X3,X1,X3))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f221])).
% 5.54/1.29 fof(f231,plain,(
% 5.54/1.29 ![A,B,P,Q]: ((~cong(A,P,B,P)|~cong(A,Q,B,Q))|perp(A,B,P,Q))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f57])).
% 5.54/1.29 fof(f232,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|perp(X0,X2,X1,X3))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f231])).
% 5.54/1.29 fof(f233,plain,(
% 5.54/1.29 ![A,B,P,Q]: (((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q))|perp(P,A,A,Q))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 5.54/1.29 fof(f234,plain,(
% 5.54/1.29 ![A,P,Q]: ((![B]: ((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q)))|perp(P,A,A,Q))),
% 5.54/1.29 inference(miniscoping,[status(thm)],[f233])).
% 5.54/1.29 fof(f235,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|~cyclic(X0,X2,X1,X3)|perp(X1,X0,X0,X3))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f234])).
% 5.54/1.29 fof(f255,plain,(
% 5.54/1.29 ![A,B,C]: (~para(A,B,A,C)|coll(A,B,C))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f67])).
% 5.54/1.29 fof(f256,plain,(
% 5.54/1.29 ![X0,X1,X2]: (~para(X0,X1,X0,X2)|coll(X0,X1,X2))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f255])).
% 5.54/1.29 fof(f257,plain,(
% 5.54/1.29 ![A,B,C]: ((~cong(A,B,A,C)|~coll(A,B,C))|midp(A,B,C))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f68])).
% 5.54/1.29 fof(f258,plain,(
% 5.54/1.29 ![X0,X1,X2]: (~cong(X0,X1,X0,X2)|~coll(X0,X1,X2)|midp(X0,X1,X2))),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f257])).
% 5.54/1.29 fof(f369,plain,(
% 5.54/1.29 (?[A,B,C,O,D,E,Q,P,S,R,NWPNT1,NWPNT2]: (((((((((((circle(O,A,B,C)&circle(O,A,D,NWPNT1))&circle(O,A,E,NWPNT2))&perp(Q,E,B,C))&coll(Q,B,C))&perp(P,E,A,B))&coll(P,A,B))&perp(S,E,A,D))&coll(S,A,D))&perp(R,E,C,D))&coll(R,C,D))&~eqangle(E,P,P,S,E,Q,Q,R)))),
% 5.54/1.29 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 5.54/1.29 fof(f370,plain,(
% 5.54/1.29 ?[E,Q,P,S,R]: ((?[C,D]: (((?[A]: (((?[B]: (((((?[O]: ((circle(O,A,B,C)&(?[NWPNT1]: circle(O,A,D,NWPNT1)))&(?[NWPNT2]: circle(O,A,E,NWPNT2))))&perp(Q,E,B,C))&coll(Q,B,C))&perp(P,E,A,B))&coll(P,A,B)))&perp(S,E,A,D))&coll(S,A,D)))&perp(R,E,C,D))&coll(R,C,D)))&~eqangle(E,P,P,S,E,Q,Q,R))),
% 5.54/1.29 inference(miniscoping,[status(thm)],[f369])).
% 5.54/1.29 fof(f371,plain,(
% 5.54/1.29 (((((((((((circle(sK29_skl,sK27_skl,sK28_skl,sK25_skl)&circle(sK29_skl,sK27_skl,sK26_skl,sK30_skl))&circle(sK29_skl,sK27_skl,sK20_skl,sK31_skl))&perp(sK21_skl,sK20_skl,sK28_skl,sK25_skl))&coll(sK21_skl,sK28_skl,sK25_skl))&perp(sK22_skl,sK20_skl,sK27_skl,sK28_skl))&coll(sK22_skl,sK27_skl,sK28_skl))&perp(sK23_skl,sK20_skl,sK27_skl,sK26_skl))&coll(sK23_skl,sK27_skl,sK26_skl))&perp(sK24_skl,sK20_skl,sK25_skl,sK26_skl))&coll(sK24_skl,sK25_skl,sK26_skl))&~eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK20_skl,sK21_skl,sK21_skl,sK24_skl))),
% 5.54/1.29 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]),skolemize(E,sK20_skl),skolemize(Q,sK21_skl),skolemize(P,sK22_skl),skolemize(S,sK23_skl),skolemize(R,sK24_skl),skolemize(C,sK25_skl),skolemize(D,sK26_skl),skolemize(A,sK27_skl),skolemize(B,sK28_skl),skolemize(O,sK29_skl),skolemize(NWPNT1,sK30_skl),skolemize(NWPNT2,sK31_skl)],[f370])).
% 5.54/1.29 fof(f375,plain,(
% 5.54/1.29 perp(sK21_skl,sK20_skl,sK28_skl,sK25_skl)),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f371])).
% 5.54/1.29 fof(f383,plain,(
% 5.54/1.29 ~eqangle(sK20_skl,sK22_skl,sK22_skl,sK23_skl,sK20_skl,sK21_skl,sK21_skl,sK24_skl)),
% 5.54/1.29 inference(cnf_transformation,[status(thm)],[f371])).
% 5.54/1.29 fof(f405,plain,(
% 5.54/1.29 ![X0,X1]: (~perp(sK28_skl,sK25_skl,X0,X1)|para(sK21_skl,sK20_skl,X0,X1))),
% 5.54/1.29 inference(resolution,[status(thm)],[f375,f117])).
% 5.54/1.29 fof(f406,plain,(
% 5.54/1.29 perp(sK28_skl,sK25_skl,sK21_skl,sK20_skl)),
% 5.54/1.29 inference(resolution,[status(thm)],[f375,f114])).
% 5.54/1.29 fof(f511,plain,(
% 5.54/1.29 para(sK21_skl,sK20_skl,sK21_skl,sK20_skl)),
% 5.54/1.29 inference(resolution,[status(thm)],[f406,f405])).
% 5.54/1.29 fof(f685,plain,(
% 5.54/1.29 ![X0,X1]: (eqangle(sK21_skl,sK20_skl,X0,X1,sK21_skl,sK20_skl,X0,X1))),
% 5.54/1.29 inference(resolution,[status(thm)],[f511,f189])).
% 5.54/1.29 fof(f1869,plain,(
% 5.54/1.29 ![X0,X1]: (eqangle(sK21_skl,sK20_skl,sK21_skl,sK20_skl,X0,X1,X0,X1))),
% 5.54/1.29 inference(resolution,[status(thm)],[f685,f144])).
% 5.54/1.29 fof(f1871,plain,(
% 5.54/1.29 ![X0,X1]: (eqangle(X0,X1,sK21_skl,sK20_skl,X0,X1,sK21_skl,sK20_skl))),
% 5.54/1.29 inference(resolution,[status(thm)],[f685,f140])).
% 5.54/1.29 fof(f3505,plain,(
% 5.54/1.29 ![X0,X1]: (para(X0,X1,X0,X1))),
% 5.54/1.29 inference(resolution,[status(thm)],[f1871,f186])).
% 5.54/1.29 fof(f3558,plain,(
% 5.54/1.29 ![X0,X1]: (coll(X0,X1,X1))),
% 5.54/1.29 inference(resolution,[status(thm)],[f3505,f256])).
% 5.54/1.29 fof(f3631,plain,(
% 5.54/1.29 ![X0,X1]: (coll(X0,X1,X0))),
% 5.54/1.29 inference(resolution,[status(thm)],[f3558,f100])).
% 5.54/1.29 fof(f3700,plain,(
% 5.54/1.29 ![X0,X1]: (coll(X0,X0,X1))),
% 5.54/1.29 inference(resolution,[status(thm)],[f3631,f98])).
% 5.54/1.29 fof(f3735,plain,(
% 5.54/1.29 ![X0,X1,X2]: (~coll(X0,X0,X1)|coll(X2,X1,X0))),
% 5.54/1.29 inference(resolution,[status(thm)],[f3700,f103])).
% 5.54/1.29 fof(f3738,plain,(
% 5.54/1.29 ![X0,X1,X2]: (coll(X0,X1,X2))),
% 5.54/1.29 inference(forward_subsumption_resolution,[status(thm)],[f3735,f3700])).
% 5.54/1.29 fof(f3745,plain,(
% 5.54/1.29 ![X0,X1,X2]: (~cong(X0,X1,X0,X2)|midp(X0,X1,X2))),
% 5.54/1.29 inference(backward_subsumption_resolution,[status(thm)],[f258,f3738])).
% 5.54/1.29 fof(f3748,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|cyclic(X1,X2,X0,X3))),
% 5.54/1.29 inference(backward_subsumption_resolution,[status(thm)],[f195,f3738])).
% 5.54/1.29 fof(f3773,plain,(
% 5.54/1.29 ![X0]: (cyclic(sK20_skl,sK20_skl,sK21_skl,X0))),
% 5.54/1.29 inference(resolution,[status(thm)],[f3748,f1869])).
% 5.54/1.29 fof(f5456,plain,(
% 5.54/1.29 ![X0,X1]: (~cyclic(sK20_skl,sK20_skl,sK21_skl,X0)|cyclic(sK20_skl,sK21_skl,X1,X0))),
% 5.54/1.29 inference(resolution,[status(thm)],[f3773,f136])).
% 5.54/1.29 fof(f5470,plain,(
% 5.54/1.29 ![X0,X1]: (cyclic(sK20_skl,sK21_skl,X0,X1))),
% 5.54/1.29 inference(forward_subsumption_resolution,[status(thm)],[f5456,f3773])).
% 5.54/1.29 fof(f5474,plain,(
% 5.54/1.29 ![X0,X1,X2]: (~cyclic(sK20_skl,sK21_skl,X0,X1)|cyclic(sK21_skl,X0,X2,X1))),
% 5.54/1.29 inference(resolution,[status(thm)],[f5470,f136])).
% 5.54/1.29 fof(f5485,plain,(
% 5.54/1.29 ![X0,X1,X2]: (cyclic(sK21_skl,X0,X1,X2))),
% 5.54/1.29 inference(forward_subsumption_resolution,[status(thm)],[f5474,f5470])).
% 5.54/1.29 fof(f5513,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (~cyclic(sK21_skl,X0,X1,X2)|cyclic(X0,X1,X3,X2))),
% 5.54/1.29 inference(resolution,[status(thm)],[f5485,f136])).
% 5.54/1.29 fof(f5517,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3))),
% 5.54/1.29 inference(forward_subsumption_resolution,[status(thm)],[f5513,f5485])).
% 5.54/1.29 fof(f5519,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|perp(X1,X0,X0,X3))),
% 5.54/1.29 inference(backward_subsumption_resolution,[status(thm)],[f235,f5517])).
% 5.54/1.29 fof(f5520,plain,(
% 5.54/1.29 ![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))),
% 5.54/1.29 inference(backward_subsumption_resolution,[status(thm)],[f198,f5517])).
% 5.54/1.29 fof(f5529,plain,(
% 5.54/1.29 ![X0,X1,X2,X3]: (eqangle(X0,X1,X0,X2,X3,X1,X3,X2))),
% 5.54/1.29 inference(backward_subsumption_resolution,[status(thm)],[f191,f5517])).
% 5.54/1.29 fof(f5530,plain,(
% 5.54/1.29 ![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))),
% 5.54/1.29 inference(forward_subsumption_resolution,[status(thm)],[f5520,f5517])).
% 5.54/1.29 fof(f5545,plain,(
% 5.54/1.29 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X0,X2,X3,X4,X3,X5)|cong(X1,X2,X4,X5))),
% 5.54/1.29 inference(forward_subsumption_resolution,[status(thm)],[f5530,f5517])).
% 5.54/1.29 fof(f5631,plain,(
% 5.54/1.29 ![X0,X1]: (cong(X0,X1,X0,X1))),
% 5.54/1.29 inference(resolution,[status(thm)],[f5529,f5545])).
% 5.54/1.30 fof(f5648,plain,(
% 5.54/1.30 ![X0,X1,X2]: (~cong(X0,X1,X0,X1)|perp(X2,X0,X0,X1))),
% 5.54/1.30 inference(resolution,[status(thm)],[f5631,f5519])).
% 5.54/1.30 fof(f5651,plain,(
% 5.54/1.30 ![X0,X1]: (midp(X0,X1,X1))),
% 5.54/1.30 inference(resolution,[status(thm)],[f5631,f3745])).
% 5.54/1.30 fof(f5660,plain,(
% 5.54/1.30 ![X0,X1,X2]: (perp(X0,X1,X1,X2))),
% 5.54/1.30 inference(forward_subsumption_resolution,[status(thm)],[f5648,f5631])).
% 5.54/1.30 fof(f5719,plain,(
% 5.54/1.30 ![X0,X1,X2,X3]: (~midp(X0,X1,X2)|cong(X1,X0,X3,X0))),
% 5.54/1.30 inference(backward_subsumption_resolution,[status(thm)],[f222,f5660])).
% 5.54/1.30 fof(f5883,plain,(
% 5.54/1.30 ![X0,X1,X2]: (cong(X0,X1,X2,X1))),
% 5.54/1.30 inference(resolution,[status(thm)],[f5719,f5651])).
% 5.54/1.30 fof(f6316,plain,(
% 5.54/1.30 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|perp(X0,X2,X1,X3))),
% 5.54/1.30 inference(backward_subsumption_resolution,[status(thm)],[f232,f5883])).
% 5.54/1.30 fof(f6335,plain,(
% 5.54/1.30 ![X0,X1,X2,X3]: (perp(X0,X1,X2,X3))),
% 5.54/1.30 inference(forward_subsumption_resolution,[status(thm)],[f6316,f5883])).
% 5.54/1.30 fof(f6336,plain,(
% 5.54/1.30 ![X0,X1,X2,X3,X4,X5]: (~perp(X0,X1,X2,X3)|para(X0,X1,X4,X5))),
% 5.54/1.30 inference(backward_subsumption_resolution,[status(thm)],[f117,f6335])).
% 5.54/1.30 fof(f6401,plain,(
% 5.54/1.30 ![X0,X1,X2,X3]: (para(X0,X1,X2,X3))),
% 5.54/1.30 inference(forward_subsumption_resolution,[status(thm)],[f6336,f6335])).
% 5.54/1.30 fof(f6442,plain,(
% 5.54/1.30 ![X0,X1,X2,X3,X4,X5]: (eqangle(X0,X1,X2,X3,X4,X5,X2,X3))),
% 5.54/1.30 inference(backward_subsumption_resolution,[status(thm)],[f189,f6401])).
% 5.54/1.30 fof(f6538,plain,(
% 5.54/1.30 ![X0,X1,X2,X3,X4,X5,X6,X7,X8,X9]: (~eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|eqangle(X8,X9,X2,X3,X4,X5,X6,X7))),
% 5.54/1.30 inference(resolution,[status(thm)],[f6442,f147])).
% 5.54/1.30 fof(f6541,plain,(
% 5.54/1.30 ![X0,X1,X2,X3,X4,X5]: (eqangle(X0,X1,X2,X3,X0,X1,X4,X5))),
% 5.54/1.30 inference(resolution,[status(thm)],[f6442,f140])).
% 5.54/1.30 fof(f6721,plain,(
% 5.54/1.30 ![X0,X1,X2,X3,X4,X5,X6,X7]: (eqangle(X0,X1,X2,X3,X4,X5,X6,X7))),
% 5.54/1.30 inference(resolution,[status(thm)],[f6541,f6538])).
% 5.54/1.30 fof(f7402,plain,(
% 5.54/1.30 $false),
% 5.54/1.30 inference(backward_subsumption_resolution,[status(thm)],[f383,f6721])).
% 5.54/1.30 % SZS output end CNFRefutation for theBenchmark.p
% 0.35/1.32 % Elapsed time: 0.935051 seconds
% 0.35/1.32 % CPU time: 7.113070 seconds
% 0.35/1.32 % Total memory used: 136.737 MB
% 0.35/1.32 % Net memory used: 130.184 MB
%------------------------------------------------------------------------------