%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO605+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 : n009.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 12:26:42 PM UTC 2026
% Result : Theorem 30.09s 4.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO605+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.51 % Computer : n009.cluster.edu
% 0.08/0.51 % Model : x86_64 x86_64
% 0.08/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.51 % Memory : 8046.5625MB
% 0.08/0.51 % OS : Linux 6.8.0-71-generic
% 0.08/0.51 % CPULimit : 300
% 0.08/0.51 % WCLimit : 300
% 0.08/0.51 % DateTime : Sun Sep 20 17:42:27 UTC 2026
% 0.08/0.51 % CPUTime :
% 0.08/0.52 % Drodi V4.1.1
% 30.09/4.42 % Refutation found
% 30.09/4.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 30.09/4.42 % SZS output start CNFRefutation for theBenchmark
% 30.09/4.42 fof(f1,axiom,(
% 30.09/4.42 (! [A,B,C] :( coll(A,B,C)=> coll(A,C,B) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f2,axiom,(
% 30.09/4.42 (! [A,B,C] :( coll(A,B,C)=> coll(B,A,C) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f3,axiom,(
% 30.09/4.42 (! [A,B,C,D] :( ( coll(A,B,C)& coll(A,B,D) )=> coll(C,D,A) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f4,axiom,(
% 30.09/4.42 (! [A,B,C,D] :( para(A,B,C,D)=> para(A,B,D,C) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f5,axiom,(
% 30.09/4.42 (! [A,B,C,D] :( para(A,B,C,D)=> para(C,D,A,B) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f8,axiom,(
% 30.09/4.42 (! [A,B,C,D] :( perp(A,B,C,D)=> perp(C,D,A,B) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f9,axiom,(
% 30.09/4.42 (! [A,B,C,D,E,F] :( ( perp(A,B,C,D)& perp(C,D,E,F) )=> para(A,B,E,F) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f11,axiom,(
% 30.09/4.42 (! [A,B,M] :( midp(M,B,A)=> midp(M,A,B) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f14,axiom,(
% 30.09/4.42 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(A,B,D,C) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f15,axiom,(
% 30.09/4.42 (! [A,B,C,D] :( cyclic(A,B,C,D)=> cyclic(A,C,B,D) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f17,axiom,(
% 30.09/4.42 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f40,axiom,(
% 30.09/4.42 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f41,axiom,(
% 30.09/4.42 (! [A,B,P,Q] :( cyclic(A,B,P,Q)=> eqangle(P,A,P,B,Q,A,Q,B) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f43,axiom,(
% 30.09/4.42 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f44,axiom,(
% 30.09/4.42 (! [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) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f58,axiom,(
% 30.09/4.42 (! [A,B,P,Q] :( ( cong(A,P,B,P)& cong(A,Q,B,Q)& cyclic(A,B,P,Q) )=> perp(P,A,A,Q) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f64,axiom,(
% 30.09/4.42 (! [A,B,C,D,M] :( ( midp(M,A,B)& midp(M,C,D) )=> para(A,C,B,D) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f67,axiom,(
% 30.09/4.42 (! [A,B,C] :( para(A,B,A,C)=> coll(A,B,C) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f83,axiom,(
% 30.09/4.42 (! [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) ) ))),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f95,conjecture,(
% 30.09/4.42 (! [M,B,C,I,IC,IB,A,O,MIDPNT1,MIDPNT2,MIDPNT3] :( ( eqangle(I,M,M,B,I,M,M,C)& eqangle(I,B,B,C,I,B,B,M)& eqangle(I,C,C,M,I,C,C,B)& perp(B,I,B,IC)& perp(C,I,C,IB)& coll(IC,C,I)& coll(IB,B,I)& midp(A,IB,IC)& midp(MIDPNT1,B,I)& perp(B,I,MIDPNT1,O)& midp(MIDPNT2,B,C)& perp(B,C,MIDPNT2,O)& midp(MIDPNT3,I,C)& perp(I,C,MIDPNT3,O) )=> perp(A,B,B,O) ) )),
% 30.09/4.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 30.09/4.42 fof(f96,negated_conjecture,(
% 30.09/4.42 ~((! [M,B,C,I,IC,IB,A,O,MIDPNT1,MIDPNT2,MIDPNT3] :( ( eqangle(I,M,M,B,I,M,M,C)& eqangle(I,B,B,C,I,B,B,M)& eqangle(I,C,C,M,I,C,C,B)& perp(B,I,B,IC)& perp(C,I,C,IB)& coll(IC,C,I)& coll(IB,B,I)& midp(A,IB,IC)& midp(MIDPNT1,B,I)& perp(B,I,MIDPNT1,O)& midp(MIDPNT2,B,C)& perp(B,C,MIDPNT2,O)& midp(MIDPNT3,I,C)& perp(I,C,MIDPNT3,O) )=> perp(A,B,B,O) ) ))),
% 30.09/4.42 inference(negated_conjecture,[status(cth)],[f95])).
% 30.09/4.42 fof(f97,plain,(
% 30.09/4.42 ![A,B,C]: (~coll(A,B,C)|coll(A,C,B))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 30.09/4.42 fof(f98,plain,(
% 30.09/4.42 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X0,X2,X1))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f97])).
% 30.09/4.42 fof(f99,plain,(
% 30.09/4.42 ![A,B,C]: (~coll(A,B,C)|coll(B,A,C))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 30.09/4.42 fof(f100,plain,(
% 30.09/4.42 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X1,X0,X2))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f99])).
% 30.09/4.42 fof(f101,plain,(
% 30.09/4.42 ![A,B,C,D]: ((~coll(A,B,C)|~coll(A,B,D))|coll(C,D,A))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 30.09/4.42 fof(f102,plain,(
% 30.09/4.42 ![A,C,D]: ((![B]: (~coll(A,B,C)|~coll(A,B,D)))|coll(C,D,A))),
% 30.09/4.42 inference(miniscoping,[status(thm)],[f101])).
% 30.09/4.42 fof(f103,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~coll(X0,X1,X2)|~coll(X0,X1,X3)|coll(X2,X3,X0))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f102])).
% 30.09/4.42 fof(f104,plain,(
% 30.09/4.42 ![A,B,C,D]: (~para(A,B,C,D)|para(A,B,D,C))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 30.09/4.42 fof(f105,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~para(X0,X1,X2,X3)|para(X0,X1,X3,X2))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f104])).
% 30.09/4.42 fof(f106,plain,(
% 30.09/4.42 ![A,B,C,D]: (~para(A,B,C,D)|para(C,D,A,B))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 30.09/4.42 fof(f107,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~para(X0,X1,X2,X3)|para(X2,X3,X0,X1))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f106])).
% 30.09/4.42 fof(f113,plain,(
% 30.09/4.42 ![A,B,C,D]: (~perp(A,B,C,D)|perp(C,D,A,B))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 30.09/4.42 fof(f114,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~perp(X0,X1,X2,X3)|perp(X2,X3,X0,X1))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f113])).
% 30.09/4.42 fof(f115,plain,(
% 30.09/4.42 ![A,B,C,D,E,F]: ((~perp(A,B,C,D)|~perp(C,D,E,F))|para(A,B,E,F))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 30.09/4.42 fof(f116,plain,(
% 30.09/4.42 ![A,B,E,F]: ((![C,D]: (~perp(A,B,C,D)|~perp(C,D,E,F)))|para(A,B,E,F))),
% 30.09/4.42 inference(miniscoping,[status(thm)],[f115])).
% 30.09/4.42 fof(f117,plain,(
% 30.09/4.42 ![X0,X1,X2,X3,X4,X5]: (~perp(X0,X1,X2,X3)|~perp(X2,X3,X4,X5)|para(X0,X1,X4,X5))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f116])).
% 30.09/4.42 fof(f121,plain,(
% 30.09/4.42 ![A,B,M]: (~midp(M,B,A)|midp(M,A,B))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 30.09/4.42 fof(f122,plain,(
% 30.09/4.42 ![X0,X1,X2]: (~midp(X0,X1,X2)|midp(X0,X2,X1))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f121])).
% 30.09/4.42 fof(f128,plain,(
% 30.09/4.42 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(A,B,D,C))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 30.09/4.42 fof(f129,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X0,X1,X3,X2))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f128])).
% 30.09/4.42 fof(f130,plain,(
% 30.09/4.42 ![A,B,C,D]: (~cyclic(A,B,C,D)|cyclic(A,C,B,D))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 30.09/4.42 fof(f131,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|cyclic(X0,X2,X1,X3))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f130])).
% 30.09/4.42 fof(f134,plain,(
% 30.09/4.42 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 30.09/4.42 fof(f135,plain,(
% 30.09/4.42 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 30.09/4.42 inference(miniscoping,[status(thm)],[f134])).
% 30.09/4.42 fof(f136,plain,(
% 30.09/4.42 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f135])).
% 30.09/4.42 fof(f187,plain,(
% 30.09/4.42 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 30.09/4.42 fof(f188,plain,(
% 30.09/4.42 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 30.09/4.42 inference(miniscoping,[status(thm)],[f187])).
% 30.09/4.42 fof(f189,plain,(
% 30.09/4.42 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f188])).
% 30.09/4.42 fof(f190,plain,(
% 30.09/4.42 ![A,B,P,Q]: (~cyclic(A,B,P,Q)|eqangle(P,A,P,B,Q,A,Q,B))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 30.09/4.42 fof(f191,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|eqangle(X2,X0,X2,X1,X3,X0,X3,X1))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f190])).
% 30.09/4.42 fof(f194,plain,(
% 30.09/4.42 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 30.09/4.42 fof(f195,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f194])).
% 30.09/4.42 fof(f196,plain,(
% 30.09/4.42 ![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))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 30.09/4.42 fof(f197,plain,(
% 30.09/4.42 ![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))),
% 30.09/4.42 inference(miniscoping,[status(thm)],[f196])).
% 30.09/4.42 fof(f198,plain,(
% 30.09/4.42 ![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))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f197])).
% 30.09/4.42 fof(f233,plain,(
% 30.09/4.42 ![A,B,P,Q]: (((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q))|perp(P,A,A,Q))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 30.09/4.42 fof(f234,plain,(
% 30.09/4.42 ![A,P,Q]: ((![B]: ((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q)))|perp(P,A,A,Q))),
% 30.09/4.42 inference(miniscoping,[status(thm)],[f233])).
% 30.09/4.42 fof(f235,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|~cyclic(X0,X2,X1,X3)|perp(X1,X0,X0,X3))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f234])).
% 30.09/4.42 fof(f247,plain,(
% 30.09/4.42 ![A,B,C,D,M]: ((~midp(M,A,B)|~midp(M,C,D))|para(A,C,B,D))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f64])).
% 30.09/4.42 fof(f248,plain,(
% 30.09/4.42 ![A,B,C,D]: ((![M]: (~midp(M,A,B)|~midp(M,C,D)))|para(A,C,B,D))),
% 30.09/4.42 inference(miniscoping,[status(thm)],[f247])).
% 30.09/4.42 fof(f249,plain,(
% 30.09/4.42 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~midp(X0,X3,X4)|para(X1,X3,X2,X4))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f248])).
% 30.09/4.42 fof(f255,plain,(
% 30.09/4.42 ![A,B,C]: (~para(A,B,A,C)|coll(A,B,C))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f67])).
% 30.09/4.42 fof(f256,plain,(
% 30.09/4.42 ![X0,X1,X2]: (~para(X0,X1,X0,X2)|coll(X0,X1,X2))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f255])).
% 30.09/4.42 fof(f309,plain,(
% 30.09/4.42 ![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)))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f83])).
% 30.09/4.42 fof(f310,plain,(
% 30.09/4.42 ![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)))),
% 30.09/4.42 inference(miniscoping,[status(thm)],[f309])).
% 30.09/4.42 fof(f311,plain,(
% 30.09/4.42 ![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)))),
% 30.09/4.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(P,sK6_skl(Q,A))],[f310])).
% 30.09/4.42 fof(f312,plain,(
% 30.09/4.42 ![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))),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f311])).
% 30.09/4.42 fof(f369,plain,(
% 30.09/4.42 (?[M,B,C,I,IC,IB,A,O,MIDPNT1,MIDPNT2,MIDPNT3]: ((((((((((((((eqangle(I,M,M,B,I,M,M,C)&eqangle(I,B,B,C,I,B,B,M))&eqangle(I,C,C,M,I,C,C,B))&perp(B,I,B,IC))&perp(C,I,C,IB))&coll(IC,C,I))&coll(IB,B,I))&midp(A,IB,IC))&midp(MIDPNT1,B,I))&perp(B,I,MIDPNT1,O))&midp(MIDPNT2,B,C))&perp(B,C,MIDPNT2,O))&midp(MIDPNT3,I,C))&perp(I,C,MIDPNT3,O))&~perp(A,B,B,O)))),
% 30.09/4.42 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 30.09/4.42 fof(f370,plain,(
% 30.09/4.42 ?[B,A,O]: ((?[C,I,MIDPNT3]: (((?[MIDPNT2]: (((?[MIDPNT1]: (((?[IC,IB]: ((((((?[M]: ((eqangle(I,M,M,B,I,M,M,C)&eqangle(I,B,B,C,I,B,B,M))&eqangle(I,C,C,M,I,C,C,B)))&perp(B,I,B,IC))&perp(C,I,C,IB))&coll(IC,C,I))&coll(IB,B,I))&midp(A,IB,IC)))&midp(MIDPNT1,B,I))&perp(B,I,MIDPNT1,O)))&midp(MIDPNT2,B,C))&perp(B,C,MIDPNT2,O)))&midp(MIDPNT3,I,C))&perp(I,C,MIDPNT3,O)))&~perp(A,B,B,O))),
% 30.09/4.42 inference(miniscoping,[status(thm)],[f369])).
% 30.09/4.42 fof(f371,plain,(
% 30.09/4.42 ((((((((((((((eqangle(sK24_skl,sK30_skl,sK30_skl,sK20_skl,sK24_skl,sK30_skl,sK30_skl,sK23_skl)&eqangle(sK24_skl,sK20_skl,sK20_skl,sK23_skl,sK24_skl,sK20_skl,sK20_skl,sK30_skl))&eqangle(sK24_skl,sK23_skl,sK23_skl,sK30_skl,sK24_skl,sK23_skl,sK23_skl,sK20_skl))&perp(sK20_skl,sK24_skl,sK20_skl,sK28_skl))&perp(sK23_skl,sK24_skl,sK23_skl,sK29_skl))&coll(sK28_skl,sK23_skl,sK24_skl))&coll(sK29_skl,sK20_skl,sK24_skl))&midp(sK21_skl,sK29_skl,sK28_skl))&midp(sK27_skl,sK20_skl,sK24_skl))&perp(sK20_skl,sK24_skl,sK27_skl,sK22_skl))&midp(sK26_skl,sK20_skl,sK23_skl))&perp(sK20_skl,sK23_skl,sK26_skl,sK22_skl))&midp(sK25_skl,sK24_skl,sK23_skl))&perp(sK24_skl,sK23_skl,sK25_skl,sK22_skl))&~perp(sK21_skl,sK20_skl,sK20_skl,sK22_skl))),
% 30.09/4.42 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]),skolemize(B,sK20_skl),skolemize(A,sK21_skl),skolemize(O,sK22_skl),skolemize(C,sK23_skl),skolemize(I,sK24_skl),skolemize(MIDPNT3,sK25_skl),skolemize(MIDPNT2,sK26_skl),skolemize(MIDPNT1,sK27_skl),skolemize(IC,sK28_skl),skolemize(IB,sK29_skl),skolemize(M,sK30_skl)],[f370])).
% 30.09/4.42 fof(f375,plain,(
% 30.09/4.42 perp(sK20_skl,sK24_skl,sK20_skl,sK28_skl)),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f371])).
% 30.09/4.42 fof(f378,plain,(
% 30.09/4.42 coll(sK29_skl,sK20_skl,sK24_skl)),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f371])).
% 30.09/4.42 fof(f380,plain,(
% 30.09/4.42 midp(sK27_skl,sK20_skl,sK24_skl)),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f371])).
% 30.09/4.42 fof(f386,plain,(
% 30.09/4.42 ~perp(sK21_skl,sK20_skl,sK20_skl,sK22_skl)),
% 30.09/4.42 inference(cnf_transformation,[status(thm)],[f371])).
% 30.09/4.42 fof(f387,plain,(
% 30.09/4.42 coll(sK29_skl,sK24_skl,sK20_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f98,f378])).
% 30.09/4.42 fof(f389,plain,(
% 30.09/4.42 coll(sK20_skl,sK29_skl,sK24_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f100,f378])).
% 30.09/4.42 fof(f393,plain,(
% 30.09/4.42 ![X0]: (~coll(sK29_skl,sK24_skl,X0)|coll(sK20_skl,X0,sK29_skl))),
% 30.09/4.42 inference(resolution,[status(thm)],[f387,f103])).
% 30.09/4.42 fof(f396,plain,(
% 30.09/4.42 ![X0,X1]: (~perp(sK20_skl,sK28_skl,X0,X1)|para(sK20_skl,sK24_skl,X0,X1))),
% 30.09/4.42 inference(resolution,[status(thm)],[f375,f117])).
% 30.09/4.42 fof(f397,plain,(
% 30.09/4.42 perp(sK20_skl,sK28_skl,sK20_skl,sK24_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f375,f114])).
% 30.09/4.42 fof(f402,plain,(
% 30.09/4.42 ![X0]: (~coll(sK20_skl,sK29_skl,X0)|coll(sK24_skl,X0,sK20_skl))),
% 30.09/4.42 inference(resolution,[status(thm)],[f389,f103])).
% 30.09/4.42 fof(f407,plain,(
% 30.09/4.42 midp(sK27_skl,sK24_skl,sK20_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f122,f380])).
% 30.09/4.42 fof(f555,plain,(
% 30.09/4.42 para(sK20_skl,sK24_skl,sK20_skl,sK24_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f397,f396])).
% 30.09/4.42 fof(f1395,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~midp(X0,X1,X2)|~coll(X1,sK20_skl,sK24_skl)|~coll(X2,sK20_skl,sK24_skl)|midp(sK6_skl(X3,sK20_skl),sK20_skl,X3))),
% 30.09/4.42 inference(resolution,[status(thm)],[f312,f380])).
% 30.09/4.42 fof(f1419,definition,(
% 30.09/4.42 ![X3]: (sQ146_spl <=> (midp(sK6_skl(X3,sK20_skl),sK20_skl,X3)))),
% 30.09/4.42 introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition])).
% 30.09/4.42 fof(f1420,plain,(
% 30.09/4.42 ![X0]: (midp(sK6_skl(X0,sK20_skl),sK20_skl,X0)|~sQ146_spl)),
% 30.09/4.42 inference(component_clause,[status(thm)],[f1419])).
% 30.09/4.42 fof(f1427,definition,(
% 30.09/4.42 ![X0,X1,X2]: (sQ148_spl <=> (~midp(X0,X1,X2)|~coll(X1,sK20_skl,sK24_skl)|~coll(X2,sK20_skl,sK24_skl)))),
% 30.09/4.42 introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition])).
% 30.09/4.42 fof(f1428,plain,(
% 30.09/4.42 ![X0,X1,X2]: (~midp(X0,X1,X2)|~coll(X1,sK20_skl,sK24_skl)|~coll(X2,sK20_skl,sK24_skl)|~sQ148_spl)),
% 30.09/4.42 inference(component_clause,[status(thm)],[f1427])).
% 30.09/4.42 fof(f1430,plain,(
% 30.09/4.42 sQ148_spl|sQ146_spl),
% 30.09/4.42 inference(split_clause,[status(thm)],[f1395,f1427,f1419])).
% 30.09/4.42 fof(f2199,plain,(
% 30.09/4.42 coll(sK20_skl,sK24_skl,sK24_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f555,f256])).
% 30.09/4.42 fof(f2201,plain,(
% 30.09/4.42 ![X0,X1]: (eqangle(sK20_skl,sK24_skl,X0,X1,sK20_skl,sK24_skl,X0,X1))),
% 30.09/4.42 inference(resolution,[status(thm)],[f555,f189])).
% 30.09/4.42 fof(f2207,plain,(
% 30.09/4.42 coll(sK24_skl,sK20_skl,sK24_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f2199,f100])).
% 30.09/4.42 fof(f2374,plain,(
% 30.09/4.42 ![X0,X1,X2]: (~midp(sK6_skl(X0,sK20_skl),X1,X2)|para(sK20_skl,X1,X0,X2)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f1420,f249])).
% 30.09/4.42 fof(f2379,plain,(
% 30.09/4.42 ![X0]: (midp(sK6_skl(X0,sK20_skl),X0,sK20_skl)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f1420,f122])).
% 30.09/4.42 fof(f2553,plain,(
% 30.09/4.42 ~coll(sK24_skl,sK20_skl,sK24_skl)|~coll(sK20_skl,sK20_skl,sK24_skl)|~sQ148_spl),
% 30.09/4.42 inference(resolution,[status(thm)],[f1428,f407])).
% 30.09/4.42 fof(f2560,definition,(
% 30.09/4.42 sQ304_spl <=> (coll(sK24_skl,sK20_skl,sK24_skl))),
% 30.09/4.42 introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition])).
% 30.09/4.42 fof(f2562,plain,(
% 30.09/4.42 ~coll(sK24_skl,sK20_skl,sK24_skl)|sQ304_spl),
% 30.09/4.42 inference(component_clause,[status(thm)],[f2560])).
% 30.09/4.42 fof(f2565,definition,(
% 30.09/4.42 sQ305_spl <=> (coll(sK20_skl,sK20_skl,sK24_skl))),
% 30.09/4.42 introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition])).
% 30.09/4.42 fof(f2567,plain,(
% 30.09/4.42 ~coll(sK20_skl,sK20_skl,sK24_skl)|sQ305_spl),
% 30.09/4.42 inference(component_clause,[status(thm)],[f2565])).
% 30.09/4.42 fof(f2570,plain,(
% 30.09/4.42 ~sQ304_spl|~sQ305_spl|~sQ148_spl),
% 30.09/4.42 inference(split_clause,[status(thm)],[f2553,f2560,f2565,f1427])).
% 30.09/4.42 fof(f2582,plain,(
% 30.09/4.42 $false|sQ304_spl),
% 30.09/4.42 inference(forward_subsumption_resolution,[status(thm)],[f2562,f2207])).
% 30.09/4.42 fof(f2583,plain,(
% 30.09/4.42 sQ304_spl),
% 30.09/4.42 inference(contradiction_clause,[status(thm)],[f2582])).
% 30.09/4.42 fof(f3196,plain,(
% 30.09/4.42 coll(sK20_skl,sK20_skl,sK29_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f393,f387])).
% 30.09/4.42 fof(f3264,plain,(
% 30.09/4.42 coll(sK20_skl,sK29_skl,sK20_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f3196,f98])).
% 30.09/4.42 fof(f3430,plain,(
% 30.09/4.42 coll(sK24_skl,sK20_skl,sK20_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f3264,f402])).
% 30.09/4.42 fof(f3613,plain,(
% 30.09/4.42 coll(sK20_skl,sK24_skl,sK20_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f3430,f100])).
% 30.09/4.42 fof(f4129,plain,(
% 30.09/4.42 coll(sK20_skl,sK20_skl,sK24_skl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f3613,f98])).
% 30.09/4.42 fof(f4130,plain,(
% 30.09/4.42 $false|sQ305_spl),
% 30.09/4.42 inference(forward_subsumption_resolution,[status(thm)],[f4129,f2567])).
% 30.09/4.42 fof(f4131,plain,(
% 30.09/4.42 sQ305_spl),
% 30.09/4.42 inference(contradiction_clause,[status(thm)],[f4130])).
% 30.09/4.42 fof(f11030,plain,(
% 30.09/4.42 ![X0]: (para(sK20_skl,X0,X0,sK20_skl)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f2374,f2379])).
% 30.09/4.42 fof(f11103,plain,(
% 30.09/4.42 ![X0]: (para(X0,sK20_skl,sK20_skl,X0)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f11030,f107])).
% 30.09/4.42 fof(f11235,plain,(
% 30.09/4.42 ![X0]: (para(X0,sK20_skl,X0,sK20_skl)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f11103,f105])).
% 30.09/4.42 fof(f11624,plain,(
% 30.09/4.42 ![X0]: (coll(X0,sK20_skl,sK20_skl)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f11235,f256])).
% 30.09/4.42 fof(f11640,plain,(
% 30.09/4.42 ![X0]: (coll(sK20_skl,X0,sK20_skl)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f11624,f100])).
% 30.09/4.42 fof(f11860,plain,(
% 30.09/4.42 ![X0]: (coll(sK20_skl,sK20_skl,X0)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f11640,f98])).
% 30.09/4.42 fof(f11864,plain,(
% 30.09/4.42 ![X0,X1]: (~coll(sK20_skl,sK20_skl,X0)|coll(X1,X0,sK20_skl)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f11860,f103])).
% 30.09/4.42 fof(f11869,plain,(
% 30.09/4.42 ![X0,X1]: (coll(X0,X1,sK20_skl)|~sQ146_spl)),
% 30.09/4.42 inference(forward_subsumption_resolution,[status(thm)],[f11864,f11860])).
% 30.09/4.42 fof(f11896,plain,(
% 30.09/4.42 ![X0,X1]: (coll(X0,sK20_skl,X1)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f11869,f98])).
% 30.09/4.42 fof(f11979,plain,(
% 30.09/4.42 ![X0,X1,X2]: (~coll(X0,sK20_skl,X1)|coll(X2,X1,X0)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f11896,f103])).
% 30.09/4.42 fof(f11985,plain,(
% 30.09/4.42 ![X0,X1,X2]: (coll(X0,X1,X2)|~sQ146_spl)),
% 30.09/4.42 inference(forward_subsumption_resolution,[status(thm)],[f11979,f11896])).
% 30.09/4.42 fof(f12005,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|cyclic(X1,X2,X0,X3)|~sQ146_spl)),
% 30.09/4.42 inference(backward_subsumption_resolution,[status(thm)],[f195,f11985])).
% 30.09/4.42 fof(f21321,plain,(
% 30.09/4.42 ![X0]: (cyclic(sK24_skl,X0,sK20_skl,sK20_skl)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f2201,f12005])).
% 30.09/4.42 fof(f21345,plain,(
% 30.09/4.42 ![X0]: (cyclic(sK24_skl,sK20_skl,X0,sK20_skl)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f21321,f131])).
% 30.09/4.42 fof(f21369,plain,(
% 30.09/4.42 ![X0]: (cyclic(sK24_skl,sK20_skl,sK20_skl,X0)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f21345,f129])).
% 30.09/4.42 fof(f22084,plain,(
% 30.09/4.42 ![X0,X1]: (~cyclic(sK24_skl,sK20_skl,sK20_skl,X0)|cyclic(sK20_skl,sK20_skl,X1,X0)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f21369,f136])).
% 30.09/4.42 fof(f22095,plain,(
% 30.09/4.42 ![X0,X1]: (cyclic(sK20_skl,sK20_skl,X0,X1)|~sQ146_spl)),
% 30.09/4.42 inference(forward_subsumption_resolution,[status(thm)],[f22084,f21369])).
% 30.09/4.42 fof(f22101,plain,(
% 30.09/4.42 ![X0,X1,X2]: (~cyclic(sK20_skl,sK20_skl,X0,X1)|cyclic(sK20_skl,X0,X2,X1)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f22095,f136])).
% 30.09/4.42 fof(f22114,plain,(
% 30.09/4.42 ![X0,X1,X2]: (cyclic(sK20_skl,X0,X1,X2)|~sQ146_spl)),
% 30.09/4.42 inference(forward_subsumption_resolution,[status(thm)],[f22101,f22095])).
% 30.09/4.42 fof(f22120,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (~cyclic(sK20_skl,X0,X1,X2)|cyclic(X0,X1,X3,X2)|~sQ146_spl)),
% 30.09/4.42 inference(resolution,[status(thm)],[f22114,f136])).
% 30.09/4.42 fof(f22126,plain,(
% 30.09/4.42 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3)|~sQ146_spl)),
% 30.09/4.42 inference(forward_subsumption_resolution,[status(thm)],[f22120,f22114])).
% 5.00/4.45 fof(f22190,plain,(
% 5.00/4.45 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|perp(X1,X0,X0,X3)|~sQ146_spl)),
% 5.00/4.45 inference(backward_subsumption_resolution,[status(thm)],[f235,f22126])).
% 5.00/4.45 fof(f22191,plain,(
% 5.00/4.45 ![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)|~sQ146_spl)),
% 5.00/4.45 inference(backward_subsumption_resolution,[status(thm)],[f198,f22126])).
% 5.00/4.45 fof(f22207,plain,(
% 5.00/4.45 ![X0,X1,X2,X3]: (eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~sQ146_spl)),
% 5.00/4.45 inference(backward_subsumption_resolution,[status(thm)],[f191,f22126])).
% 5.00/4.45 fof(f22208,plain,(
% 5.00/4.45 ![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)|~sQ146_spl)),
% 5.00/4.45 inference(forward_subsumption_resolution,[status(thm)],[f22191,f22126])).
% 5.00/4.45 fof(f22270,plain,(
% 5.00/4.45 ![X0,X1,X2,X3,X4,X5]: (~eqangle(X0,X1,X0,X2,X3,X4,X3,X5)|cong(X1,X2,X4,X5)|~sQ146_spl)),
% 5.00/4.45 inference(forward_subsumption_resolution,[status(thm)],[f22208,f22126])).
% 5.00/4.45 fof(f23299,plain,(
% 5.00/4.45 ![X0,X1]: (cong(X0,X1,X0,X1)|~sQ146_spl)),
% 5.00/4.45 inference(resolution,[status(thm)],[f22207,f22270])).
% 5.00/4.45 fof(f23326,plain,(
% 5.00/4.45 ![X0,X1,X2]: (~cong(X0,X1,X0,X1)|perp(X2,X0,X0,X1)|~sQ146_spl)),
% 5.00/4.45 inference(resolution,[status(thm)],[f23299,f22190])).
% 5.00/4.45 fof(f23338,plain,(
% 5.00/4.45 ![X0,X1,X2]: (perp(X0,X1,X1,X2)|~sQ146_spl)),
% 5.00/4.45 inference(forward_subsumption_resolution,[status(thm)],[f23326,f23299])).
% 5.00/4.45 fof(f23525,plain,(
% 5.00/4.45 $false|~sQ146_spl),
% 5.00/4.45 inference(backward_subsumption_resolution,[status(thm)],[f386,f23338])).
% 5.00/4.45 fof(f23596,plain,(
% 5.00/4.45 ~sQ146_spl),
% 5.00/4.45 inference(contradiction_clause,[status(thm)],[f23525])).
% 5.00/4.45 fof(f23597,plain,(
% 5.00/4.45 $false),
% 5.00/4.45 inference(sat_refutation,[status(thm)],[f1430,f2570,f2583,f4131,f23596])).
% 5.00/4.45 % SZS output end CNFRefutation for theBenchmark.p
% 5.00/4.47 % Elapsed time: 3.940676 seconds
% 5.00/4.47 % CPU time: 30.962568 seconds
% 5.00/4.47 % Total memory used: 265.231 MB
% 5.00/4.47 % Net memory used: 243.452 MB
%------------------------------------------------------------------------------