%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO616+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 : n014.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 12:26:43 PM UTC 2026
% Result : Theorem 3.30s 0.84s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO616+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 : n014.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 17:53:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 3.30/0.84 % Refutation found
% 3.30/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.30/0.84 % SZS output start CNFRefutation for theBenchmark
% 3.30/0.84 fof(f1,axiom,(
% 3.30/0.84 (! [A,B,C] :( coll(A,B,C)=> coll(A,C,B) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f2,axiom,(
% 3.30/0.84 (! [A,B,C] :( coll(A,B,C)=> coll(B,A,C) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f3,axiom,(
% 3.30/0.84 (! [A,B,C,D] :( ( coll(A,B,C)& coll(A,B,D) )=> coll(C,D,A) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f7,axiom,(
% 3.30/0.84 (! [A,B,C,D] :( perp(A,B,C,D)=> perp(A,B,D,C) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f8,axiom,(
% 3.30/0.84 (! [A,B,C,D] :( perp(A,B,C,D)=> perp(C,D,A,B) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f11,axiom,(
% 3.30/0.84 (! [A,B,M] :( midp(M,B,A)=> midp(M,A,B) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f12,axiom,(
% 3.30/0.84 (! [A,B,C,O] :( ( cong(O,A,O,B)& cong(O,A,O,C) )=> circle(O,A,B,C) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f14,axiom,(
% 3.30/0.84 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(A,B,D,C) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f15,axiom,(
% 3.30/0.84 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(A,C,B,D) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f17,axiom,(
% 3.30/0.84 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f23,axiom,(
% 3.30/0.84 (! [A,B,C,D] :( cong(A,B,C,D)=> cong(A,B,D,C) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f24,axiom,(
% 3.30/0.84 (! [A,B,C,D] :( cong(A,B,C,D)=> cong(C,D,A,B) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f40,axiom,(
% 3.30/0.84 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f43,axiom,(
% 3.30/0.84 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f44,axiom,(
% 3.30/0.84 (! [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) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f53,axiom,(
% 3.30/0.84 (! [A,B,C,M] :( ( perp(A,B,B,C)& midp(M,A,C) )=> cong(A,M,B,M) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f54,axiom,(
% 3.30/0.84 (! [A,B,C,O] :( ( circle(O,A,B,C)& coll(O,A,C) )=> perp(A,B,B,C) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f58,axiom,(
% 3.30/0.84 (! [A,B,P,Q] :( ( cong(A,P,B,P)& cong(A,Q,B,Q)& cyclic(A,B,P,Q) )=> perp(P,A,A,Q) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f64,axiom,(
% 3.30/0.84 (! [A,B,C,D,M] :( ( midp(M,A,B)& midp(M,C,D) )=> para(A,C,B,D) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f68,axiom,(
% 3.30/0.84 (! [A,B,C] :( ( cong(A,B,A,C)& coll(A,B,C) )=> midp(A,B,C) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f69,axiom,(
% 3.30/0.84 (! [A,B,C] :( midp(A,B,C)=> cong(A,B,A,C) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f70,axiom,(
% 3.30/0.84 (! [A,B,C] :( midp(A,B,C)=> coll(A,B,C) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f83,axiom,(
% 3.30/0.84 (! [A,B,C,D,M,N,Q] :(? [P] :( ( midp(M,A,B)& midp(N,C,D)& coll(C,A,B)& coll(D,A,B) )=> midp(P,A,Q) ) ))),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f95,conjecture,(
% 3.30/0.84 (! [A,B,C,O,G,E,K,H,N,NWPNT1] :( ( circle(O,A,B,C)& midp(G,C,B)& coll(E,O,G)& circle(O,A,E,NWPNT1)& perp(K,E,A,B)& coll(K,A,B)& perp(H,A,O,G)& coll(H,O,G)& circle(N,K,G,H) )=> perp(E,K,K,N) ) )),
% 3.30/0.84 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.30/0.84 fof(f96,negated_conjecture,(
% 3.30/0.84 ~((! [A,B,C,O,G,E,K,H,N,NWPNT1] :( ( circle(O,A,B,C)& midp(G,C,B)& coll(E,O,G)& circle(O,A,E,NWPNT1)& perp(K,E,A,B)& coll(K,A,B)& perp(H,A,O,G)& coll(H,O,G)& circle(N,K,G,H) )=> perp(E,K,K,N) ) ))),
% 3.30/0.84 inference(negated_conjecture,[status(cth)],[f95])).
% 3.30/0.84 fof(f97,plain,(
% 3.30/0.84 ![A,B,C]: (~coll(A,B,C)|coll(A,C,B))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 3.30/0.84 fof(f98,plain,(
% 3.30/0.84 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X0,X2,X1))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f97])).
% 3.30/0.84 fof(f99,plain,(
% 3.30/0.84 ![A,B,C]: (~coll(A,B,C)|coll(B,A,C))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 3.30/0.84 fof(f100,plain,(
% 3.30/0.84 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X1,X0,X2))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f99])).
% 3.30/0.84 fof(f101,plain,(
% 3.30/0.84 ![A,B,C,D]: ((~coll(A,B,C)|~coll(A,B,D))|coll(C,D,A))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 3.30/0.84 fof(f102,plain,(
% 3.30/0.84 ![A,C,D]: ((![B]: (~coll(A,B,C)|~coll(A,B,D)))|coll(C,D,A))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f101])).
% 3.30/0.84 fof(f103,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~coll(X0,X1,X2)|~coll(X0,X1,X3)|coll(X2,X3,X0))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f102])).
% 3.30/0.84 fof(f111,plain,(
% 3.30/0.84 ![A,B,C,D]: (~perp(A,B,C,D)|perp(A,B,D,C))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 3.30/0.84 fof(f112,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~perp(X0,X1,X2,X3)|perp(X0,X1,X3,X2))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f111])).
% 3.30/0.84 fof(f113,plain,(
% 3.30/0.84 ![A,B,C,D]: (~perp(A,B,C,D)|perp(C,D,A,B))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 3.30/0.84 fof(f114,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~perp(X0,X1,X2,X3)|perp(X2,X3,X0,X1))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f113])).
% 3.30/0.84 fof(f121,plain,(
% 3.30/0.84 ![A,B,M]: (~midp(M,B,A)|midp(M,A,B))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 3.30/0.84 fof(f122,plain,(
% 3.30/0.84 ![X0,X1,X2]: (~midp(X0,X1,X2)|midp(X0,X2,X1))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f121])).
% 3.30/0.84 fof(f123,plain,(
% 3.30/0.84 ![A,B,C,O]: ((~cong(O,A,O,B)|~cong(O,A,O,C))|circle(O,A,B,C))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 3.30/0.84 fof(f124,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~cong(X0,X1,X0,X2)|~cong(X0,X1,X0,X3)|circle(X0,X1,X2,X3))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f123])).
% 3.30/0.84 fof(f128,plain,(
% 3.30/0.84 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(A,B,D,C))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 3.30/0.84 fof(f129,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X0,X1,X3,X2))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f128])).
% 3.30/0.84 fof(f130,plain,(
% 3.30/0.84 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(A,C,B,D))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 3.30/0.84 fof(f131,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X0,X2,X1,X3))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f130])).
% 3.30/0.84 fof(f134,plain,(
% 3.30/0.84 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 3.30/0.84 fof(f135,plain,(
% 3.30/0.84 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f134])).
% 3.30/0.84 fof(f136,plain,(
% 3.30/0.84 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f135])).
% 3.30/0.84 fof(f148,plain,(
% 3.30/0.84 ![A,B,C,D]: (~cong(A,B,C,D)|cong(A,B,D,C))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 3.30/0.84 fof(f149,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X3)|cong(X0,X1,X3,X2))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f148])).
% 3.30/0.84 fof(f150,plain,(
% 3.30/0.84 ![A,B,C,D]: (~cong(A,B,C,D)|cong(C,D,A,B))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 3.30/0.84 fof(f151,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X3)|cong(X2,X3,X0,X1))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f150])).
% 3.30/0.84 fof(f187,plain,(
% 3.30/0.84 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 3.30/0.84 fof(f188,plain,(
% 3.30/0.84 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f187])).
% 3.30/0.84 fof(f189,plain,(
% 3.30/0.84 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f188])).
% 3.30/0.84 fof(f194,plain,(
% 3.30/0.84 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 3.30/0.84 fof(f195,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f194])).
% 3.30/0.84 fof(f196,plain,(
% 3.30/0.84 ![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))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 3.30/0.84 fof(f197,plain,(
% 3.30/0.84 ![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))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f196])).
% 3.30/0.84 fof(f198,plain,(
% 3.30/0.84 ![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))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f197])).
% 3.30/0.84 fof(f220,plain,(
% 3.30/0.84 ![A,B,C,M]: ((~perp(A,B,B,C)|~midp(M,A,C))|cong(A,M,B,M))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f53])).
% 3.30/0.84 fof(f221,plain,(
% 3.30/0.84 ![A,B,M]: ((![C]: (~perp(A,B,B,C)|~midp(M,A,C)))|cong(A,M,B,M))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f220])).
% 3.30/0.84 fof(f222,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~perp(X0,X1,X1,X2)|~midp(X3,X0,X2)|cong(X0,X3,X1,X3))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f221])).
% 3.30/0.84 fof(f223,plain,(
% 3.30/0.84 ![A,B,C,O]: ((~circle(O,A,B,C)|~coll(O,A,C))|perp(A,B,B,C))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f54])).
% 3.30/0.84 fof(f224,plain,(
% 3.30/0.84 ![A,B,C]: ((![O]: (~circle(O,A,B,C)|~coll(O,A,C)))|perp(A,B,B,C))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f223])).
% 3.30/0.84 fof(f225,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~circle(X0,X1,X2,X3)|~coll(X0,X1,X3)|perp(X1,X2,X2,X3))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f224])).
% 3.30/0.84 fof(f233,plain,(
% 3.30/0.84 ![A,B,P,Q]: (((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q))|perp(P,A,A,Q))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 3.30/0.84 fof(f234,plain,(
% 3.30/0.84 ![A,P,Q]: ((![B]: ((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q)))|perp(P,A,A,Q))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f233])).
% 3.30/0.84 fof(f235,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|~cyclic(X0,X2,X1,X3)|perp(X1,X0,X0,X3))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f234])).
% 3.30/0.84 fof(f247,plain,(
% 3.30/0.84 ![A,B,C,D,M]: ((~midp(M,A,B)|~midp(M,C,D))|para(A,C,B,D))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f64])).
% 3.30/0.84 fof(f248,plain,(
% 3.30/0.84 ![A,B,C,D]: ((![M]: (~midp(M,A,B)|~midp(M,C,D)))|para(A,C,B,D))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f247])).
% 3.30/0.84 fof(f249,plain,(
% 3.30/0.84 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~midp(X0,X3,X4)|para(X1,X3,X2,X4))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f248])).
% 3.30/0.84 fof(f257,plain,(
% 3.30/0.84 ![A,B,C]: ((~cong(A,B,A,C)|~coll(A,B,C))|midp(A,B,C))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f68])).
% 3.30/0.84 fof(f258,plain,(
% 3.30/0.84 ![X0,X1,X2]: (~cong(X0,X1,X0,X2)|~coll(X0,X1,X2)|midp(X0,X1,X2))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f257])).
% 3.30/0.84 fof(f259,plain,(
% 3.30/0.84 ![A,B,C]: (~midp(A,B,C)|cong(A,B,A,C))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f69])).
% 3.30/0.84 fof(f260,plain,(
% 3.30/0.84 ![X0,X1,X2]: (~midp(X0,X1,X2)|cong(X0,X1,X0,X2))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f259])).
% 3.30/0.84 fof(f261,plain,(
% 3.30/0.84 ![A,B,C]: (~midp(A,B,C)|coll(A,B,C))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f70])).
% 3.30/0.84 fof(f262,plain,(
% 3.30/0.84 ![X0,X1,X2]: (~midp(X0,X1,X2)|coll(X0,X1,X2))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f261])).
% 3.30/0.84 fof(f309,plain,(
% 3.30/0.84 ![A,B,C,D,M,N,Q]: (?[P]: ((((~midp(M,A,B)|~midp(N,C,D))|~coll(C,A,B))|~coll(D,A,B))|midp(P,A,Q)))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f83])).
% 3.30/0.84 fof(f310,plain,(
% 3.30/0.84 ![A]: ((![B,D]: ((![C]: (((![M]: ~midp(M,A,B))|(![N]: ~midp(N,C,D)))|~coll(C,A,B)))|~coll(D,A,B)))|(![Q]: ?[P]: midp(P,A,Q)))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f309])).
% 3.30/0.84 fof(f311,plain,(
% 3.30/0.84 ![A]: ((![B,D]: ((![C]: (((![M]: ~midp(M,A,B))|(![N]: ~midp(N,C,D)))|~coll(C,A,B)))|~coll(D,A,B)))|(![Q]: midp(sK6_skl(Q,A),A,Q)))),
% 3.30/0.84 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(P,sK6_skl(Q,A))],[f310])).
% 3.30/0.84 fof(f312,plain,(
% 3.30/0.84 ![X0,X1,X2,X3,X4,X5,X6]: (~midp(X0,X1,X2)|~midp(X3,X4,X5)|~coll(X4,X1,X2)|~coll(X5,X1,X2)|midp(sK6_skl(X6,X1),X1,X6))),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f311])).
% 3.30/0.84 fof(f369,plain,(
% 3.30/0.84 (?[A,B,C,O,G,E,K,H,N,NWPNT1]: (((((((((circle(O,A,B,C)&midp(G,C,B))&coll(E,O,G))&circle(O,A,E,NWPNT1))&perp(K,E,A,B))&coll(K,A,B))&perp(H,A,O,G))&coll(H,O,G))&circle(N,K,G,H))&~perp(E,K,K,N)))),
% 3.30/0.84 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 3.30/0.84 fof(f370,plain,(
% 3.30/0.84 ?[E,K,N]: ((?[G,H]: ((?[O]: ((?[A]: ((?[B]: (((((?[C]: (circle(O,A,B,C)&midp(G,C,B)))&coll(E,O,G))&(?[NWPNT1]: circle(O,A,E,NWPNT1)))&perp(K,E,A,B))&coll(K,A,B)))&perp(H,A,O,G)))&coll(H,O,G)))&circle(N,K,G,H)))&~perp(E,K,K,N))),
% 3.30/0.84 inference(miniscoping,[status(thm)],[f369])).
% 3.30/0.84 fof(f371,plain,(
% 3.30/0.84 (((((((((circle(sK25_skl,sK26_skl,sK27_skl,sK28_skl)&midp(sK23_skl,sK28_skl,sK27_skl))&coll(sK20_skl,sK25_skl,sK23_skl))&circle(sK25_skl,sK26_skl,sK20_skl,sK29_skl))&perp(sK21_skl,sK20_skl,sK26_skl,sK27_skl))&coll(sK21_skl,sK26_skl,sK27_skl))&perp(sK24_skl,sK26_skl,sK25_skl,sK23_skl))&coll(sK24_skl,sK25_skl,sK23_skl))&circle(sK22_skl,sK21_skl,sK23_skl,sK24_skl))&~perp(sK20_skl,sK21_skl,sK21_skl,sK22_skl))),
% 3.30/0.84 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(E,sK20_skl),skolemize(K,sK21_skl),skolemize(N,sK22_skl),skolemize(G,sK23_skl),skolemize(H,sK24_skl),skolemize(O,sK25_skl),skolemize(A,sK26_skl),skolemize(B,sK27_skl),skolemize(C,sK28_skl),skolemize(NWPNT1,sK29_skl)],[f370])).
% 3.30/0.84 fof(f373,plain,(
% 3.30/0.84 midp(sK23_skl,sK28_skl,sK27_skl)),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f371])).
% 3.30/0.84 fof(f379,plain,(
% 3.30/0.84 coll(sK24_skl,sK25_skl,sK23_skl)),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f371])).
% 3.30/0.84 fof(f381,plain,(
% 3.30/0.84 ~perp(sK20_skl,sK21_skl,sK21_skl,sK22_skl)),
% 3.30/0.84 inference(cnf_transformation,[status(thm)],[f371])).
% 3.30/0.84 fof(f392,plain,(
% 3.30/0.84 coll(sK23_skl,sK23_skl,sK24_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f103,f379])).
% 3.30/0.84 fof(f449,plain,(
% 3.30/0.84 coll(sK23_skl,sK24_skl,sK23_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f392,f98])).
% 3.30/0.84 fof(f492,plain,(
% 3.30/0.84 midp(sK23_skl,sK27_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f122,f373])).
% 3.30/0.84 fof(f559,plain,(
% 3.30/0.84 coll(sK23_skl,sK23_skl,sK23_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f449,f103])).
% 3.30/0.84 fof(f627,plain,(
% 3.30/0.84 ![X0]: (~perp(sK28_skl,X0,X0,sK27_skl)|cong(sK28_skl,sK23_skl,X0,sK23_skl))),
% 3.30/0.84 inference(resolution,[status(thm)],[f222,f373])).
% 3.30/0.84 fof(f674,plain,(
% 3.30/0.84 cong(sK23_skl,sK27_skl,sK23_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f260,f492])).
% 3.30/0.84 fof(f732,plain,(
% 3.30/0.84 coll(sK23_skl,sK27_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f262,f492])).
% 3.30/0.84 fof(f858,plain,(
% 3.30/0.84 coll(sK28_skl,sK28_skl,sK23_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f732,f103])).
% 3.30/0.84 fof(f894,plain,(
% 3.30/0.84 coll(sK23_skl,sK23_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f858,f103])).
% 3.30/0.84 fof(f899,plain,(
% 3.30/0.84 coll(sK28_skl,sK23_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f858,f98])).
% 3.30/0.84 fof(f923,plain,(
% 3.30/0.84 coll(sK23_skl,sK28_skl,sK23_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f894,f98])).
% 3.30/0.84 fof(f924,plain,(
% 3.30/0.84 coll(sK28_skl,sK28_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f899,f103])).
% 3.30/0.84 fof(f928,plain,(
% 3.30/0.84 coll(sK23_skl,sK28_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f899,f100])).
% 3.30/0.84 fof(f984,plain,(
% 3.30/0.84 coll(sK28_skl,sK23_skl,sK23_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f923,f100])).
% 3.30/0.84 fof(f1165,plain,(
% 3.30/0.84 circle(sK23_skl,sK27_skl,sK28_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f674,f124])).
% 3.30/0.84 fof(f1285,plain,(
% 3.30/0.84 ~coll(sK23_skl,sK27_skl,sK28_skl)|perp(sK27_skl,sK28_skl,sK28_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f1165,f225])).
% 3.30/0.84 fof(f1289,plain,(
% 3.30/0.84 perp(sK27_skl,sK28_skl,sK28_skl,sK28_skl)),
% 3.30/0.84 inference(forward_subsumption_resolution,[status(thm)],[f1285,f732])).
% 3.30/0.84 fof(f1434,plain,(
% 3.30/0.84 perp(sK28_skl,sK28_skl,sK27_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f1289,f114])).
% 3.30/0.84 fof(f2115,plain,(
% 3.30/0.84 perp(sK28_skl,sK28_skl,sK28_skl,sK27_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f1434,f112])).
% 3.30/0.84 fof(f2222,plain,(
% 3.30/0.84 cong(sK28_skl,sK23_skl,sK28_skl,sK23_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f2115,f627])).
% 3.30/0.84 fof(f2381,plain,(
% 3.30/0.84 ~coll(sK28_skl,sK23_skl,sK23_skl)|midp(sK28_skl,sK23_skl,sK23_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f2222,f258])).
% 3.30/0.84 fof(f2383,plain,(
% 3.30/0.84 cong(sK28_skl,sK23_skl,sK23_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f2222,f149])).
% 3.30/0.84 fof(f2394,plain,(
% 3.30/0.84 midp(sK28_skl,sK23_skl,sK23_skl)),
% 3.30/0.84 inference(forward_subsumption_resolution,[status(thm)],[f2381,f984])).
% 3.30/0.84 fof(f2478,plain,(
% 3.30/0.84 cong(sK23_skl,sK28_skl,sK28_skl,sK23_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f2383,f151])).
% 3.30/0.84 fof(f2583,plain,(
% 3.30/0.84 cong(sK23_skl,sK28_skl,sK23_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f2478,f149])).
% 3.30/0.84 fof(f2593,plain,(
% 3.30/0.84 ![X0]: (~coll(sK23_skl,sK23_skl,sK23_skl)|~coll(sK23_skl,sK23_skl,sK23_skl)|midp(sK6_skl(X0,sK23_skl),sK23_skl,X0))),
% 3.30/0.84 inference(resolution,[status(thm)],[f312,f2394])).
% 3.30/0.84 fof(f2932,plain,(
% 3.30/0.84 ![X0]: (~coll(sK23_skl,sK23_skl,sK23_skl)|midp(sK6_skl(X0,sK23_skl),sK23_skl,X0))),
% 3.30/0.84 inference(duplicate_literals_removal,[status(thm)],[f2593])).
% 3.30/0.84 fof(f2933,plain,(
% 3.30/0.84 ![X0]: (midp(sK6_skl(X0,sK23_skl),sK23_skl,X0))),
% 3.30/0.84 inference(forward_subsumption_resolution,[status(thm)],[f2932,f559])).
% 3.30/0.84 fof(f3185,plain,(
% 3.30/0.84 ~coll(sK23_skl,sK28_skl,sK28_skl)|midp(sK23_skl,sK28_skl,sK28_skl)),
% 3.30/0.84 inference(resolution,[status(thm)],[f2583,f258])).
% 3.30/0.84 fof(f3198,plain,(
% 3.30/0.84 midp(sK23_skl,sK28_skl,sK28_skl)),
% 3.30/0.84 inference(forward_subsumption_resolution,[status(thm)],[f3185,f928])).
% 3.30/0.84 fof(f3204,plain,(
% 3.30/0.84 ![X0]: (~coll(sK28_skl,sK28_skl,sK28_skl)|~coll(sK28_skl,sK28_skl,sK28_skl)|midp(sK6_skl(X0,sK28_skl),sK28_skl,X0))),
% 3.30/0.84 inference(resolution,[status(thm)],[f3198,f312])).
% 3.30/0.84 fof(f3241,plain,(
% 3.30/0.84 ![X0]: (~coll(sK28_skl,sK28_skl,sK28_skl)|midp(sK6_skl(X0,sK28_skl),sK28_skl,X0))),
% 3.30/0.84 inference(duplicate_literals_removal,[status(thm)],[f3204])).
% 3.30/0.84 fof(f3242,plain,(
% 3.30/0.84 ![X0]: (midp(sK6_skl(X0,sK28_skl),sK28_skl,X0))),
% 3.30/0.84 inference(forward_subsumption_resolution,[status(thm)],[f3241,f924])).
% 3.30/0.84 fof(f3281,plain,(
% 3.30/0.84 ![X0]: (coll(sK6_skl(X0,sK23_skl),sK23_skl,X0))),
% 3.30/0.84 inference(resolution,[status(thm)],[f2933,f262])).
% 3.30/0.84 fof(f3715,plain,(
% 3.30/0.84 ![X0]: (midp(sK6_skl(X0,sK28_skl),X0,sK28_skl))),
% 3.30/0.84 inference(resolution,[status(thm)],[f3242,f122])).
% 3.30/0.84 fof(f3831,plain,(
% 3.30/0.84 ![X0]: (coll(sK23_skl,sK6_skl(X0,sK23_skl),X0))),
% 3.30/0.84 inference(resolution,[status(thm)],[f3281,f100])).
% 3.30/0.84 fof(f4646,plain,(
% 3.30/0.84 ![X0]: (coll(X0,X0,sK23_skl))),
% 3.30/0.84 inference(resolution,[status(thm)],[f3831,f103])).
% 3.30/0.84 fof(f4663,plain,(
% 3.30/0.84 ![X0]: (coll(sK23_skl,sK23_skl,X0))),
% 3.30/0.84 inference(resolution,[status(thm)],[f4646,f103])).
% 3.30/0.84 fof(f4776,plain,(
% 3.30/0.84 ![X0,X1]: (~coll(sK23_skl,sK23_skl,X0)|coll(X0,X1,sK23_skl))),
% 3.30/0.84 inference(resolution,[status(thm)],[f4663,f103])).
% 3.30/0.84 fof(f4783,plain,(
% 3.30/0.84 ![X0,X1]: (coll(X0,X1,sK23_skl))),
% 3.30/0.84 inference(forward_subsumption_resolution,[status(thm)],[f4776,f4663])).
% 3.30/0.84 fof(f4807,plain,(
% 3.30/0.84 ![X0,X1]: (coll(X0,sK23_skl,X1))),
% 3.30/0.84 inference(resolution,[status(thm)],[f4783,f98])).
% 3.30/0.84 fof(f4833,plain,(
% 3.30/0.84 ![X0,X1,X2]: (~coll(X0,sK23_skl,X1)|coll(X1,X2,X0))),
% 3.30/0.84 inference(resolution,[status(thm)],[f4807,f103])).
% 3.30/0.84 fof(f4840,plain,(
% 3.30/0.84 ![X0,X1,X2]: (coll(X0,X1,X2))),
% 3.30/0.84 inference(forward_subsumption_resolution,[status(thm)],[f4833,f4807])).
% 3.30/0.84 fof(f4868,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|cyclic(X1,X2,X0,X3))),
% 3.30/0.84 inference(backward_subsumption_resolution,[status(thm)],[f195,f4840])).
% 3.30/0.84 fof(f4875,plain,(
% 3.30/0.84 ![X0,X1,X2,X3,X4,X5,X6]: (~midp(X0,X1,X2)|~midp(X3,X4,X5)|~coll(X4,X1,X2)|midp(sK6_skl(X6,X1),X1,X6))),
% 3.30/0.84 inference(backward_subsumption_resolution,[status(thm)],[f312,f4840])).
% 3.30/0.84 fof(f4878,plain,(
% 3.30/0.84 ![X0,X1,X2,X3,X4,X5,X6]: (~midp(X0,X1,X2)|~midp(X3,X4,X5)|midp(sK6_skl(X6,X1),X1,X6))),
% 3.30/0.84 inference(forward_subsumption_resolution,[status(thm)],[f4875,f4840])).
% 3.30/0.84 fof(f4999,plain,(
% 3.30/0.84 ![X0,X1]: (midp(sK6_skl(X0,X1),X1,X0))),
% 3.30/0.84 inference(resolution,[status(thm)],[f4878,f3715])).
% 3.30/0.84 fof(f5053,plain,(
% 3.30/0.84 ![X0,X1]: (para(X0,X0,X1,X1))),
% 3.30/0.84 inference(resolution,[status(thm)],[f4999,f249])).
% 3.30/0.84 fof(f5077,plain,(
% 3.30/0.84 ![X0,X1,X2,X3]: (eqangle(X0,X0,X1,X2,X3,X3,X1,X2))),
% 3.30/0.84 inference(resolution,[status(thm)],[f5053,f189])).
% 3.30/0.84 fof(f5278,plain,(
% 3.30/0.84 ![X0,X1]: (cyclic(X0,X1,X0,X0))),
% 3.30/0.84 inference(resolution,[status(thm)],[f5077,f4868])).
% 3.30/0.84 fof(f5311,plain,(
% 3.30/0.84 ![X0,X1]: (cyclic(X0,X0,X1,X0))),
% 3.30/0.84 inference(resolution,[status(thm)],[f5278,f131])).
% 3.30/0.84 fof(f5334,plain,(
% 3.30/0.84 ![X0,X1]: (cyclic(X0,X0,X0,X1))),
% 3.30/0.84 inference(resolution,[status(thm)],[f5311,f129])).
% 3.30/0.84 fof(f5339,plain,(
% 3.30/0.84 ![X0,X1,X2]: (~cyclic(X0,X0,X0,X1)|cyclic(X0,X0,X1,X2))),
% 3.30/0.85 inference(resolution,[status(thm)],[f5334,f136])).
% 3.30/0.85 fof(f5345,plain,(
% 3.30/0.85 ![X0,X1,X2]: (cyclic(X0,X0,X1,X2))),
% 3.30/0.85 inference(forward_subsumption_resolution,[status(thm)],[f5339,f5334])).
% 3.30/0.85 fof(f5362,plain,(
% 3.30/0.85 ![X0,X1,X2,X3]: (~cyclic(X0,X0,X1,X2)|cyclic(X0,X1,X2,X3))),
% 3.30/0.85 inference(resolution,[status(thm)],[f5345,f136])).
% 3.30/0.85 fof(f5368,plain,(
% 3.30/0.85 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3))),
% 3.30/0.85 inference(forward_subsumption_resolution,[status(thm)],[f5362,f5345])).
% 3.30/0.85 fof(f5393,plain,(
% 3.30/0.85 ![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))),
% 3.30/0.85 inference(backward_subsumption_resolution,[status(thm)],[f198,f5368])).
% 3.30/0.85 fof(f5395,plain,(
% 3.30/0.85 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|perp(X1,X0,X0,X3))),
% 3.30/0.85 inference(backward_subsumption_resolution,[status(thm)],[f235,f5368])).
% 3.30/0.85 fof(f5397,plain,(
% 3.30/0.85 ![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))),
% 3.30/0.85 inference(forward_subsumption_resolution,[status(thm)],[f5393,f5368])).
% 3.30/0.85 fof(f5467,plain,(
% 3.30/0.85 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X0,X2,X3,X4,X3,X5)|cong(X1,X2,X4,X5))),
% 3.30/0.85 inference(forward_subsumption_resolution,[status(thm)],[f5397,f5368])).
% 3.30/0.85 fof(f5468,plain,(
% 3.30/0.85 ![X0,X1]: (cong(X0,X1,X0,X1))),
% 3.30/0.85 inference(resolution,[status(thm)],[f5467,f5077])).
% 3.30/0.85 fof(f5612,plain,(
% 3.30/0.85 ![X0,X1,X2]: (~cong(X0,X1,X0,X1)|perp(X2,X0,X0,X1))),
% 3.30/0.85 inference(resolution,[status(thm)],[f5395,f5468])).
% 3.30/0.85 fof(f5616,plain,(
% 3.30/0.85 ![X0,X1,X2]: (perp(X0,X1,X1,X2))),
% 3.30/0.85 inference(forward_subsumption_resolution,[status(thm)],[f5612,f5468])).
% 3.30/0.85 fof(f5757,plain,(
% 3.30/0.85 $false),
% 3.30/0.85 inference(backward_subsumption_resolution,[status(thm)],[f381,f5616])).
% 3.30/0.85 % SZS output end CNFRefutation for theBenchmark.p
% 3.30/0.88 % Elapsed time: 0.494676 seconds
% 3.30/0.88 % CPU time: 3.653542 seconds
% 3.30/0.88 % Total memory used: 122.213 MB
% 3.30/0.88 % Net memory used: 118.513 MB
%------------------------------------------------------------------------------