%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO629+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:26:44 PM UTC 2026
% Result : Theorem 4.61s 1.03s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO629+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
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % 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 18:03:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 4.61/1.03 % Refutation found
% 4.61/1.03 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.61/1.03 % SZS output start CNFRefutation for theBenchmark
% 4.61/1.03 fof(f1,axiom,(
% 4.61/1.03 (! [A,B,C] :( coll(A,B,C)=> coll(A,C,B) ) )),
% 4.61/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.03 fof(f2,axiom,(
% 4.61/1.03 (! [A,B,C] :( coll(A,B,C)=> coll(B,A,C) ) )),
% 4.61/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.03 fof(f3,axiom,(
% 4.61/1.03 (! [A,B,C,D] :( ( coll(A,B,C)& coll(A,B,D) )=> coll(C,D,A) ) )),
% 4.61/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.03 fof(f4,axiom,(
% 4.61/1.03 (! [A,B,C,D] :( para(A,B,C,D)=> para(A,B,D,C) ) )),
% 4.61/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.03 fof(f11,axiom,(
% 4.61/1.03 (! [A,B,M] :( midp(M,B,A)=> midp(M,A,B) ) )),
% 4.61/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.03 fof(f17,axiom,(
% 4.61/1.03 (! [A,B,C,D,E] :( ( cyclic(A,B,C,D)& cyclic(A,B,C,E) )=> cyclic(B,C,D,E) ) )),
% 4.61/1.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.03 fof(f18,axiom,(
% 4.61/1.03 (! [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) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f19,axiom,(
% 4.61/1.04 (! [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) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f20,axiom,(
% 4.61/1.04 (! [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) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f21,axiom,(
% 4.61/1.04 (! [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) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f40,axiom,(
% 4.61/1.04 (! [A,B,C,D,P,Q] :( para(A,B,C,D)=> eqangle(A,B,P,Q,C,D,P,Q) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f41,axiom,(
% 4.61/1.04 (! [A,B,P,Q] :( cyclic(A,B,P,Q)=> eqangle(P,A,P,B,Q,A,Q,B) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f43,axiom,(
% 4.61/1.04 (! [A,B,P,Q] :( ( eqangle(P,A,P,B,Q,A,Q,B)& coll(P,Q,B) )=> cyclic(A,B,P,Q) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f44,axiom,(
% 4.61/1.04 (! [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) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f46,axiom,(
% 4.61/1.04 (! [A,B,C,E,F] :( ( midp(E,A,B)& para(E,F,B,C)& coll(F,A,C) )=> midp(F,A,C) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f56,axiom,(
% 4.61/1.04 (! [A,B,M,O] :( ( midp(M,A,B)& perp(O,M,A,B) )=> cong(O,A,O,B) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f58,axiom,(
% 4.61/1.04 (! [A,B,P,Q] :( ( cong(A,P,B,P)& cong(A,Q,B,Q)& cyclic(A,B,P,Q) )=> perp(P,A,A,Q) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f64,axiom,(
% 4.61/1.04 (! [A,B,C,D,M] :( ( midp(M,A,B)& midp(M,C,D) )=> para(A,C,B,D) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f67,axiom,(
% 4.61/1.04 (! [A,B,C] :( para(A,B,A,C)=> coll(A,B,C) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f68,axiom,(
% 4.61/1.04 (! [A,B,C] :( ( cong(A,B,A,C)& coll(A,B,C) )=> midp(A,B,C) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f74,axiom,(
% 4.61/1.04 (! [A,B,C,D,P,Q,U,V] :( ( eqangle(A,B,C,D,P,Q,U,V)& para(P,Q,U,V) )=> para(A,B,C,D) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f95,conjecture,(
% 4.61/1.04 (! [A,B,C,O,P1,F1,G1,P,F,G,K,NWPNT1,NWPNT2,NWPNT3] :( ( circle(O,A,B,C)& circle(O,A,P1,NWPNT1)& perp(F1,P1,A,C)& coll(F1,A,C)& perp(G1,P1,A,B)& coll(G1,A,B)& circle(O,A,P,NWPNT2)& perp(F,P,A,C)& coll(F,A,C)& perp(G,P,A,B)& coll(G,A,B)& para(F1,G1,K,P)& circle(O,A,K,NWPNT3) )=> para(K,P1,G,F) ) )),
% 4.61/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 4.61/1.04 fof(f96,negated_conjecture,(
% 4.61/1.04 ~((! [A,B,C,O,P1,F1,G1,P,F,G,K,NWPNT1,NWPNT2,NWPNT3] :( ( circle(O,A,B,C)& circle(O,A,P1,NWPNT1)& perp(F1,P1,A,C)& coll(F1,A,C)& perp(G1,P1,A,B)& coll(G1,A,B)& circle(O,A,P,NWPNT2)& perp(F,P,A,C)& coll(F,A,C)& perp(G,P,A,B)& coll(G,A,B)& para(F1,G1,K,P)& circle(O,A,K,NWPNT3) )=> para(K,P1,G,F) ) ))),
% 4.61/1.04 inference(negated_conjecture,[status(cth)],[f95])).
% 4.61/1.04 fof(f97,plain,(
% 4.61/1.04 ![A,B,C]: (~coll(A,B,C)|coll(A,C,B))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 4.61/1.04 fof(f98,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X0,X2,X1))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f97])).
% 4.61/1.04 fof(f99,plain,(
% 4.61/1.04 ![A,B,C]: (~coll(A,B,C)|coll(B,A,C))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 4.61/1.04 fof(f100,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~coll(X0,X1,X2)|coll(X1,X0,X2))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f99])).
% 4.61/1.04 fof(f101,plain,(
% 4.61/1.04 ![A,B,C,D]: ((~coll(A,B,C)|~coll(A,B,D))|coll(C,D,A))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 4.61/1.04 fof(f102,plain,(
% 4.61/1.04 ![A,C,D]: ((![B]: (~coll(A,B,C)|~coll(A,B,D)))|coll(C,D,A))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f101])).
% 4.61/1.04 fof(f103,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (~coll(X0,X1,X2)|~coll(X0,X1,X3)|coll(X2,X3,X0))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f102])).
% 4.61/1.04 fof(f104,plain,(
% 4.61/1.04 ![A,B,C,D]: (~para(A,B,C,D)|para(A,B,D,C))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 4.61/1.04 fof(f105,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (~para(X0,X1,X2,X3)|para(X0,X1,X3,X2))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f104])).
% 4.61/1.04 fof(f121,plain,(
% 4.61/1.04 ![A,B,M]: (~midp(M,B,A)|midp(M,A,B))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 4.61/1.04 fof(f122,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~midp(X0,X1,X2)|midp(X0,X2,X1))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f121])).
% 4.61/1.04 fof(f134,plain,(
% 4.61/1.04 ![A,B,C,D,E]: ((~cyclic(A,B,C,D)|~cyclic(A,B,C,E))|cyclic(B,C,D,E))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 4.61/1.04 fof(f135,plain,(
% 4.61/1.04 ![B,C,D,E]: ((![A]: (~cyclic(A,B,C,D)|~cyclic(A,B,C,E)))|cyclic(B,C,D,E))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f134])).
% 4.61/1.04 fof(f136,plain,(
% 4.61/1.04 ![X0,X1,X2,X3,X4]: (~cyclic(X0,X1,X2,X3)|~cyclic(X0,X1,X2,X4)|cyclic(X1,X2,X3,X4))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f135])).
% 4.61/1.04 fof(f137,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 4.61/1.04 fof(f138,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f137])).
% 4.61/1.04 fof(f139,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 4.61/1.04 fof(f140,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f139])).
% 4.61/1.04 fof(f141,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 4.61/1.04 fof(f142,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f141])).
% 4.61/1.04 fof(f143,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 4.61/1.04 fof(f144,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f143])).
% 4.61/1.04 fof(f187,plain,(
% 4.61/1.04 ![A,B,C,D,P,Q]: (~para(A,B,C,D)|eqangle(A,B,P,Q,C,D,P,Q))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 4.61/1.04 fof(f188,plain,(
% 4.61/1.04 ![A,B,C,D]: (~para(A,B,C,D)|(![P,Q]: eqangle(A,B,P,Q,C,D,P,Q)))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f187])).
% 4.61/1.04 fof(f189,plain,(
% 4.61/1.04 ![X0,X1,X2,X3,X4,X5]: (~para(X0,X1,X2,X3)|eqangle(X0,X1,X4,X5,X2,X3,X4,X5))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f188])).
% 4.61/1.04 fof(f190,plain,(
% 4.61/1.04 ![A,B,P,Q]: (~cyclic(A,B,P,Q)|eqangle(P,A,P,B,Q,A,Q,B))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 4.61/1.04 fof(f191,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (~cyclic(X0,X1,X2,X3)|eqangle(X2,X0,X2,X1,X3,X0,X3,X1))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f190])).
% 4.61/1.04 fof(f194,plain,(
% 4.61/1.04 ![A,B,P,Q]: ((~eqangle(P,A,P,B,Q,A,Q,B)|~coll(P,Q,B))|cyclic(A,B,P,Q))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f43])).
% 4.61/1.04 fof(f195,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~coll(X0,X3,X2)|cyclic(X1,X2,X0,X3))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f194])).
% 4.61/1.04 fof(f196,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f44])).
% 4.61/1.04 fof(f197,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f196])).
% 4.61/1.04 fof(f198,plain,(
% 4.61/1.04 ![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))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f197])).
% 4.61/1.04 fof(f202,plain,(
% 4.61/1.04 ![A,B,C,E,F]: (((~midp(E,A,B)|~para(E,F,B,C))|~coll(F,A,C))|midp(F,A,C))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 4.61/1.04 fof(f203,plain,(
% 4.61/1.04 ![A,C,F]: (((![B,E]: (~midp(E,A,B)|~para(E,F,B,C)))|~coll(F,A,C))|midp(F,A,C))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f202])).
% 4.61/1.04 fof(f204,plain,(
% 4.61/1.04 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~para(X0,X3,X2,X4)|~coll(X3,X1,X4)|midp(X3,X1,X4))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f203])).
% 4.61/1.04 fof(f228,plain,(
% 4.61/1.04 ![A,B,M,O]: ((~midp(M,A,B)|~perp(O,M,A,B))|cong(O,A,O,B))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f56])).
% 4.61/1.04 fof(f229,plain,(
% 4.61/1.04 ![A,B,O]: ((![M]: (~midp(M,A,B)|~perp(O,M,A,B)))|cong(O,A,O,B))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f228])).
% 4.61/1.04 fof(f230,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (~midp(X0,X1,X2)|~perp(X3,X0,X1,X2)|cong(X3,X1,X3,X2))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f229])).
% 4.61/1.04 fof(f233,plain,(
% 4.61/1.04 ![A,B,P,Q]: (((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q))|perp(P,A,A,Q))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f58])).
% 4.61/1.04 fof(f234,plain,(
% 4.61/1.04 ![A,P,Q]: ((![B]: ((~cong(A,P,B,P)|~cong(A,Q,B,Q))|~cyclic(A,B,P,Q)))|perp(P,A,A,Q))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f233])).
% 4.61/1.04 fof(f235,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|~cyclic(X0,X2,X1,X3)|perp(X1,X0,X0,X3))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f234])).
% 4.61/1.04 fof(f247,plain,(
% 4.61/1.04 ![A,B,C,D,M]: ((~midp(M,A,B)|~midp(M,C,D))|para(A,C,B,D))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f64])).
% 4.61/1.04 fof(f248,plain,(
% 4.61/1.04 ![A,B,C,D]: ((![M]: (~midp(M,A,B)|~midp(M,C,D)))|para(A,C,B,D))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f247])).
% 4.61/1.04 fof(f249,plain,(
% 4.61/1.04 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~midp(X0,X3,X4)|para(X1,X3,X2,X4))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f248])).
% 4.61/1.04 fof(f255,plain,(
% 4.61/1.04 ![A,B,C]: (~para(A,B,A,C)|coll(A,B,C))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f67])).
% 4.61/1.04 fof(f256,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~para(X0,X1,X0,X2)|coll(X0,X1,X2))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f255])).
% 4.61/1.04 fof(f257,plain,(
% 4.61/1.04 ![A,B,C]: ((~cong(A,B,A,C)|~coll(A,B,C))|midp(A,B,C))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f68])).
% 4.61/1.04 fof(f258,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~cong(X0,X1,X0,X2)|~coll(X0,X1,X2)|midp(X0,X1,X2))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f257])).
% 4.61/1.04 fof(f269,plain,(
% 4.61/1.04 ![A,B,C,D,P,Q,U,V]: ((~eqangle(A,B,C,D,P,Q,U,V)|~para(P,Q,U,V))|para(A,B,C,D))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f74])).
% 4.61/1.04 fof(f270,plain,(
% 4.61/1.04 ![A,B,C,D]: ((![P,Q,U,V]: (~eqangle(A,B,C,D,P,Q,U,V)|~para(P,Q,U,V)))|para(A,B,C,D))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f269])).
% 4.61/1.04 fof(f271,plain,(
% 4.61/1.04 ![X0,X1,X2,X3,X4,X5,X6,X7]: (~eqangle(X0,X1,X2,X3,X4,X5,X6,X7)|~para(X4,X5,X6,X7)|para(X0,X1,X2,X3))),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f270])).
% 4.61/1.04 fof(f369,plain,(
% 4.61/1.04 (?[A,B,C,O,P1,F1,G1,P,F,G,K,NWPNT1,NWPNT2,NWPNT3]: (((((((((((((circle(O,A,B,C)&circle(O,A,P1,NWPNT1))&perp(F1,P1,A,C))&coll(F1,A,C))&perp(G1,P1,A,B))&coll(G1,A,B))&circle(O,A,P,NWPNT2))&perp(F,P,A,C))&coll(F,A,C))&perp(G,P,A,B))&coll(G,A,B))¶(F1,G1,K,P))&circle(O,A,K,NWPNT3))&~para(K,P1,G,F)))),
% 4.61/1.04 inference(pre_NNF_transformation,[status(thm)],[f96])).
% 4.61/1.04 fof(f370,plain,(
% 4.61/1.04 ?[P1,F,G,K]: ((?[A,O]: ((?[F1,G1,P]: ((?[B]: (((?[C]: ((((((((circle(O,A,B,C)&(?[NWPNT1]: circle(O,A,P1,NWPNT1)))&perp(F1,P1,A,C))&coll(F1,A,C))&perp(G1,P1,A,B))&coll(G1,A,B))&(?[NWPNT2]: circle(O,A,P,NWPNT2)))&perp(F,P,A,C))&coll(F,A,C)))&perp(G,P,A,B))&coll(G,A,B)))¶(F1,G1,K,P)))&(?[NWPNT3]: circle(O,A,K,NWPNT3))))&~para(K,P1,G,F))),
% 4.61/1.04 inference(miniscoping,[status(thm)],[f369])).
% 4.61/1.04 fof(f371,plain,(
% 4.61/1.04 (((((((((((((circle(sK25_skl,sK24_skl,sK29_skl,sK30_skl)&circle(sK25_skl,sK24_skl,sK20_skl,sK31_skl))&perp(sK26_skl,sK20_skl,sK24_skl,sK30_skl))&coll(sK26_skl,sK24_skl,sK30_skl))&perp(sK27_skl,sK20_skl,sK24_skl,sK29_skl))&coll(sK27_skl,sK24_skl,sK29_skl))&circle(sK25_skl,sK24_skl,sK28_skl,sK32_skl))&perp(sK21_skl,sK28_skl,sK24_skl,sK30_skl))&coll(sK21_skl,sK24_skl,sK30_skl))&perp(sK22_skl,sK28_skl,sK24_skl,sK29_skl))&coll(sK22_skl,sK24_skl,sK29_skl))¶(sK26_skl,sK27_skl,sK23_skl,sK28_skl))&circle(sK25_skl,sK24_skl,sK23_skl,sK33_skl))&~para(sK23_skl,sK20_skl,sK22_skl,sK21_skl))),
% 4.61/1.04 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]),skolemize(P1,sK20_skl),skolemize(F,sK21_skl),skolemize(G,sK22_skl),skolemize(K,sK23_skl),skolemize(A,sK24_skl),skolemize(O,sK25_skl),skolemize(F1,sK26_skl),skolemize(G1,sK27_skl),skolemize(P,sK28_skl),skolemize(B,sK29_skl),skolemize(C,sK30_skl),skolemize(NWPNT1,sK31_skl),skolemize(NWPNT2,sK32_skl),skolemize(NWPNT3,sK33_skl)],[f370])).
% 4.61/1.04 fof(f383,plain,(
% 4.61/1.04 para(sK26_skl,sK27_skl,sK23_skl,sK28_skl)),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f371])).
% 4.61/1.04 fof(f385,plain,(
% 4.61/1.04 ~para(sK23_skl,sK20_skl,sK22_skl,sK21_skl)),
% 4.61/1.04 inference(cnf_transformation,[status(thm)],[f371])).
% 4.61/1.04 fof(f469,plain,(
% 4.61/1.04 ![X0,X1]: (eqangle(sK26_skl,sK27_skl,X0,X1,sK23_skl,sK28_skl,X0,X1))),
% 4.61/1.04 inference(resolution,[status(thm)],[f189,f383])).
% 4.61/1.04 fof(f602,plain,(
% 4.61/1.04 ![X0,X1]: (eqangle(X0,X1,sK26_skl,sK27_skl,X0,X1,sK23_skl,sK28_skl))),
% 4.61/1.04 inference(resolution,[status(thm)],[f140,f469])).
% 4.61/1.04 fof(f608,plain,(
% 4.61/1.04 ![X0,X1]: (eqangle(X0,X1,sK26_skl,sK27_skl,X1,X0,sK23_skl,sK28_skl))),
% 4.61/1.04 inference(resolution,[status(thm)],[f602,f138])).
% 4.61/1.04 fof(f635,plain,(
% 4.61/1.04 ![X0,X1]: (eqangle(X0,X1,X1,X0,sK26_skl,sK27_skl,sK23_skl,sK28_skl))),
% 4.61/1.04 inference(resolution,[status(thm)],[f144,f608])).
% 4.61/1.04 fof(f741,definition,(
% 4.61/1.04 sQ23_spl <=> (para(sK26_skl,sK27_skl,sK23_skl,sK28_skl))),
% 4.61/1.04 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 4.61/1.04 fof(f743,plain,(
% 4.61/1.04 ~para(sK26_skl,sK27_skl,sK23_skl,sK28_skl)|sQ23_spl),
% 4.61/1.04 inference(component_clause,[status(thm)],[f741])).
% 4.61/1.04 fof(f779,plain,(
% 4.61/1.04 ![X0,X1]: (~para(sK26_skl,sK27_skl,sK23_skl,sK28_skl)|para(X0,X1,X1,X0))),
% 4.61/1.04 inference(resolution,[status(thm)],[f635,f271])).
% 4.61/1.04 fof(f782,definition,(
% 4.61/1.04 ![X0,X1]: (sQ26_spl <=> (para(X0,X1,X1,X0)))),
% 4.61/1.04 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 4.61/1.04 fof(f783,plain,(
% 4.61/1.04 ![X0,X1]: (para(X0,X1,X1,X0)|~sQ26_spl)),
% 4.61/1.04 inference(component_clause,[status(thm)],[f782])).
% 4.61/1.04 fof(f785,plain,(
% 4.61/1.04 ~sQ23_spl|sQ26_spl),
% 4.61/1.04 inference(split_clause,[status(thm)],[f779,f741,f782])).
% 4.61/1.04 fof(f786,plain,(
% 4.61/1.04 $false|sQ23_spl),
% 4.61/1.04 inference(forward_subsumption_resolution,[status(thm)],[f743,f383])).
% 4.61/1.04 fof(f787,plain,(
% 4.61/1.04 sQ23_spl),
% 4.61/1.04 inference(contradiction_clause,[status(thm)],[f786])).
% 4.61/1.04 fof(f794,plain,(
% 4.61/1.04 ![X0,X1]: (para(X0,X1,X0,X1)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f783,f105])).
% 4.61/1.04 fof(f798,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (eqangle(X0,X1,X2,X3,X0,X1,X2,X3)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f794,f189])).
% 4.61/1.04 fof(f801,plain,(
% 4.61/1.04 ![X0,X1]: (coll(X0,X1,X1)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f794,f256])).
% 4.61/1.04 fof(f808,plain,(
% 4.61/1.04 ![X0,X1]: (coll(X0,X1,X0)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f801,f100])).
% 4.61/1.04 fof(f816,plain,(
% 4.61/1.04 ![X0,X1]: (coll(X0,X0,X1)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f808,f98])).
% 4.61/1.04 fof(f821,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~coll(X0,X0,X1)|coll(X1,X2,X0)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f816,f103])).
% 4.61/1.04 fof(f824,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~cong(X0,X1,X0,X2)|midp(X0,X1,X2)|~sQ26_spl)),
% 4.61/1.04 inference(backward_subsumption_resolution,[status(thm)],[f258,f836])).
% 4.61/1.04 fof(f834,plain,(
% 4.61/1.04 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|~para(X0,X3,X2,X4)|midp(X3,X1,X4)|~sQ26_spl)),
% 4.61/1.04 inference(backward_subsumption_resolution,[status(thm)],[f204,f836])).
% 4.61/1.04 fof(f835,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (~eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|cyclic(X1,X2,X0,X3)|~sQ26_spl)),
% 4.61/1.04 inference(backward_subsumption_resolution,[status(thm)],[f195,f836])).
% 4.61/1.04 fof(f836,plain,(
% 4.61/1.04 ![X0,X1,X2]: (coll(X0,X1,X2)|~sQ26_spl)),
% 4.61/1.04 inference(forward_subsumption_resolution,[status(thm)],[f821,f816])).
% 4.61/1.04 fof(f853,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (eqangle(X0,X1,X0,X1,X2,X3,X2,X3)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f798,f144])).
% 4.61/1.04 fof(f1191,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~midp(X0,X1,X0)|midp(X2,X1,X2)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f834,f794])).
% 4.61/1.04 fof(f1286,plain,(
% 4.61/1.04 ![X0,X1,X2]: (cyclic(X0,X0,X1,X2)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f835,f853])).
% 4.61/1.04 fof(f1291,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (~cyclic(X0,X0,X1,X2)|cyclic(X0,X1,X2,X3)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1286,f136])).
% 4.61/1.04 fof(f1296,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (eqangle(X0,X1,X0,X2,X3,X1,X3,X2)|~sQ26_spl)),
% 4.61/1.04 inference(backward_subsumption_resolution,[status(thm)],[f191,f1302])).
% 4.61/1.04 fof(f1299,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (~cong(X0,X1,X2,X1)|~cong(X0,X3,X2,X3)|perp(X1,X0,X0,X3)|~sQ26_spl)),
% 4.61/1.04 inference(backward_subsumption_resolution,[status(thm)],[f235,f1302])).
% 4.61/1.04 fof(f1301,plain,(
% 4.61/1.04 ![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)|~sQ26_spl)),
% 4.61/1.04 inference(backward_subsumption_resolution,[status(thm)],[f198,f1302])).
% 4.61/1.04 fof(f1302,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (cyclic(X0,X1,X2,X3)|~sQ26_spl)),
% 4.61/1.04 inference(forward_subsumption_resolution,[status(thm)],[f1291,f1286])).
% 4.61/1.04 fof(f1303,plain,(
% 4.61/1.04 ![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)|~sQ26_spl)),
% 4.61/1.04 inference(forward_subsumption_resolution,[status(thm)],[f1301,f1302])).
% 4.61/1.04 fof(f1351,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (eqangle(X0,X1,X1,X2,X3,X0,X3,X2)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1296,f138])).
% 4.61/1.04 fof(f1437,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (eqangle(X0,X1,X0,X2,X1,X3,X3,X2)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1351,f142])).
% 4.61/1.04 fof(f1438,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (eqangle(X0,X1,X2,X0,X3,X1,X3,X2)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1351,f140])).
% 4.61/1.04 fof(f1539,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (eqangle(X0,X1,X1,X2,X0,X3,X3,X2)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1437,f138])).
% 4.61/1.04 fof(f1549,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (eqangle(X0,X1,X2,X1,X3,X0,X3,X2)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1438,f138])).
% 4.61/1.04 fof(f1682,plain,(
% 4.61/1.04 ![X0,X1]: (~cyclic(X0,X0,X1,X1)|cong(X0,X0,X1,X1)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1303,f1549])).
% 4.61/1.04 fof(f1683,plain,(
% 4.61/1.04 ![X0,X1]: (~cyclic(X0,X1,X0,X1)|cong(X0,X1,X0,X1)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1303,f1539])).
% 4.61/1.04 fof(f1785,plain,(
% 4.61/1.04 ![X0,X1]: (cong(X0,X0,X1,X1)|~sQ26_spl)),
% 4.61/1.04 inference(forward_subsumption_resolution,[status(thm)],[f1682,f1302])).
% 4.61/1.04 fof(f1786,plain,(
% 4.61/1.04 ![X0,X1]: (cong(X0,X1,X0,X1)|~sQ26_spl)),
% 4.61/1.04 inference(forward_subsumption_resolution,[status(thm)],[f1683,f1302])).
% 4.61/1.04 fof(f1790,plain,(
% 4.61/1.04 ![X0]: (midp(X0,X0,X0)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1785,f824])).
% 4.61/1.04 fof(f1800,plain,(
% 4.61/1.04 ![X0,X1]: (midp(X0,X1,X0)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1790,f1191])).
% 4.61/1.04 fof(f1810,plain,(
% 4.61/1.04 ![X0,X1]: (midp(X0,X0,X1)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1800,f122])).
% 4.61/1.04 fof(f1822,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~cong(X0,X1,X0,X1)|perp(X1,X0,X0,X2)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1786,f1299])).
% 4.61/1.04 fof(f1838,plain,(
% 4.61/1.04 ![X0,X1,X2]: (perp(X0,X1,X1,X2)|~sQ26_spl)),
% 4.61/1.04 inference(forward_subsumption_resolution,[status(thm)],[f1822,f1786])).
% 4.61/1.04 fof(f1855,plain,(
% 4.61/1.04 ![X0,X1,X2]: (~midp(X0,X0,X1)|cong(X2,X0,X2,X1)|~sQ26_spl)),
% 4.61/1.04 inference(resolution,[status(thm)],[f1838,f230])).
% 4.61/1.04 fof(f1861,plain,(
% 4.61/1.04 ![X0,X1,X2]: (midp(X0,X1,X2)|~sQ26_spl)),
% 4.61/1.04 inference(backward_subsumption_resolution,[status(thm)],[f824,f1868])).
% 4.61/1.04 fof(f1868,plain,(
% 4.61/1.04 ![X0,X1,X2]: (cong(X0,X1,X0,X2)|~sQ26_spl)),
% 4.61/1.04 inference(forward_subsumption_resolution,[status(thm)],[f1855,f1810])).
% 4.61/1.04 fof(f1873,plain,(
% 4.61/1.04 ![X0,X1,X2,X3,X4]: (~midp(X0,X1,X2)|para(X3,X1,X4,X2)|~sQ26_spl)),
% 4.61/1.04 inference(backward_subsumption_resolution,[status(thm)],[f249,f1861])).
% 4.61/1.04 fof(f1901,plain,(
% 4.61/1.04 $false|~sQ26_spl),
% 4.61/1.04 inference(backward_subsumption_resolution,[status(thm)],[f385,f1913])).
% 4.61/1.04 fof(f1913,plain,(
% 4.61/1.04 ![X0,X1,X2,X3]: (para(X0,X1,X2,X3)|~sQ26_spl)),
% 4.61/1.04 inference(forward_subsumption_resolution,[status(thm)],[f1873,f1861])).
% 4.61/1.04 fof(f1924,plain,(
% 4.61/1.04 ~sQ26_spl),
% 4.61/1.04 inference(contradiction_clause,[status(thm)],[f1901])).
% 4.61/1.04 fof(f1925,plain,(
% 4.61/1.04 $false),
% 4.61/1.04 inference(sat_refutation,[status(thm)],[f785,f787,f1924])).
% 4.61/1.04 % SZS output end CNFRefutation for theBenchmark.p
% 4.61/1.05 % Elapsed time: 0.664188 seconds
% 4.61/1.05 % CPU time: 4.933461 seconds
% 4.61/1.05 % Total memory used: 126.584 MB
% 4.61/1.05 % Net memory used: 121.044 MB
%------------------------------------------------------------------------------